Untitled
2023-05-20
library(arules)## Loading required package: Matrix##
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## abbreviate, writelibrary(caret)## Loading required package: ggplot2## Loading required package: latticelibrary(catboost)
library(cluster)
library(dplyr)##
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## intersect, setdiff, setequal, unionlibrary(e1071)
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(ggplot2)
library(glmnet)## Loaded glmnet 4.1-7library(lattice)
library(lightgbm)## Loading required package: R6##
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## slicelibrary(mlrMBO)## Loading required package: mlr## Loading required package: ParamHelpers## Warning message: 'mlr' is in 'maintenance-only' mode since July 2019.
## Future development will only happen in 'mlr3'
## (<https://mlr3.mlr-org.com>). Due to the focus on 'mlr3' there might be
## uncaught bugs meanwhile in {mlr} - please consider switching.##
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## train## Loading required package: smoof## Loading required package: checkmatelibrary(randomForest)## randomForest 4.7-1.1## Type rfNews() to see new features/changes/bug fixes.##
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## marginlibrary(tidyr)##
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## expand, pack, unpacklibrary(viridis)## Loading required package: viridisLitelibrary(xgboost)##
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## slicelibrary(Metrics)##
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## precision, recalllibrary(Rtsne)
library(DiceKriging)##
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## checkNamessource("data_cleaning.r")##
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## combine##
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## AUC, ICC, SD## The following objects are masked from 'package:caret':
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## MAE, RMSE## corrplot 0.92 loaded## Total rows & columns: 1460 81
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## 'data.frame': 1460 obs. of 81 variables:
## $ Id : int 1 2 3 4 5 6 7 8 9 10 ...
## $ MSSubClass : int 60 20 60 70 60 50 20 60 50 190 ...
## $ MSZoning : chr "RL" "RL" "RL" "RL" ...
## $ LotFrontage : int 65 80 68 60 84 85 75 NA 51 50 ...
## $ LotArea : int 8450 9600 11250 9550 14260 14115 10084 10382 6120 7420 ...
## $ Street : chr "Pave" "Pave" "Pave" "Pave" ...
## $ Alley : chr NA NA NA NA ...
## $ LotShape : chr "Reg" "Reg" "IR1" "IR1" ...
## $ LandContour : chr "Lvl" "Lvl" "Lvl" "Lvl" ...
## $ Utilities : chr "AllPub" "AllPub" "AllPub" "AllPub" ...
## $ LotConfig : chr "Inside" "FR2" "Inside" "Corner" ...
## $ LandSlope : chr "Gtl" "Gtl" "Gtl" "Gtl" ...
## $ Neighborhood : chr "CollgCr" "Veenker" "CollgCr" "Crawfor" ...
## $ Condition1 : chr "Norm" "Feedr" "Norm" "Norm" ...
## $ Condition2 : chr "Norm" "Norm" "Norm" "Norm" ...
## $ BldgType : chr "1Fam" "1Fam" "1Fam" "1Fam" ...
## $ HouseStyle : chr "2Story" "1Story" "2Story" "2Story" ...
## $ OverallQual : int 7 6 7 7 8 5 8 7 7 5 ...
## $ OverallCond : int 5 8 5 5 5 5 5 6 5 6 ...
## $ YearBuilt : int 2003 1976 2001 1915 2000 1993 2004 1973 1931 1939 ...
## $ YearRemodAdd : int 2003 1976 2002 1970 2000 1995 2005 1973 1950 1950 ...
## $ RoofStyle : chr "Gable" "Gable" "Gable" "Gable" ...
## $ RoofMatl : chr "CompShg" "CompShg" "CompShg" "CompShg" ...
## $ Exterior1st : chr "VinylSd" "MetalSd" "VinylSd" "Wd Sdng" ...
## $ Exterior2nd : chr "VinylSd" "MetalSd" "VinylSd" "Wd Shng" ...
## $ MasVnrType : chr "BrkFace" "None" "BrkFace" "None" ...
## $ MasVnrArea : int 196 0 162 0 350 0 186 240 0 0 ...
## $ ExterQual : chr "Gd" "TA" "Gd" "TA" ...
## $ ExterCond : chr "TA" "TA" "TA" "TA" ...
## $ Foundation : chr "PConc" "CBlock" "PConc" "BrkTil" ...
## $ BsmtQual : chr "Gd" "Gd" "Gd" "TA" ...
## $ BsmtCond : chr "TA" "TA" "TA" "Gd" ...
## $ BsmtExposure : chr "No" "Gd" "Mn" "No" ...
## $ BsmtFinType1 : chr "GLQ" "ALQ" "GLQ" "ALQ" ...
## $ BsmtFinSF1 : int 706 978 486 216 655 732 1369 859 0 851 ...
## $ BsmtFinType2 : chr "Unf" "Unf" "Unf" "Unf" ...
## $ BsmtFinSF2 : int 0 0 0 0 0 0 0 32 0 0 ...
## $ BsmtUnfSF : int 150 284 434 540 490 64 317 216 952 140 ...
## $ TotalBsmtSF : int 856 1262 920 756 1145 796 1686 1107 952 991 ...
## $ Heating : chr "GasA" "GasA" "GasA" "GasA" ...
## $ HeatingQC : chr "Ex" "Ex" "Ex" "Gd" ...
## $ CentralAir : chr "Y" "Y" "Y" "Y" ...
## $ Electrical : chr "SBrkr" "SBrkr" "SBrkr" "SBrkr" ...
## $ X1stFlrSF : int 856 1262 920 961 1145 796 1694 1107 1022 1077 ...
## $ X2ndFlrSF : int 854 0 866 756 1053 566 0 983 752 0 ...
## $ LowQualFinSF : int 0 0 0 0 0 0 0 0 0 0 ...
## $ GrLivArea : int 1710 1262 1786 1717 2198 1362 1694 2090 1774 1077 ...
## $ BsmtFullBath : int 1 0 1 1 1 1 1 1 0 1 ...
## $ BsmtHalfBath : int 0 1 0 0 0 0 0 0 0 0 ...
## $ FullBath : int 2 2 2 1 2 1 2 2 2 1 ...
## $ HalfBath : int 1 0 1 0 1 1 0 1 0 0 ...
## $ BedroomAbvGr : int 3 3 3 3 4 1 3 3 2 2 ...
## $ KitchenAbvGr : int 1 1 1 1 1 1 1 1 2 2 ...
## $ KitchenQual : chr "Gd" "TA" "Gd" "Gd" ...
## $ TotRmsAbvGrd : int 8 6 6 7 9 5 7 7 8 5 ...
## $ Functional : chr "Typ" "Typ" "Typ" "Typ" ...
## $ Fireplaces : int 0 1 1 1 1 0 1 2 2 2 ...
## $ FireplaceQu : chr NA "TA" "TA" "Gd" ...
## $ GarageType : chr "Attchd" "Attchd" "Attchd" "Detchd" ...
## $ GarageYrBlt : int 2003 1976 2001 1998 2000 1993 2004 1973 1931 1939 ...
## $ GarageFinish : chr "RFn" "RFn" "RFn" "Unf" ...
## $ GarageCars : int 2 2 2 3 3 2 2 2 2 1 ...
## $ GarageArea : int 548 460 608 642 836 480 636 484 468 205 ...
## $ GarageQual : chr "TA" "TA" "TA" "TA" ...
## $ GarageCond : chr "TA" "TA" "TA" "TA" ...
## $ PavedDrive : chr "Y" "Y" "Y" "Y" ...
## $ WoodDeckSF : int 0 298 0 0 192 40 255 235 90 0 ...
## $ OpenPorchSF : int 61 0 42 35 84 30 57 204 0 4 ...
## $ EnclosedPorch: int 0 0 0 272 0 0 0 228 205 0 ...
## $ X3SsnPorch : int 0 0 0 0 0 320 0 0 0 0 ...
## $ ScreenPorch : int 0 0 0 0 0 0 0 0 0 0 ...
## $ PoolArea : int 0 0 0 0 0 0 0 0 0 0 ...
## $ PoolQC : chr NA NA NA NA ...
## $ Fence : chr NA NA NA NA ...
## $ MiscFeature : chr NA NA NA NA ...
## $ MiscVal : int 0 0 0 0 0 700 0 350 0 0 ...
## $ MoSold : int 2 5 9 2 12 10 8 11 4 1 ...
## $ YrSold : int 2008 2007 2008 2006 2008 2009 2007 2009 2008 2008 ...
## $ SaleType : chr "WD" "WD" "WD" "WD" ...
## $ SaleCondition: chr "Normal" "Normal" "Normal" "Abnorml" ...
## $ SalePrice : int 208500 181500 223500 140000 250000 143000 307000 200000 129900 118000 ...
## Number of duplicates: 0 column_name missing_percentage
## PoolQC PoolQC 99.52054795
## MiscFeature MiscFeature 96.30136986
## Alley Alley 93.76712329
## Fence Fence 80.75342466
## FireplaceQu FireplaceQu 47.26027397
## LotFrontage LotFrontage 17.73972603
## GarageType GarageType 5.54794521
## GarageFinish GarageFinish 5.54794521
## GarageQual GarageQual 5.54794521
## GarageCond GarageCond 5.54794521
## BsmtExposure BsmtExposure 2.60273973
## BsmtFinType2 BsmtFinType2 2.60273973
## BsmtQual BsmtQual 2.53424658
## BsmtCond BsmtCond 2.53424658
## BsmtFinType1 BsmtFinType1 2.53424658
## MasVnrType MasVnrType 0.54794521
## MasVnrArea MasVnrArea 0.54794521
## Electrical Electrical 0.06849315
## MSSubClass LotFrontage LotArea OverallQual OverallCond
## MSSubClass 1.000000000 -0.357055878 -0.139781082 0.03262771 -0.059315817
## LotFrontage -0.357055878 1.000000000 0.306794605 0.23419623 -0.052820100
## LotArea -0.139781082 0.306794605 1.000000000 0.10580574 -0.005636270
## OverallQual 0.032627708 0.234196231 0.105805742 1.00000000 -0.091932343
## OverallCond -0.059315817 -0.052820100 -0.005636270 -0.09193234 1.000000000
## YearBuilt 0.027850137 0.117597979 0.014227652 0.57232277 -0.375983196
## YearRemodAdd 0.040581045 0.082745885 0.013788427 0.55068392 0.073741498
## MasVnrArea 0.022894690 0.179283452 0.103960227 0.41023774 -0.127788119
## BsmtFinSF1 -0.069835749 0.215828435 0.214103131 0.23966597 -0.046230856
## BsmtFinSF2 -0.065648579 0.043339566 0.111169745 -0.05911869 0.040229170
## BsmtUnfSF -0.140759481 0.122155600 -0.002618360 0.30815893 -0.136840570
## TotalBsmtSF -0.238518409 0.363357723 0.260833135 0.53780850 -0.171097515
## X1stFlrSF -0.251758352 0.414266394 0.299474579 0.47622383 -0.144202784
## X2ndFlrSF 0.307885721 0.072482666 0.050985948 0.29549288 0.028942116
## LowQualFinSF 0.046473756 0.036848721 0.004778970 -0.03042928 0.025494320
## GrLivArea 0.074853180 0.368391966 0.263116167 0.59300743 -0.079685865
## BsmtFullBath 0.003491026 0.091480992 0.158154531 0.11109779 -0.054941515
## BsmtHalfBath -0.002332535 -0.006419220 0.048045571 -0.04015016 0.117820915
## FullBath 0.131608222 0.180424206 0.126030627 0.55059971 -0.194149489
## HalfBath 0.177354389 0.048258362 0.014259469 0.27345810 -0.060769327
## BedroomAbvGr -0.023438028 0.237023227 0.119689908 0.10167636 0.012980060
## KitchenAbvGr 0.281721040 -0.005804607 -0.017783871 -0.18388223 -0.087000855
## Fireplaces -0.045569340 0.235754565 0.271364010 0.39676504 -0.023819978
## GarageArea -0.098671543 0.323662899 0.180402755 0.56202176 -0.151521371
## WoodDeckSF -0.012579358 0.077106221 0.171697687 0.23892339 -0.003333699
## OpenPorchSF -0.006100121 0.137454496 0.084773809 0.30881882 -0.032588814
## EnclosedPorch -0.012036622 0.009790061 -0.018339734 -0.11393686 0.070356184
## X3SsnPorch -0.043824549 0.062335471 0.020422830 0.03037057 0.025503660
## ScreenPorch -0.026030177 0.037684305 0.043160378 0.06488636 0.054810529
## PoolArea 0.008282708 0.180867647 0.077672392 0.06516584 -0.001984942
## MiscVal -0.007683291 0.001168275 0.038067692 -0.03140621 0.068776806
## MoSold -0.013584643 0.010157807 0.001204988 0.07081517 -0.003510839
## YrSold -0.021407038 0.006768250 -0.014261407 -0.02734671 0.043949746
## SalePrice -0.084284135 0.334900852 0.263843354 0.79098160 -0.077855894
## YearBuilt YearRemodAdd MasVnrArea BsmtFinSF1 BsmtFinSF2
## MSSubClass 0.027850137 0.040581045 0.022894690 -0.069835749 -0.065648579
## LotFrontage 0.117597979 0.082745885 0.179283452 0.215828435 0.043339566
## LotArea 0.014227652 0.013788427 0.103960227 0.214103131 0.111169745
## OverallQual 0.572322769 0.550683924 0.410237736 0.239665966 -0.059118693
## OverallCond -0.375983196 0.073741498 -0.127788119 -0.046230856 0.040229170
## YearBuilt 1.000000000 0.592854976 0.314745023 0.249503197 -0.049106831
## YearRemodAdd 0.592854976 1.000000000 0.179186495 0.128450547 -0.067758514
## MasVnrArea 0.314745023 0.179186495 1.000000000 0.263582388 -0.072302247
## BsmtFinSF1 0.249503197 0.128450547 0.263582388 1.000000000 -0.050117400
## BsmtFinSF2 -0.049106831 -0.067758514 -0.072302247 -0.050117400 1.000000000
## BsmtUnfSF 0.149040392 0.181133087 0.114183659 -0.495251469 -0.209294492
## TotalBsmtSF 0.391452002 0.291065583 0.362452094 0.522396052 0.104809538
## X1stFlrSF 0.281985859 0.240379268 0.342160338 0.445862656 0.097117448
## X2ndFlrSF 0.010307660 0.140023779 0.174019344 -0.137078986 -0.099260316
## LowQualFinSF -0.183784344 -0.062419100 -0.069068105 -0.064502597 0.014806998
## GrLivArea 0.199009714 0.287388520 0.389892916 0.208171130 -0.009639892
## BsmtFullBath 0.187598550 0.119469879 0.085054528 0.649211754 0.158678061
## BsmtHalfBath -0.038161806 -0.012337032 0.026668558 0.067418478 0.070948134
## FullBath 0.468270787 0.439046484 0.275729847 0.058543137 -0.076443862
## HalfBath 0.242655910 0.183330612 0.200802357 0.004262424 -0.032147837
## BedroomAbvGr -0.070651217 -0.040580928 0.102417471 -0.107354677 -0.015728114
## KitchenAbvGr -0.174800246 -0.149597521 -0.037364011 -0.081006851 -0.040751236
## Fireplaces 0.147716399 0.112581318 0.247906285 0.260010920 0.046920709
## GarageArea 0.478953820 0.371599809 0.372567013 0.296970385 -0.018226592
## WoodDeckSF 0.224880142 0.205725920 0.159349430 0.204306145 0.067898326
## OpenPorchSF 0.188685840 0.226297633 0.124965275 0.111760613 0.003092562
## EnclosedPorch -0.387267783 -0.193919147 -0.109848652 -0.102303306 0.036543339
## X3SsnPorch 0.031354513 0.045285810 0.018794814 0.026450506 -0.029993398
## ScreenPorch -0.050364435 -0.038740011 0.061453179 0.062020623 0.088871251
## PoolArea 0.004949728 0.005829372 0.011722909 0.140491286 0.041709055
## MiscVal -0.034383139 -0.010286249 -0.029814762 0.003571473 0.004939781
## MoSold 0.012398471 0.021490002 -0.005939579 -0.015726948 -0.015210738
## YrSold -0.013617680 0.035743247 -0.008183639 0.014358922 0.031705637
## SalePrice 0.522897333 0.507100967 0.475241317 0.386419806 -0.011378121
## BsmtUnfSF TotalBsmtSF X1stFlrSF X2ndFlrSF
## MSSubClass -0.140759481 -0.2385184093 -0.251758352 0.307885721
## LotFrontage 0.122155600 0.3633577228 0.414266394 0.072482666
## LotArea -0.002618360 0.2608331345 0.299474579 0.050985948
## OverallQual 0.308158927 0.5378084986 0.476223829 0.295492879
## OverallCond -0.136840570 -0.1710975146 -0.144202784 0.028942116
## YearBuilt 0.149040392 0.3914520021 0.281985859 0.010307660
## YearRemodAdd 0.181133087 0.2910655826 0.240379268 0.140023779
## MasVnrArea 0.114183659 0.3624520941 0.342160338 0.174019344
## BsmtFinSF1 -0.495251469 0.5223960520 0.445862656 -0.137078986
## BsmtFinSF2 -0.209294492 0.1048095376 0.097117448 -0.099260316
## BsmtUnfSF 1.000000000 0.4153596052 0.317987438 0.004469092
## TotalBsmtSF 0.415359605 1.0000000000 0.819529975 -0.174511950
## X1stFlrSF 0.317987438 0.8195299750 1.000000000 -0.202646181
## X2ndFlrSF 0.004469092 -0.1745119501 -0.202646181 1.000000000
## LowQualFinSF 0.028166688 -0.0332453873 -0.014240673 0.063352950
## GrLivArea 0.240257268 0.4548682025 0.566023969 0.687501064
## BsmtFullBath -0.422900477 0.3073505537 0.244671104 -0.169493952
## BsmtHalfBath -0.095804288 -0.0003145818 0.001955654 -0.023854784
## FullBath 0.288886055 0.3237224136 0.380637495 0.421377983
## HalfBath -0.041117530 -0.0488037386 -0.119915909 0.609707300
## BedroomAbvGr 0.166643317 0.0504499555 0.127400749 0.502900613
## KitchenAbvGr 0.030085868 -0.0689006426 0.068100588 0.059305753
## Fireplaces 0.051574882 0.3395193239 0.410531085 0.194560892
## GarageArea 0.183302698 0.4866654638 0.489781654 0.138346959
## WoodDeckSF -0.005316424 0.2320186091 0.235458623 0.092165418
## OpenPorchSF 0.129005415 0.2472637463 0.211671225 0.208026063
## EnclosedPorch -0.002537855 -0.0954777367 -0.065291701 0.061988691
## X3SsnPorch 0.020764006 0.0373837273 0.056104374 -0.024357648
## ScreenPorch -0.012579273 0.0844889859 0.088758073 0.040606448
## PoolArea -0.035092241 0.1260531321 0.131524976 0.081486878
## MiscVal -0.023836645 -0.0184789224 -0.021095719 0.016196875
## MoSold 0.034888443 0.0131961786 0.031371560 0.035164427
## YrSold -0.041258195 -0.0149686480 -0.013603771 -0.028699914
## SalePrice 0.214479106 0.6135805516 0.605852185 0.319333803
## LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath
## MSSubClass 0.0464737559 0.074853180 0.0034910258 -0.0023325346
## LotFrontage 0.0368487208 0.368391966 0.0914809919 -0.0064192197
## LotArea 0.0047789699 0.263116167 0.1581545311 0.0480455709
## OverallQual -0.0304292840 0.593007430 0.1110977861 -0.0401501577
## OverallCond 0.0254943199 -0.079685865 -0.0549415154 0.1178209151
## YearBuilt -0.1837843444 0.199009714 0.1875985500 -0.0381618057
## YearRemodAdd -0.0624191001 0.287388520 0.1194698791 -0.0123370321
## MasVnrArea -0.0690681050 0.389892916 0.0850545278 0.0266685579
## BsmtFinSF1 -0.0645025969 0.208171130 0.6492117536 0.0674184779
## BsmtFinSF2 0.0148069979 -0.009639892 0.1586780608 0.0709481337
## BsmtUnfSF 0.0281666881 0.240257268 -0.4229004774 -0.0958042882
## TotalBsmtSF -0.0332453873 0.454868203 0.3073505537 -0.0003145818
## X1stFlrSF -0.0142406727 0.566023969 0.2446711042 0.0019556536
## X2ndFlrSF 0.0633529501 0.687501064 -0.1694939517 -0.0238547839
## LowQualFinSF 1.0000000000 0.134682813 -0.0471434219 -0.0058415048
## GrLivArea 0.1346828130 1.000000000 0.0348360495 -0.0189184832
## BsmtFullBath -0.0471434219 0.034836050 1.0000000000 -0.1478709605
## BsmtHalfBath -0.0058415048 -0.018918483 -0.1478709605 1.0000000000
## FullBath -0.0007095096 0.630011646 -0.0645120486 -0.0545358120
## HalfBath -0.0270800493 0.415771636 -0.0309049591 -0.0123399001
## BedroomAbvGr 0.1056065685 0.521269511 -0.1506728092 0.0465188484
## KitchenAbvGr 0.0075217443 0.100063165 -0.0415025464 -0.0379443502
## Fireplaces -0.0212721434 0.461679134 0.1379277084 0.0289755866
## GarageArea -0.0676014132 0.468997477 0.1791894804 -0.0245355796
## WoodDeckSF -0.0254436480 0.247432821 0.1753151901 0.0401612233
## OpenPorchSF 0.0182510391 0.330223962 0.0673414614 -0.0253237579
## EnclosedPorch 0.0610812378 0.009113210 -0.0499106491 -0.0085553339
## X3SsnPorch -0.0042956104 0.020643190 -0.0001060915 0.0351136309
## ScreenPorch 0.0267994130 0.101510396 0.0231477258 0.0321214072
## PoolArea 0.0621573723 0.170205336 0.0676155562 0.0200246298
## MiscVal -0.0037928708 -0.002415640 -0.0230470249 -0.0073665245
## MoSold -0.0221739606 0.050239681 -0.0253608943 0.0328727052
## YrSold -0.0289208798 -0.036525820 0.0670491377 -0.0465238818
## SalePrice -0.0256061300 0.708624478 0.2271222331 -0.0168441543
## FullBath HalfBath BedroomAbvGr KitchenAbvGr Fireplaces
## MSSubClass 0.1316082224 0.177354389 -0.023438028 0.281721040 -0.045569340
## LotFrontage 0.1804242055 0.048258362 0.237023227 -0.005804607 0.235754565
## LotArea 0.1260306265 0.014259469 0.119689908 -0.017783871 0.271364010
## OverallQual 0.5505997094 0.273458099 0.101676356 -0.183882235 0.396765038
## OverallCond -0.1941494887 -0.060769327 0.012980060 -0.087000855 -0.023819978
## YearBuilt 0.4682707872 0.242655910 -0.070651217 -0.174800246 0.147716399
## YearRemodAdd 0.4390464839 0.183330612 -0.040580928 -0.149597521 0.112581318
## MasVnrArea 0.2757298473 0.200802357 0.102417471 -0.037364011 0.247906285
## BsmtFinSF1 0.0585431369 0.004262424 -0.107354677 -0.081006851 0.260010920
## BsmtFinSF2 -0.0764438620 -0.032147837 -0.015728114 -0.040751236 0.046920709
## BsmtUnfSF 0.2888860555 -0.041117530 0.166643317 0.030085868 0.051574882
## TotalBsmtSF 0.3237224136 -0.048803739 0.050449956 -0.068900643 0.339519324
## X1stFlrSF 0.3806374950 -0.119915909 0.127400749 0.068100588 0.410531085
## X2ndFlrSF 0.4213779829 0.609707300 0.502900613 0.059305753 0.194560892
## LowQualFinSF -0.0007095096 -0.027080049 0.105606569 0.007521744 -0.021272143
## GrLivArea 0.6300116463 0.415771636 0.521269511 0.100063165 0.461679134
## BsmtFullBath -0.0645120486 -0.030904959 -0.150672809 -0.041502546 0.137927708
## BsmtHalfBath -0.0545358120 -0.012339900 0.046518848 -0.037944350 0.028975587
## FullBath 1.0000000000 0.136380589 0.363251983 0.133115214 0.243670503
## HalfBath 0.1363805887 1.000000000 0.226651484 -0.068262549 0.203648508
## BedroomAbvGr 0.3632519830 0.226651484 1.000000000 0.198596758 0.107569681
## KitchenAbvGr 0.1331152142 -0.068262549 0.198596758 1.000000000 -0.123936235
## Fireplaces 0.2436705031 0.203648508 0.107569681 -0.123936235 1.000000000
## GarageArea 0.4056562085 0.163549364 0.065252530 -0.064433047 0.269141238
## WoodDeckSF 0.1877032138 0.108080303 0.046853773 -0.090130273 0.200018796
## OpenPorchSF 0.2599774255 0.199740148 0.093809572 -0.070090610 0.169405327
## EnclosedPorch -0.1150929635 -0.095316526 0.041570435 0.037312385 -0.024821869
## X3SsnPorch 0.0353530166 -0.004972488 -0.024477796 -0.024600359 0.011257239
## ScreenPorch -0.0081060933 0.072425845 0.044299691 -0.051613366 0.184530270
## PoolArea 0.0496038256 0.022381498 0.070702584 -0.014525116 0.095073522
## MiscVal -0.0142898450 0.001290145 0.007766972 0.062340724 0.001408605
## MoSold 0.0558721290 -0.009049888 0.046543860 0.026588907 0.046357102
## YrSold -0.0196688407 -0.010268669 -0.036013893 0.031687207 -0.024095565
## SalePrice 0.5606637627 0.284107676 0.168213154 -0.135907371 0.466928837
## GarageArea WoodDeckSF OpenPorchSF EnclosedPorch X3SsnPorch
## MSSubClass -0.09867154 -0.012579358 -0.006100121 -0.012036622 -0.0438245492
## LotFrontage 0.32366290 0.077106221 0.137454496 0.009790061 0.0623354713
## LotArea 0.18040276 0.171697687 0.084773809 -0.018339734 0.0204228296
## OverallQual 0.56202176 0.238923392 0.308818823 -0.113936859 0.0303705671
## OverallCond -0.15152137 -0.003333699 -0.032588814 0.070356184 0.0255036600
## YearBuilt 0.47895382 0.224880142 0.188685840 -0.387267783 0.0313545131
## YearRemodAdd 0.37159981 0.205725920 0.226297633 -0.193919147 0.0452858098
## MasVnrArea 0.37256701 0.159349430 0.124965275 -0.109848652 0.0187948145
## BsmtFinSF1 0.29697039 0.204306145 0.111760613 -0.102303306 0.0264505062
## BsmtFinSF2 -0.01822659 0.067898326 0.003092562 0.036543339 -0.0299933980
## BsmtUnfSF 0.18330270 -0.005316424 0.129005415 -0.002537855 0.0207640057
## TotalBsmtSF 0.48666546 0.232018609 0.247263746 -0.095477737 0.0373837273
## X1stFlrSF 0.48978165 0.235458623 0.211671225 -0.065291701 0.0561043745
## X2ndFlrSF 0.13834696 0.092165418 0.208026063 0.061988691 -0.0243576484
## LowQualFinSF -0.06760141 -0.025443648 0.018251039 0.061081238 -0.0042956104
## GrLivArea 0.46899748 0.247432821 0.330223962 0.009113210 0.0206431897
## BsmtFullBath 0.17918948 0.175315190 0.067341461 -0.049910649 -0.0001060915
## BsmtHalfBath -0.02453558 0.040161223 -0.025323758 -0.008555334 0.0351136309
## FullBath 0.40565621 0.187703214 0.259977425 -0.115092963 0.0353530166
## HalfBath 0.16354936 0.108080303 0.199740148 -0.095316526 -0.0049724884
## BedroomAbvGr 0.06525253 0.046853773 0.093809572 0.041570435 -0.0244777964
## KitchenAbvGr -0.06443305 -0.090130273 -0.070090610 0.037312385 -0.0246003587
## Fireplaces 0.26914124 0.200018796 0.169405327 -0.024821869 0.0112572390
## GarageArea 1.00000000 0.224666307 0.241434672 -0.121776720 0.0350867002
## WoodDeckSF 0.22466631 1.000000000 0.058660609 -0.125988888 -0.0327706336
## OpenPorchSF 0.24143467 0.058660609 1.000000000 -0.093079318 -0.0058424993
## EnclosedPorch -0.12177672 -0.125988888 -0.093079318 1.000000000 -0.0373052828
## X3SsnPorch 0.03508670 -0.032770634 -0.005842499 -0.037305283 1.0000000000
## ScreenPorch 0.05141176 -0.074181351 0.074303944 -0.082864245 -0.0314358470
## PoolArea 0.06104727 0.073378207 0.060762111 0.054202562 -0.0079915489
## MiscVal -0.02739991 -0.009551228 -0.018583739 0.018360600 0.0003539653
## MoSold 0.02797380 0.021011044 0.071254885 -0.028887266 0.0294737952
## YrSold -0.02737794 0.022270451 -0.057619360 -0.009915937 0.0186449254
## SalePrice 0.62343144 0.324413445 0.315856227 -0.128577958 0.0445836653
## ScreenPorch PoolArea MiscVal MoSold YrSold
## MSSubClass -0.026030177 0.008282708 -0.0076832913 -0.013584643 -0.021407038
## LotFrontage 0.037684305 0.180867647 0.0011682749 0.010157807 0.006768250
## LotArea 0.043160378 0.077672392 0.0380676920 0.001204988 -0.014261407
## OverallQual 0.064886360 0.065165844 -0.0314062105 0.070815172 -0.027346708
## OverallCond 0.054810529 -0.001984942 0.0687768061 -0.003510839 0.043949746
## YearBuilt -0.050364435 0.004949728 -0.0343831387 0.012398471 -0.013617680
## YearRemodAdd -0.038740011 0.005829372 -0.0102862488 0.021490002 0.035743247
## MasVnrArea 0.061453179 0.011722909 -0.0298147620 -0.005939579 -0.008183639
## BsmtFinSF1 0.062020623 0.140491286 0.0035714735 -0.015726948 0.014358922
## BsmtFinSF2 0.088871251 0.041709055 0.0049397812 -0.015210738 0.031705637
## BsmtUnfSF -0.012579273 -0.035092241 -0.0238366451 0.034888443 -0.041258195
## TotalBsmtSF 0.084488986 0.126053132 -0.0184789224 0.013196179 -0.014968648
## X1stFlrSF 0.088758073 0.131524976 -0.0210957195 0.031371560 -0.013603771
## X2ndFlrSF 0.040606448 0.081486878 0.0161968746 0.035164427 -0.028699914
## LowQualFinSF 0.026799413 0.062157372 -0.0037928708 -0.022173961 -0.028920880
## GrLivArea 0.101510396 0.170205336 -0.0024156396 0.050239681 -0.036525820
## BsmtFullBath 0.023147726 0.067615556 -0.0230470249 -0.025360894 0.067049138
## BsmtHalfBath 0.032121407 0.020024630 -0.0073665245 0.032872705 -0.046523882
## FullBath -0.008106093 0.049603826 -0.0142898450 0.055872129 -0.019668841
## HalfBath 0.072425845 0.022381498 0.0012901448 -0.009049888 -0.010268669
## BedroomAbvGr 0.044299691 0.070702584 0.0077669720 0.046543860 -0.036013893
## KitchenAbvGr -0.051613366 -0.014525116 0.0623407240 0.026588907 0.031687207
## Fireplaces 0.184530270 0.095073522 0.0014086054 0.046357102 -0.024095565
## GarageArea 0.051411762 0.061047272 -0.0273999144 0.027973800 -0.027377940
## WoodDeckSF -0.074181351 0.073378207 -0.0095512282 0.021011044 0.022270451
## OpenPorchSF 0.074303944 0.060762111 -0.0185837390 0.071254885 -0.057619360
## EnclosedPorch -0.082864245 0.054202562 0.0183606001 -0.028887266 -0.009915937
## X3SsnPorch -0.031435847 -0.007991549 0.0003539653 0.029473795 0.018644925
## ScreenPorch 1.000000000 0.051307395 0.0319457608 0.023216992 0.010694106
## PoolArea 0.051307395 1.000000000 0.0296686509 -0.033736640 -0.059688932
## MiscVal 0.031945761 0.029668651 1.0000000000 -0.006494550 0.004906262
## MoSold 0.023216992 -0.033736640 -0.0064945502 1.000000000 -0.145721413
## YrSold 0.010694106 -0.059688932 0.0049062625 -0.145721413 1.000000000
## SalePrice 0.111446571 0.092403549 -0.0211895796 0.046432245 -0.028922585
## SalePrice
## MSSubClass -0.08428414
## LotFrontage 0.33490085
## LotArea 0.26384335
## OverallQual 0.79098160
## OverallCond -0.07785589
## YearBuilt 0.52289733
## YearRemodAdd 0.50710097
## MasVnrArea 0.47524132
## BsmtFinSF1 0.38641981
## BsmtFinSF2 -0.01137812
## BsmtUnfSF 0.21447911
## TotalBsmtSF 0.61358055
## X1stFlrSF 0.60585218
## X2ndFlrSF 0.31933380
## LowQualFinSF -0.02560613
## GrLivArea 0.70862448
## BsmtFullBath 0.22712223
## BsmtHalfBath -0.01684415
## FullBath 0.56066376
## HalfBath 0.28410768
## BedroomAbvGr 0.16821315
## KitchenAbvGr -0.13590737
## Fireplaces 0.46692884
## GarageArea 0.62343144
## WoodDeckSF 0.32441344
## OpenPorchSF 0.31585623
## EnclosedPorch -0.12857796
## X3SsnPorch 0.04458367
## ScreenPorch 0.11144657
## PoolArea 0.09240355
## MiscVal -0.02118958
## MoSold 0.04643225
## YrSold -0.02892259
## SalePrice 1.00000000## MSSubClass LotFrontage LotArea OverallQual OverallCond
## MSSubClass 1.000000000 -0.357055878 -0.139781082 0.03262771 -0.059315817
## LotFrontage -0.357055878 1.000000000 0.306794605 0.23419623 -0.052820100
## LotArea -0.139781082 0.306794605 1.000000000 0.10580574 -0.005636270
## OverallQual 0.032627708 0.234196231 0.105805742 1.00000000 -0.091932343
## OverallCond -0.059315817 -0.052820100 -0.005636270 -0.09193234 1.000000000
## YearBuilt 0.027850137 0.117597979 0.014227652 0.57232277 -0.375983196
## YearRemodAdd 0.040581045 0.082745885 0.013788427 0.55068392 0.073741498
## MasVnrArea 0.022894690 0.179283452 0.103960227 0.41023774 -0.127788119
## BsmtFinSF1 -0.069835749 0.215828435 0.214103131 0.23966597 -0.046230856
## BsmtFinSF2 -0.065648579 0.043339566 0.111169745 -0.05911869 0.040229170
## BsmtUnfSF -0.140759481 0.122155600 -0.002618360 0.30815893 -0.136840570
## TotalBsmtSF -0.238518409 0.363357723 0.260833135 0.53780850 -0.171097515
## X1stFlrSF -0.251758352 0.414266394 0.299474579 0.47622383 -0.144202784
## X2ndFlrSF 0.307885721 0.072482666 0.050985948 0.29549288 0.028942116
## LowQualFinSF 0.046473756 0.036848721 0.004778970 -0.03042928 0.025494320
## GrLivArea 0.074853180 0.368391966 0.263116167 0.59300743 -0.079685865
## BsmtFullBath 0.003491026 0.091480992 0.158154531 0.11109779 -0.054941515
## BsmtHalfBath -0.002332535 -0.006419220 0.048045571 -0.04015016 0.117820915
## FullBath 0.131608222 0.180424206 0.126030627 0.55059971 -0.194149489
## HalfBath 0.177354389 0.048258362 0.014259469 0.27345810 -0.060769327
## BedroomAbvGr -0.023438028 0.237023227 0.119689908 0.10167636 0.012980060
## KitchenAbvGr 0.281721040 -0.005804607 -0.017783871 -0.18388223 -0.087000855
## Fireplaces -0.045569340 0.235754565 0.271364010 0.39676504 -0.023819978
## GarageArea -0.098671543 0.323662899 0.180402755 0.56202176 -0.151521371
## WoodDeckSF -0.012579358 0.077106221 0.171697687 0.23892339 -0.003333699
## OpenPorchSF -0.006100121 0.137454496 0.084773809 0.30881882 -0.032588814
## EnclosedPorch -0.012036622 0.009790061 -0.018339734 -0.11393686 0.070356184
## X3SsnPorch -0.043824549 0.062335471 0.020422830 0.03037057 0.025503660
## ScreenPorch -0.026030177 0.037684305 0.043160378 0.06488636 0.054810529
## PoolArea 0.008282708 0.180867647 0.077672392 0.06516584 -0.001984942
## MiscVal -0.007683291 0.001168275 0.038067692 -0.03140621 0.068776806
## MoSold -0.013584643 0.010157807 0.001204988 0.07081517 -0.003510839
## YrSold -0.021407038 0.006768250 -0.014261407 -0.02734671 0.043949746
## SalePrice -0.084284135 0.334900852 0.263843354 0.79098160 -0.077855894
## YearBuilt YearRemodAdd MasVnrArea BsmtFinSF1 BsmtFinSF2
## MSSubClass 0.027850137 0.040581045 0.022894690 -0.069835749 -0.065648579
## LotFrontage 0.117597979 0.082745885 0.179283452 0.215828435 0.043339566
## LotArea 0.014227652 0.013788427 0.103960227 0.214103131 0.111169745
## OverallQual 0.572322769 0.550683924 0.410237736 0.239665966 -0.059118693
## OverallCond -0.375983196 0.073741498 -0.127788119 -0.046230856 0.040229170
## YearBuilt 1.000000000 0.592854976 0.314745023 0.249503197 -0.049106831
## YearRemodAdd 0.592854976 1.000000000 0.179186495 0.128450547 -0.067758514
## MasVnrArea 0.314745023 0.179186495 1.000000000 0.263582388 -0.072302247
## BsmtFinSF1 0.249503197 0.128450547 0.263582388 1.000000000 -0.050117400
## BsmtFinSF2 -0.049106831 -0.067758514 -0.072302247 -0.050117400 1.000000000
## BsmtUnfSF 0.149040392 0.181133087 0.114183659 -0.495251469 -0.209294492
## TotalBsmtSF 0.391452002 0.291065583 0.362452094 0.522396052 0.104809538
## X1stFlrSF 0.281985859 0.240379268 0.342160338 0.445862656 0.097117448
## X2ndFlrSF 0.010307660 0.140023779 0.174019344 -0.137078986 -0.099260316
## LowQualFinSF -0.183784344 -0.062419100 -0.069068105 -0.064502597 0.014806998
## GrLivArea 0.199009714 0.287388520 0.389892916 0.208171130 -0.009639892
## BsmtFullBath 0.187598550 0.119469879 0.085054528 0.649211754 0.158678061
## BsmtHalfBath -0.038161806 -0.012337032 0.026668558 0.067418478 0.070948134
## FullBath 0.468270787 0.439046484 0.275729847 0.058543137 -0.076443862
## HalfBath 0.242655910 0.183330612 0.200802357 0.004262424 -0.032147837
## BedroomAbvGr -0.070651217 -0.040580928 0.102417471 -0.107354677 -0.015728114
## KitchenAbvGr -0.174800246 -0.149597521 -0.037364011 -0.081006851 -0.040751236
## Fireplaces 0.147716399 0.112581318 0.247906285 0.260010920 0.046920709
## GarageArea 0.478953820 0.371599809 0.372567013 0.296970385 -0.018226592
## WoodDeckSF 0.224880142 0.205725920 0.159349430 0.204306145 0.067898326
## OpenPorchSF 0.188685840 0.226297633 0.124965275 0.111760613 0.003092562
## EnclosedPorch -0.387267783 -0.193919147 -0.109848652 -0.102303306 0.036543339
## X3SsnPorch 0.031354513 0.045285810 0.018794814 0.026450506 -0.029993398
## ScreenPorch -0.050364435 -0.038740011 0.061453179 0.062020623 0.088871251
## PoolArea 0.004949728 0.005829372 0.011722909 0.140491286 0.041709055
## MiscVal -0.034383139 -0.010286249 -0.029814762 0.003571473 0.004939781
## MoSold 0.012398471 0.021490002 -0.005939579 -0.015726948 -0.015210738
## YrSold -0.013617680 0.035743247 -0.008183639 0.014358922 0.031705637
## SalePrice 0.522897333 0.507100967 0.475241317 0.386419806 -0.011378121
## BsmtUnfSF TotalBsmtSF X1stFlrSF X2ndFlrSF
## MSSubClass -0.140759481 -0.2385184093 -0.251758352 0.307885721
## LotFrontage 0.122155600 0.3633577228 0.414266394 0.072482666
## LotArea -0.002618360 0.2608331345 0.299474579 0.050985948
## OverallQual 0.308158927 0.5378084986 0.476223829 0.295492879
## OverallCond -0.136840570 -0.1710975146 -0.144202784 0.028942116
## YearBuilt 0.149040392 0.3914520021 0.281985859 0.010307660
## YearRemodAdd 0.181133087 0.2910655826 0.240379268 0.140023779
## MasVnrArea 0.114183659 0.3624520941 0.342160338 0.174019344
## BsmtFinSF1 -0.495251469 0.5223960520 0.445862656 -0.137078986
## BsmtFinSF2 -0.209294492 0.1048095376 0.097117448 -0.099260316
## BsmtUnfSF 1.000000000 0.4153596052 0.317987438 0.004469092
## TotalBsmtSF 0.415359605 1.0000000000 0.819529975 -0.174511950
## X1stFlrSF 0.317987438 0.8195299750 1.000000000 -0.202646181
## X2ndFlrSF 0.004469092 -0.1745119501 -0.202646181 1.000000000
## LowQualFinSF 0.028166688 -0.0332453873 -0.014240673 0.063352950
## GrLivArea 0.240257268 0.4548682025 0.566023969 0.687501064
## BsmtFullBath -0.422900477 0.3073505537 0.244671104 -0.169493952
## BsmtHalfBath -0.095804288 -0.0003145818 0.001955654 -0.023854784
## FullBath 0.288886055 0.3237224136 0.380637495 0.421377983
## HalfBath -0.041117530 -0.0488037386 -0.119915909 0.609707300
## BedroomAbvGr 0.166643317 0.0504499555 0.127400749 0.502900613
## KitchenAbvGr 0.030085868 -0.0689006426 0.068100588 0.059305753
## Fireplaces 0.051574882 0.3395193239 0.410531085 0.194560892
## GarageArea 0.183302698 0.4866654638 0.489781654 0.138346959
## WoodDeckSF -0.005316424 0.2320186091 0.235458623 0.092165418
## OpenPorchSF 0.129005415 0.2472637463 0.211671225 0.208026063
## EnclosedPorch -0.002537855 -0.0954777367 -0.065291701 0.061988691
## X3SsnPorch 0.020764006 0.0373837273 0.056104374 -0.024357648
## ScreenPorch -0.012579273 0.0844889859 0.088758073 0.040606448
## PoolArea -0.035092241 0.1260531321 0.131524976 0.081486878
## MiscVal -0.023836645 -0.0184789224 -0.021095719 0.016196875
## MoSold 0.034888443 0.0131961786 0.031371560 0.035164427
## YrSold -0.041258195 -0.0149686480 -0.013603771 -0.028699914
## SalePrice 0.214479106 0.6135805516 0.605852185 0.319333803
## LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath
## MSSubClass 0.0464737559 0.074853180 0.0034910258 -0.0023325346
## LotFrontage 0.0368487208 0.368391966 0.0914809919 -0.0064192197
## LotArea 0.0047789699 0.263116167 0.1581545311 0.0480455709
## OverallQual -0.0304292840 0.593007430 0.1110977861 -0.0401501577
## OverallCond 0.0254943199 -0.079685865 -0.0549415154 0.1178209151
## YearBuilt -0.1837843444 0.199009714 0.1875985500 -0.0381618057
## YearRemodAdd -0.0624191001 0.287388520 0.1194698791 -0.0123370321
## MasVnrArea -0.0690681050 0.389892916 0.0850545278 0.0266685579
## BsmtFinSF1 -0.0645025969 0.208171130 0.6492117536 0.0674184779
## BsmtFinSF2 0.0148069979 -0.009639892 0.1586780608 0.0709481337
## BsmtUnfSF 0.0281666881 0.240257268 -0.4229004774 -0.0958042882
## TotalBsmtSF -0.0332453873 0.454868203 0.3073505537 -0.0003145818
## X1stFlrSF -0.0142406727 0.566023969 0.2446711042 0.0019556536
## X2ndFlrSF 0.0633529501 0.687501064 -0.1694939517 -0.0238547839
## LowQualFinSF 1.0000000000 0.134682813 -0.0471434219 -0.0058415048
## GrLivArea 0.1346828130 1.000000000 0.0348360495 -0.0189184832
## BsmtFullBath -0.0471434219 0.034836050 1.0000000000 -0.1478709605
## BsmtHalfBath -0.0058415048 -0.018918483 -0.1478709605 1.0000000000
## FullBath -0.0007095096 0.630011646 -0.0645120486 -0.0545358120
## HalfBath -0.0270800493 0.415771636 -0.0309049591 -0.0123399001
## BedroomAbvGr 0.1056065685 0.521269511 -0.1506728092 0.0465188484
## KitchenAbvGr 0.0075217443 0.100063165 -0.0415025464 -0.0379443502
## Fireplaces -0.0212721434 0.461679134 0.1379277084 0.0289755866
## GarageArea -0.0676014132 0.468997477 0.1791894804 -0.0245355796
## WoodDeckSF -0.0254436480 0.247432821 0.1753151901 0.0401612233
## OpenPorchSF 0.0182510391 0.330223962 0.0673414614 -0.0253237579
## EnclosedPorch 0.0610812378 0.009113210 -0.0499106491 -0.0085553339
## X3SsnPorch -0.0042956104 0.020643190 -0.0001060915 0.0351136309
## ScreenPorch 0.0267994130 0.101510396 0.0231477258 0.0321214072
## PoolArea 0.0621573723 0.170205336 0.0676155562 0.0200246298
## MiscVal -0.0037928708 -0.002415640 -0.0230470249 -0.0073665245
## MoSold -0.0221739606 0.050239681 -0.0253608943 0.0328727052
## YrSold -0.0289208798 -0.036525820 0.0670491377 -0.0465238818
## SalePrice -0.0256061300 0.708624478 0.2271222331 -0.0168441543
## FullBath HalfBath BedroomAbvGr KitchenAbvGr Fireplaces
## MSSubClass 0.1316082224 0.177354389 -0.023438028 0.281721040 -0.045569340
## LotFrontage 0.1804242055 0.048258362 0.237023227 -0.005804607 0.235754565
## LotArea 0.1260306265 0.014259469 0.119689908 -0.017783871 0.271364010
## OverallQual 0.5505997094 0.273458099 0.101676356 -0.183882235 0.396765038
## OverallCond -0.1941494887 -0.060769327 0.012980060 -0.087000855 -0.023819978
## YearBuilt 0.4682707872 0.242655910 -0.070651217 -0.174800246 0.147716399
## YearRemodAdd 0.4390464839 0.183330612 -0.040580928 -0.149597521 0.112581318
## MasVnrArea 0.2757298473 0.200802357 0.102417471 -0.037364011 0.247906285
## BsmtFinSF1 0.0585431369 0.004262424 -0.107354677 -0.081006851 0.260010920
## BsmtFinSF2 -0.0764438620 -0.032147837 -0.015728114 -0.040751236 0.046920709
## BsmtUnfSF 0.2888860555 -0.041117530 0.166643317 0.030085868 0.051574882
## TotalBsmtSF 0.3237224136 -0.048803739 0.050449956 -0.068900643 0.339519324
## X1stFlrSF 0.3806374950 -0.119915909 0.127400749 0.068100588 0.410531085
## X2ndFlrSF 0.4213779829 0.609707300 0.502900613 0.059305753 0.194560892
## LowQualFinSF -0.0007095096 -0.027080049 0.105606569 0.007521744 -0.021272143
## GrLivArea 0.6300116463 0.415771636 0.521269511 0.100063165 0.461679134
## BsmtFullBath -0.0645120486 -0.030904959 -0.150672809 -0.041502546 0.137927708
## BsmtHalfBath -0.0545358120 -0.012339900 0.046518848 -0.037944350 0.028975587
## FullBath 1.0000000000 0.136380589 0.363251983 0.133115214 0.243670503
## HalfBath 0.1363805887 1.000000000 0.226651484 -0.068262549 0.203648508
## BedroomAbvGr 0.3632519830 0.226651484 1.000000000 0.198596758 0.107569681
## KitchenAbvGr 0.1331152142 -0.068262549 0.198596758 1.000000000 -0.123936235
## Fireplaces 0.2436705031 0.203648508 0.107569681 -0.123936235 1.000000000
## GarageArea 0.4056562085 0.163549364 0.065252530 -0.064433047 0.269141238
## WoodDeckSF 0.1877032138 0.108080303 0.046853773 -0.090130273 0.200018796
## OpenPorchSF 0.2599774255 0.199740148 0.093809572 -0.070090610 0.169405327
## EnclosedPorch -0.1150929635 -0.095316526 0.041570435 0.037312385 -0.024821869
## X3SsnPorch 0.0353530166 -0.004972488 -0.024477796 -0.024600359 0.011257239
## ScreenPorch -0.0081060933 0.072425845 0.044299691 -0.051613366 0.184530270
## PoolArea 0.0496038256 0.022381498 0.070702584 -0.014525116 0.095073522
## MiscVal -0.0142898450 0.001290145 0.007766972 0.062340724 0.001408605
## MoSold 0.0558721290 -0.009049888 0.046543860 0.026588907 0.046357102
## YrSold -0.0196688407 -0.010268669 -0.036013893 0.031687207 -0.024095565
## SalePrice 0.5606637627 0.284107676 0.168213154 -0.135907371 0.466928837
## GarageArea WoodDeckSF OpenPorchSF EnclosedPorch X3SsnPorch
## MSSubClass -0.09867154 -0.012579358 -0.006100121 -0.012036622 -0.0438245492
## LotFrontage 0.32366290 0.077106221 0.137454496 0.009790061 0.0623354713
## LotArea 0.18040276 0.171697687 0.084773809 -0.018339734 0.0204228296
## OverallQual 0.56202176 0.238923392 0.308818823 -0.113936859 0.0303705671
## OverallCond -0.15152137 -0.003333699 -0.032588814 0.070356184 0.0255036600
## YearBuilt 0.47895382 0.224880142 0.188685840 -0.387267783 0.0313545131
## YearRemodAdd 0.37159981 0.205725920 0.226297633 -0.193919147 0.0452858098
## MasVnrArea 0.37256701 0.159349430 0.124965275 -0.109848652 0.0187948145
## BsmtFinSF1 0.29697039 0.204306145 0.111760613 -0.102303306 0.0264505062
## BsmtFinSF2 -0.01822659 0.067898326 0.003092562 0.036543339 -0.0299933980
## BsmtUnfSF 0.18330270 -0.005316424 0.129005415 -0.002537855 0.0207640057
## TotalBsmtSF 0.48666546 0.232018609 0.247263746 -0.095477737 0.0373837273
## X1stFlrSF 0.48978165 0.235458623 0.211671225 -0.065291701 0.0561043745
## X2ndFlrSF 0.13834696 0.092165418 0.208026063 0.061988691 -0.0243576484
## LowQualFinSF -0.06760141 -0.025443648 0.018251039 0.061081238 -0.0042956104
## GrLivArea 0.46899748 0.247432821 0.330223962 0.009113210 0.0206431897
## BsmtFullBath 0.17918948 0.175315190 0.067341461 -0.049910649 -0.0001060915
## BsmtHalfBath -0.02453558 0.040161223 -0.025323758 -0.008555334 0.0351136309
## FullBath 0.40565621 0.187703214 0.259977425 -0.115092963 0.0353530166
## HalfBath 0.16354936 0.108080303 0.199740148 -0.095316526 -0.0049724884
## BedroomAbvGr 0.06525253 0.046853773 0.093809572 0.041570435 -0.0244777964
## KitchenAbvGr -0.06443305 -0.090130273 -0.070090610 0.037312385 -0.0246003587
## Fireplaces 0.26914124 0.200018796 0.169405327 -0.024821869 0.0112572390
## GarageArea 1.00000000 0.224666307 0.241434672 -0.121776720 0.0350867002
## WoodDeckSF 0.22466631 1.000000000 0.058660609 -0.125988888 -0.0327706336
## OpenPorchSF 0.24143467 0.058660609 1.000000000 -0.093079318 -0.0058424993
## EnclosedPorch -0.12177672 -0.125988888 -0.093079318 1.000000000 -0.0373052828
## X3SsnPorch 0.03508670 -0.032770634 -0.005842499 -0.037305283 1.0000000000
## ScreenPorch 0.05141176 -0.074181351 0.074303944 -0.082864245 -0.0314358470
## PoolArea 0.06104727 0.073378207 0.060762111 0.054202562 -0.0079915489
## MiscVal -0.02739991 -0.009551228 -0.018583739 0.018360600 0.0003539653
## MoSold 0.02797380 0.021011044 0.071254885 -0.028887266 0.0294737952
## YrSold -0.02737794 0.022270451 -0.057619360 -0.009915937 0.0186449254
## SalePrice 0.62343144 0.324413445 0.315856227 -0.128577958 0.0445836653
## ScreenPorch PoolArea MiscVal MoSold YrSold
## MSSubClass -0.026030177 0.008282708 -0.0076832913 -0.013584643 -0.021407038
## LotFrontage 0.037684305 0.180867647 0.0011682749 0.010157807 0.006768250
## LotArea 0.043160378 0.077672392 0.0380676920 0.001204988 -0.014261407
## OverallQual 0.064886360 0.065165844 -0.0314062105 0.070815172 -0.027346708
## OverallCond 0.054810529 -0.001984942 0.0687768061 -0.003510839 0.043949746
## YearBuilt -0.050364435 0.004949728 -0.0343831387 0.012398471 -0.013617680
## YearRemodAdd -0.038740011 0.005829372 -0.0102862488 0.021490002 0.035743247
## MasVnrArea 0.061453179 0.011722909 -0.0298147620 -0.005939579 -0.008183639
## BsmtFinSF1 0.062020623 0.140491286 0.0035714735 -0.015726948 0.014358922
## BsmtFinSF2 0.088871251 0.041709055 0.0049397812 -0.015210738 0.031705637
## BsmtUnfSF -0.012579273 -0.035092241 -0.0238366451 0.034888443 -0.041258195
## TotalBsmtSF 0.084488986 0.126053132 -0.0184789224 0.013196179 -0.014968648
## X1stFlrSF 0.088758073 0.131524976 -0.0210957195 0.031371560 -0.013603771
## X2ndFlrSF 0.040606448 0.081486878 0.0161968746 0.035164427 -0.028699914
## LowQualFinSF 0.026799413 0.062157372 -0.0037928708 -0.022173961 -0.028920880
## GrLivArea 0.101510396 0.170205336 -0.0024156396 0.050239681 -0.036525820
## BsmtFullBath 0.023147726 0.067615556 -0.0230470249 -0.025360894 0.067049138
## BsmtHalfBath 0.032121407 0.020024630 -0.0073665245 0.032872705 -0.046523882
## FullBath -0.008106093 0.049603826 -0.0142898450 0.055872129 -0.019668841
## HalfBath 0.072425845 0.022381498 0.0012901448 -0.009049888 -0.010268669
## BedroomAbvGr 0.044299691 0.070702584 0.0077669720 0.046543860 -0.036013893
## KitchenAbvGr -0.051613366 -0.014525116 0.0623407240 0.026588907 0.031687207
## Fireplaces 0.184530270 0.095073522 0.0014086054 0.046357102 -0.024095565
## GarageArea 0.051411762 0.061047272 -0.0273999144 0.027973800 -0.027377940
## WoodDeckSF -0.074181351 0.073378207 -0.0095512282 0.021011044 0.022270451
## OpenPorchSF 0.074303944 0.060762111 -0.0185837390 0.071254885 -0.057619360
## EnclosedPorch -0.082864245 0.054202562 0.0183606001 -0.028887266 -0.009915937
## X3SsnPorch -0.031435847 -0.007991549 0.0003539653 0.029473795 0.018644925
## ScreenPorch 1.000000000 0.051307395 0.0319457608 0.023216992 0.010694106
## PoolArea 0.051307395 1.000000000 0.0296686509 -0.033736640 -0.059688932
## MiscVal 0.031945761 0.029668651 1.0000000000 -0.006494550 0.004906262
## MoSold 0.023216992 -0.033736640 -0.0064945502 1.000000000 -0.145721413
## YrSold 0.010694106 -0.059688932 0.0049062625 -0.145721413 1.000000000
## SalePrice 0.111446571 0.092403549 -0.0211895796 0.046432245 -0.028922585
## SalePrice
## MSSubClass -0.08428414
## LotFrontage 0.33490085
## LotArea 0.26384335
## OverallQual 0.79098160
## OverallCond -0.07785589
## YearBuilt 0.52289733
## YearRemodAdd 0.50710097
## MasVnrArea 0.47524132
## BsmtFinSF1 0.38641981
## BsmtFinSF2 -0.01137812
## BsmtUnfSF 0.21447911
## TotalBsmtSF 0.61358055
## X1stFlrSF 0.60585218
## X2ndFlrSF 0.31933380
## LowQualFinSF -0.02560613
## GrLivArea 0.70862448
## BsmtFullBath 0.22712223
## BsmtHalfBath -0.01684415
## FullBath 0.56066376
## HalfBath 0.28410768
## BedroomAbvGr 0.16821315
## KitchenAbvGr -0.13590737
## Fireplaces 0.46692884
## GarageArea 0.62343144
## WoodDeckSF 0.32441344
## OpenPorchSF 0.31585623
## EnclosedPorch -0.12857796
## X3SsnPorch 0.04458367
## ScreenPorch 0.11144657
## PoolArea 0.09240355
## MiscVal -0.02118958
## MoSold 0.04643225
## YrSold -0.02892259
## SalePrice 1.00000000## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Data Transformation/Scaling
Split the numerical variables into features and the target variable.
X_num <- subset(numerical_data, select = -c(SalePrice))
y <- subset(numerical_data, select = c(SalePrice))$SalePriceLog Transformation for numerical features.
skewness_before <- sapply(X_num, function(x) {
e1071::skewness(x)
})
X_num_skewed <- skewness_before[abs(skewness_before) > 0.75]
for (x in names(X_num_skewed)) {
# bc <- BoxCoxTrans(X_num[[x]], lambda = 0.15)
# X_num[[x]] <- predict(bc, X_num[[x]])
X_num[[x]] <- log1p(X_num[[x]])
}
skewness_after <- sapply(X_num, function(x) {
e1071::skewness(x)
})
data.frame(skewness_before, skewness_after)## skewness_before skewness_after
## MSSubClass 1.40476562 0.248485705
## LotFrontage 2.38005182 -0.890144743
## LotArea 12.18261502 -0.137122272
## OverallQual 0.21649836 0.216498356
## OverallCond 0.69164401 0.691644012
## YearBuilt -0.61220121 -0.612201211
## YearRemodAdd -0.50252776 -0.502527759
## MasVnrArea 2.67091482 0.480131975
## BsmtFinSF1 1.68204129 -0.617139693
## BsmtFinSF2 4.24652141 2.518510460
## BsmtUnfSF 0.91837835 -2.182012816
## TotalBsmtSF 1.52112395 -5.144083032
## X1stFlrSF 1.37392896 0.079949547
## X2ndFlrSF 0.81135997 0.289048572
## LowQualFinSF 8.99283329 7.444994097
## GrLivArea 1.36375364 -0.006127642
## BsmtFullBath 0.59484237 0.594842375
## BsmtHalfBath 4.09497490 3.924985577
## FullBath 0.03648647 0.036486466
## HalfBath 0.67450925 0.674509252
## BedroomAbvGr 0.21135511 0.211355110
## KitchenAbvGr 4.47917826 3.861466484
## Fireplaces 0.64823107 0.648231070
## GarageArea 0.17961125 0.179611252
## WoodDeckSF 1.53820999 0.153221248
## OpenPorchSF 2.35948572 -0.023349240
## EnclosedPorch 3.08352575 2.107936639
## X3SsnPorch 10.28317840 7.719088344
## ScreenPorch 4.11374731 3.143938375
## PoolArea 14.79791829 14.333602712
## MiscVal 24.42652237 5.160083979
## MoSold 0.21161746 0.211617459
## YrSold 0.09607079 0.096070792Log Transformation for the target variable.
skewness_before <- e1071::skewness(y)
y_t <- log1p(y)
skewness_after <- e1071::skewness(y_t)
sprintf("Before: %f, After: %f", skewness_before, skewness_after)## [1] "Before: 1.879009, After: 0.121097"Scaling
X_num <- scale(X_num)One-Hot Encoding for categorical variables.
encoder <- dummyVars(~., data = categorical_data)
X_cat <- predict(encoder, newdata = categorical_data)
X_cat <- data.frame(X_cat)Split into train and validation and test sets.
X <- cbind(X_cat, X_num)
train_idx <- createDataPartition(y_t, p = 0.7, list = F)
X_train <- X[train_idx, ]
y_train <- y_t[train_idx]
X_test <- X[-train_idx, ]
y_test <- y_t[-train_idx]
train_val_idx <- createDataPartition(y_train, p = 0.8, list = FALSE)
X_train <- X_train[train_val_idx, ]
y_train <- y_train[train_val_idx]
X_val <- X_train[-train_val_idx, ]
y_val <- y_train[-train_val_idx]
X_train_val <- rbind(X_train, X_val)
y_train_val <- c(y_train, y_val)dim(X)## [1] 1460 251length(y)## [1] 1460dim(X_train)## [1] 821 251length(y_train)## [1] 821dim(X_val)## [1] 170 251length(y_val)## [1] 170names(X)## [1] "MSZoningC..all." "MSZoningFV" "MSZoningRH"
## [4] "MSZoningRL" "MSZoningRM" "StreetGrvl"
## [7] "StreetPave" "LotShapeIR1" "LotShapeIR2"
## [10] "LotShapeIR3" "LotShapeReg" "LandContourBnk"
## [13] "LandContourHLS" "LandContourLow" "LandContourLvl"
## [16] "UtilitiesAllPub" "UtilitiesNoSeWa" "LotConfigCorner"
## [19] "LotConfigCulDSac" "LotConfigFR2" "LotConfigFR3"
## [22] "LotConfigInside" "LandSlopeGtl" "LandSlopeMod"
## [25] "LandSlopeSev" "NeighborhoodBlmngtn" "NeighborhoodBlueste"
## [28] "NeighborhoodBrDale" "NeighborhoodBrkSide" "NeighborhoodClearCr"
## [31] "NeighborhoodCollgCr" "NeighborhoodCrawfor" "NeighborhoodEdwards"
## [34] "NeighborhoodGilbert" "NeighborhoodIDOTRR" "NeighborhoodMeadowV"
## [37] "NeighborhoodMitchel" "NeighborhoodNAmes" "NeighborhoodNoRidge"
## [40] "NeighborhoodNPkVill" "NeighborhoodNridgHt" "NeighborhoodNWAmes"
## [43] "NeighborhoodOldTown" "NeighborhoodSawyer" "NeighborhoodSawyerW"
## [46] "NeighborhoodSomerst" "NeighborhoodStoneBr" "NeighborhoodSWISU"
## [49] "NeighborhoodTimber" "NeighborhoodVeenker" "Condition1Artery"
## [52] "Condition1Feedr" "Condition1Norm" "Condition1PosA"
## [55] "Condition1PosN" "Condition1RRAe" "Condition1RRAn"
## [58] "Condition1RRNe" "Condition1RRNn" "Condition2Artery"
## [61] "Condition2Feedr" "Condition2Norm" "Condition2PosA"
## [64] "Condition2PosN" "Condition2RRAe" "Condition2RRAn"
## [67] "Condition2RRNn" "BldgType1Fam" "BldgType2fmCon"
## [70] "BldgTypeDuplex" "BldgTypeTwnhs" "BldgTypeTwnhsE"
## [73] "HouseStyle1.5Fin" "HouseStyle1.5Unf" "HouseStyle1Story"
## [76] "HouseStyle2.5Fin" "HouseStyle2.5Unf" "HouseStyle2Story"
## [79] "HouseStyleSFoyer" "HouseStyleSLvl" "RoofStyleFlat"
## [82] "RoofStyleGable" "RoofStyleGambrel" "RoofStyleHip"
## [85] "RoofStyleMansard" "RoofStyleShed" "RoofMatlClyTile"
## [88] "RoofMatlCompShg" "RoofMatlMembran" "RoofMatlMetal"
## [91] "RoofMatlRoll" "RoofMatlTar.Grv" "RoofMatlWdShake"
## [94] "RoofMatlWdShngl" "Exterior1stAsbShng" "Exterior1stAsphShn"
## [97] "Exterior1stBrkComm" "Exterior1stBrkFace" "Exterior1stCBlock"
## [100] "Exterior1stCemntBd" "Exterior1stHdBoard" "Exterior1stImStucc"
## [103] "Exterior1stMetalSd" "Exterior1stPlywood" "Exterior1stStone"
## [106] "Exterior1stStucco" "Exterior1stVinylSd" "Exterior1stWd.Sdng"
## [109] "Exterior1stWdShing" "MasVnrTypeBrkCmn" "MasVnrTypeBrkFace"
## [112] "MasVnrTypeNone" "MasVnrTypeStone" "ExterQualEx"
## [115] "ExterQualFa" "ExterQualGd" "ExterQualTA"
## [118] "ExterCondEx" "ExterCondFa" "ExterCondGd"
## [121] "ExterCondPo" "ExterCondTA" "FoundationBrkTil"
## [124] "FoundationCBlock" "FoundationPConc" "FoundationSlab"
## [127] "FoundationStone" "FoundationWood" "BsmtQualEx"
## [130] "BsmtQualFa" "BsmtQualGd" "BsmtQualTA"
## [133] "BsmtCondFa" "BsmtCondGd" "BsmtCondPo"
## [136] "BsmtCondTA" "BsmtExposureAv" "BsmtExposureGd"
## [139] "BsmtExposureMn" "BsmtExposureNo" "BsmtFinType1ALQ"
## [142] "BsmtFinType1BLQ" "BsmtFinType1GLQ" "BsmtFinType1LwQ"
## [145] "BsmtFinType1Rec" "BsmtFinType1Unf" "BsmtFinType2ALQ"
## [148] "BsmtFinType2BLQ" "BsmtFinType2GLQ" "BsmtFinType2LwQ"
## [151] "BsmtFinType2Rec" "BsmtFinType2Unf" "HeatingFloor"
## [154] "HeatingGasA" "HeatingGasW" "HeatingGrav"
## [157] "HeatingOthW" "HeatingWall" "HeatingQCEx"
## [160] "HeatingQCFa" "HeatingQCGd" "HeatingQCPo"
## [163] "HeatingQCTA" "CentralAirN" "CentralAirY"
## [166] "ElectricalFuseA" "ElectricalFuseF" "ElectricalFuseP"
## [169] "ElectricalMix" "ElectricalSBrkr" "KitchenQualEx"
## [172] "KitchenQualFa" "KitchenQualGd" "KitchenQualTA"
## [175] "FunctionalMaj1" "FunctionalMaj2" "FunctionalMin1"
## [178] "FunctionalMin2" "FunctionalMod" "FunctionalSev"
## [181] "FunctionalTyp" "GarageType2Types" "GarageTypeAttchd"
## [184] "GarageTypeBasment" "GarageTypeBuiltIn" "GarageTypeCarPort"
## [187] "GarageTypeDetchd" "GarageFinishFin" "GarageFinishRFn"
## [190] "GarageFinishUnf" "GarageQualEx" "GarageQualFa"
## [193] "GarageQualGd" "GarageQualPo" "GarageQualTA"
## [196] "GarageCondEx" "GarageCondFa" "GarageCondGd"
## [199] "GarageCondPo" "GarageCondTA" "PavedDriveN"
## [202] "PavedDriveP" "PavedDriveY" "SaleTypeCOD"
## [205] "SaleTypeCon" "SaleTypeConLD" "SaleTypeConLI"
## [208] "SaleTypeConLw" "SaleTypeCWD" "SaleTypeNew"
## [211] "SaleTypeOth" "SaleTypeWD" "SaleConditionAbnorml"
## [214] "SaleConditionAdjLand" "SaleConditionAlloca" "SaleConditionFamily"
## [217] "SaleConditionNormal" "SaleConditionPartial" "MSSubClass"
## [220] "LotFrontage" "LotArea" "OverallQual"
## [223] "OverallCond" "YearBuilt" "YearRemodAdd"
## [226] "MasVnrArea" "BsmtFinSF1" "BsmtFinSF2"
## [229] "BsmtUnfSF" "TotalBsmtSF" "X1stFlrSF"
## [232] "X2ndFlrSF" "LowQualFinSF" "GrLivArea"
## [235] "BsmtFullBath" "BsmtHalfBath" "FullBath"
## [238] "HalfBath" "BedroomAbvGr" "KitchenAbvGr"
## [241] "Fireplaces" "GarageArea" "WoodDeckSF"
## [244] "OpenPorchSF" "EnclosedPorch" "X3SsnPorch"
## [247] "ScreenPorch" "PoolArea" "MiscVal"
## [250] "MoSold" "YrSold"Clustering
PCA
# Load the necessary libraries
library(stats)
library(factoextra)
# Perform PCA on the data matrix
pca_result <- prcomp(X)
# Extract the principal components
principal_components <- as.data.frame(pca_result$x)
# Determine the optimal number of clusters using the elbow method
fviz_nbclust(principal_components, kmeans, method = "wss")
k <- 3
# Perform K-means clustering on the principal components
kmeans_result <- kmeans(principal_components, centers = k)
cluster_assignments <- kmeans_result$cluster
print(cluster_assignments)## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 3 2 3 2 3 2 3 3 2 2 2 3 2 3 2 2
## 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
## 2 2 2 2 3 2 3 1 2 3 2 3 2 2 2 2
## 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
## 3 2 3 3 3 2 2 2 2 2 2 2 2 3 3 3
## 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
## 2 2 3 2 2 3 2 2 1 3 3 2 3 2 1 2
## 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## 3 3 3 3 2 2 3 2 3 2 2 1 2 2 2 2
## 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
## 3 1 3 2 3 3 3 1 2 2 2 2 2 2 3 3
## 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
## 3 2 2 2 3 3 2 3 2 3 2 2 2 3 2 3
## 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128
## 3 3 2 1 2 2 3 3 2 2 2 1 2 2 1 2
## 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## 2 2 3 3 2 3 2 3 2 3 3 3 2 3 2 3
## 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
## 2 1 2 3 2 2 2 3 3 2 2 2 2 3 3 3
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176
## 2 3 3 2 2 2 2 3 3 3 2 3 1 2 3 2
## 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192
## 3 2 3 2 1 2 2 3 2 3 3 2 2 1 3 2
## 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208
## 3 1 2 1 3 3 2 3 2 2 2 1 2 3 2 2
## 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224
## 3 2 2 3 3 2 2 2 3 2 3 1 3 3 3 2
## 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
## 3 1 3 1 2 1 2 3 1 2 3 1 3 3 3 2
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256
## 3 2 2 2 3 3 2 2 3 3 2 1 3 2 2 3
## 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272
## 3 3 3 2 2 3 2 2 2 3 3 2 2 2 3 2
## 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288
## 3 2 2 2 3 2 3 3 3 3 1 3 1 1 2 2
## 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304
## 2 2 3 2 2 3 2 2 2 3 2 2 2 3 3 2
## 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320
## 3 3 3 2 2 3 3 2 2 3 2 3 3 3 3 3
## 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336
## 3 3 3 2 3 2 1 2 2 2 2 2 3 1 3 3
## 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352
## 3 3 3 2 3 2 2 3 1 2 2 2 1 3 3 3
## 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368
## 2 2 2 3 3 1 2 3 2 2 3 1 3 2 3 2
## 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384
## 2 2 3 2 1 2 3 2 2 3 3 3 2 3 3 2
## 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
## 3 1 2 2 3 3 2 3 2 2 2 2 2 2 2 3
## 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416
## 1 3 2 3 3 2 2 2 3 3 2 2 3 2 3 3
## 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432
## 2 2 2 2 1 3 2 3 2 2 3 2 3 2 1 2
## 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448
## 1 3 1 3 2 2 2 2 3 2 2 1 3 2 3 3
## 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
## 2 2 2 3 3 3 2 2 2 3 2 2 3 2 2 2
## 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480
## 2 1 2 2 3 3 1 3 1 3 1 2 3 3 3 2
## 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496
## 3 3 2 1 2 2 2 2 2 1 1 2 3 2 2 2
## 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512
## 3 2 2 2 1 3 2 3 1 2 3 3 2 2 2 1
## 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
## 2 2 2 3 3 3 3 2 2 2 2 3 3 3 2 3
## 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544
## 2 3 3 2 2 2 3 2 3 2 2 3 3 3 3 1
## 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560
## 3 3 2 2 2 3 1 2 3 2 3 2 2 2 3 1
## 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576
## 2 2 2 2 3 2 3 3 3 2 2 2 3 3 2 2
## 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592
## 2 2 1 2 2 3 2 3 2 3 2 2 2 2 3 3
## 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608
## 2 1 2 3 2 1 2 1 3 2 3 1 3 3 2 2
## 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624
## 3 2 3 2 3 2 1 2 3 2 3 3 2 3 2 1
## 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640
## 3 2 2 2 3 2 2 1 3 2 2 2 2 2 2 1
## 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656
## 3 3 3 2 3 2 2 2 2 1 3 2 3 2 3 1
## 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672
## 2 2 2 2 3 3 2 2 3 3 3 3 2 2 3 2
## 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688
## 2 3 2 1 2 2 3 2 1 2 1 3 3 3 3 1
## 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704
## 3 3 1 3 3 2 2 2 2 2 2 1 3 2 3 2
## 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720
## 3 2 3 1 3 2 2 2 1 2 3 2 2 2 3 2
## 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736
## 3 1 2 2 3 2 3 3 2 2 1 3 3 2 2 2
## 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752
## 2 3 2 3 2 2 3 2 1 3 3 2 3 2 2 3
## 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768
## 3 3 2 1 3 3 1 3 2 2 3 3 1 3 3 2
## 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
## 3 3 2 2 2 2 3 1 3 2 2 2 3 3 3 1
## 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
## 2 2 2 3 2 3 1 2 3 3 3 3 2 2 3 2
## 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
## 3 2 3 3 2 3 2 3 2 2 2 1 2 2 2 3
## 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832
## 2 3 2 1 3 2 3 2 3 3 2 3 2 1 2 1
## 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848
## 3 2 2 2 2 1 2 2 2 2 2 2 2 2 3 2
## 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864
## 3 3 1 1 2 2 2 2 2 3 2 3 2 2 2 2
## 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880
## 3 2 3 2 2 3 2 3 2 2 2 3 2 3 2 2
## 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896
## 2 3 3 2 2 1 3 2 3 2 2 3 2 2 2 2
## 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912
## 2 2 3 2 2 2 3 3 2 2 3 2 2 3 2 2
## 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928
## 2 2 1 1 2 2 3 2 3 2 3 1 3 2 3 3
## 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944
## 3 3 3 2 3 3 3 2 3 3 3 2 2 3 2 2
## 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960
## 2 2 2 3 3 2 2 2 2 3 1 2 1 2 3 1
## 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976
## 2 3 1 3 3 3 2 2 2 2 2 1 2 3 2 1
## 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992
## 2 1 2 2 2 3 1 3 2 2 2 3 3 3 3 2
## 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008
## 3 3 3 2 2 2 2 3 2 2 3 2 1 2 2 1
## 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024
## 3 2 2 2 2 2 2 3 3 1 3 1 3 3 2 1
## 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040
## 3 2 2 3 2 1 2 3 3 3 2 2 3 3 1 1
## 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056
## 2 2 1 3 3 2 3 2 2 2 3 3 2 2 3 2
## 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072
## 1 3 3 2 1 2 2 2 2 3 3 2 1 2 2 2
## 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088
## 2 2 3 2 2 2 1 2 3 2 3 2 3 2 1 3
## 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104
## 1 1 2 1 2 2 2 3 2 1 2 3 2 2 2 2
## 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120
## 1 3 3 3 3 3 3 3 2 2 2 3 3 2 2 2
## 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136
## 2 3 2 2 3 2 1 3 3 1 2 2 2 3 3 2
## 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152
## 2 2 3 2 2 3 3 2 2 2 3 2 2 2 2 3
## 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168
## 2 2 3 3 2 1 3 3 1 3 2 2 3 3 3 3
## 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184
## 2 3 2 2 1 2 2 3 2 2 2 2 3 3 3 2
## 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200
## 3 2 2 3 3 3 3 1 2 1 2 3 3 2 3 2
## 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216
## 2 3 2 3 2 3 2 3 2 3 3 3 2 2 2 2
## 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232
## 2 3 2 1 2 2 2 2 3 2 3 2 3 2 3 2
## 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248
## 2 2 2 2 1 3 2 3 3 3 3 3 2 3 3 2
## 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264
## 2 2 3 1 2 3 3 2 3 2 3 2 3 2 2 2
## 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280
## 1 1 2 3 3 2 3 2 2 2 2 2 2 3 3 2
## 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296
## 3 3 2 2 2 2 2 2 1 3 2 1 2 3 2 2
## 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312
## 2 1 3 2 3 2 3 3 1 3 1 2 2 3 3 3
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328
## 3 3 2 3 3 1 3 2 2 2 3 2 3 2 2 2
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344
## 2 3 3 2 2 2 1 2 2 2 3 2 2 2 3 2
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360
## 3 2 3 3 3 2 3 2 2 3 3 3 2 2 1 3
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376
## 2 3 2 3 1 3 3 1 1 3 2 2 3 3 3 3
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392
## 2 2 1 3 2 3 2 2 2 2 3 2 3 2 3 2
## 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408
## 2 2 1 3 2 2 2 2 2 3 3 3 2 1 2 2
## 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424
## 2 3 3 2 2 3 2 1 2 3 2 3 3 1 1 3
## 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440
## 2 2 3 2 2 3 3 1 2 3 2 3 2 3 2 3
## 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456
## 2 1 3 2 3 2 2 3 2 1 2 3 1 2 3 3
## 1457 1458 1459 1460
## 3 3 2 2# Add the cluster assignments to the principal components data
principal_components$cluster <- as.factor(cluster_assignments)
ggplot(principal_components, aes(PC1, PC2, color = cluster)) +
geom_point() +
labs(x = "Principal Component 1", y = "Principal Component 2") +
scale_color_discrete(name = "Cluster") +
theme_minimal()
t-SNE
tsne <- Rtsne(X)
tsne_df <- data.frame(tsne)dist_mat <- dist(tsne$Y, method = "euclidean")
hclust_avg <- hclust(dist_mat, method = "average")
dend <- as.dendrogram(hclust_avg)
plot(dend)
k = 15
cut_avg <- cutree(hclust_avg, k)
tsne_df$cluster <- cut_avg
getCentroid <- function(points) {
xy <- numeric(2)
xy[1] = mean(points[, 1])
xy[2] = mean(points[, 2])
return(xy)
}
centroids = matrix(0, k, 2)
for (i in unique(cut_avg)) centroids[i, ] <- getCentroid(tsne$Y[cut_avg == i,])tsne_df## N Y.1 Y.2 costs itercosts origD perplexity
## 1 1460 1.986541e+01 0.61696248 6.312128e-04 73.771148 50 30
## 2 1460 3.704116e+00 17.12829597 8.232540e-04 71.150987 50 30
## 3 1460 2.014823e+01 -0.70238402 8.511462e-04 71.034367 50 30
## 4 1460 -2.776097e+01 7.42146480 3.518235e-04 71.035404 50 30
## 5 1460 2.049439e+01 -2.68081918 5.377578e-04 71.037731 50 30
## 6 1460 8.551878e+00 -9.86640159 1.835220e-04 1.555216 50 30
## 7 1460 -1.365457e-01 -19.74222937 1.439053e-03 1.312321 50 30
## 8 1460 7.018594e+00 24.49087648 8.079059e-04 1.228241 50 30
## 9 1460 -2.974571e+01 -9.98391754 5.951550e-04 1.196858 50 30
## 10 1460 -3.572762e+00 -2.29372078 8.088329e-04 1.176920 50 30
## 11 1460 -8.876179e+00 5.88658564 1.742382e-03 1.164909 50 30
## 12 1460 2.327253e+01 -6.33412442 3.948003e-04 1.155632 50 30
## 13 1460 3.767144e+00 -0.01074932 8.627069e-04 1.148755 50 30
## 14 1460 -2.724445e+00 -27.21039124 5.896907e-04 1.143827 50 30
## 15 1460 -6.929143e+00 -2.70460989 9.837242e-04 1.139748 50 30
## 16 1460 -1.866745e+01 8.81821619 7.690628e-04 1.135437 50 30
## 17 1460 -5.033253e+00 19.69411388 1.129143e-03 1.131049 50 30
## 18 1460 -2.249028e+01 29.56426190 2.261055e-04 1.127886 50 30
## 19 1460 -1.260445e+01 -11.32737087 1.099444e-03 1.125117 50 30
## 20 1460 -1.189045e+01 4.14226659 1.052478e-03 1.123256 50 30
## 21 1460 2.828610e+01 -3.24507358 4.173264e-04 73.771148 50 30
## 22 1460 -2.255078e+01 11.97767458 7.400350e-04 71.150987 50 30
## 23 1460 -4.039918e+00 -27.97222117 7.656355e-04 71.034367 50 30
## 24 1460 7.770521e+00 -5.53522565 1.558227e-03 71.035404 50 30
## 25 1460 7.334040e-01 10.27577087 7.199786e-04 71.037731 50 30
## 26 1460 -2.375303e+00 -25.78658325 4.094778e-04 1.555216 50 30
## 27 1460 2.885874e+00 19.20802716 4.868814e-04 1.312321 50 30
## 28 1460 -3.038099e-01 -21.78084086 1.050677e-03 1.228241 50 30
## 29 1460 -4.256321e+00 -5.49863836 5.379093e-04 1.196858 50 30
## 30 1460 -1.994594e+01 13.78177044 2.389868e-04 1.176920 50 30
## 31 1460 -2.439541e+01 13.23623861 9.066452e-04 1.164909 50 30
## 32 1460 -1.414430e+01 -5.07683992 1.486820e-03 1.155632 50 30
## 33 1460 -8.564948e+00 -25.51218076 2.359553e-04 1.148755 50 30
## 34 1460 4.226560e+00 14.97345959 5.513542e-04 1.143827 50 30
## 35 1460 1.025058e+01 -22.37488610 6.141026e-04 1.139748 50 30
## 36 1460 2.780281e+01 -2.87848877 4.092666e-04 1.135437 50 30
## 37 1460 -1.511928e+01 -12.21702278 1.154713e-03 1.131049 50 30
## 38 1460 4.070995e+00 16.12912804 8.755048e-04 1.127886 50 30
## 39 1460 -8.898812e+00 9.37688585 8.266751e-04 1.125117 50 30
## 40 1460 -2.208428e+01 30.39641844 1.668854e-04 1.123256 50 30
## 41 1460 -8.200685e+00 -3.66998674 1.044667e-03 73.771148 50 30
## 42 1460 4.179280e+00 15.00092016 6.410947e-04 71.150987 50 30
## 43 1460 -2.915433e+00 5.21787108 7.706347e-04 71.034367 50 30
## 44 1460 -7.690188e-01 7.63334436 4.243941e-04 71.035404 50 30
## 45 1460 -1.810113e+00 8.53811196 1.030059e-03 71.037731 50 30
## 46 1460 9.933275e+00 -22.66429833 4.929111e-04 1.555216 50 30
## 47 1460 1.337784e+01 -14.37573786 7.182959e-04 1.312321 50 30
## 48 1460 -5.131762e+00 -24.05535921 4.866584e-04 1.228241 50 30
## 49 1460 -2.911821e+01 -11.21216077 2.437323e-04 1.196858 50 30
## 50 1460 -8.860755e+00 6.10262860 1.134323e-03 1.176920 50 30
## 51 1460 8.619451e+00 17.62880279 7.982909e-04 1.164909 50 30
## 52 1460 -3.615796e+01 6.94109880 6.071872e-04 1.155632 50 30
## 53 1460 4.220717e-01 5.80851697 3.188263e-04 1.148755 50 30
## 54 1460 1.335188e+01 -10.28527035 7.715632e-04 1.143827 50 30
## 55 1460 -1.307171e+01 1.08902214 9.764671e-04 1.139748 50 30
## 56 1460 7.070279e+00 -10.40681970 6.254991e-04 1.135437 50 30
## 57 1460 3.922133e+01 -1.67168525 3.399996e-04 1.131049 50 30
## 58 1460 2.877218e+01 3.83968560 5.696405e-04 1.127886 50 30
## 59 1460 2.759604e+01 -4.56450990 2.092763e-04 1.125117 50 30
## 60 1460 -9.355720e+00 5.14343379 8.723019e-04 1.123256 50 30
## 61 1460 -1.278215e+01 -11.46681586 6.454594e-04 73.771148 50 30
## 62 1460 -2.743416e+01 12.32781556 1.314707e-03 71.150987 50 30
## 63 1460 1.238512e+01 -23.13568151 6.718501e-04 71.034367 50 30
## 64 1460 -2.816901e+01 9.28321673 6.910749e-04 71.035404 50 30
## 65 1460 1.884554e+01 -0.62760277 5.203892e-04 71.037731 50 30
## 66 1460 2.767114e+01 -2.30007907 7.324863e-04 1.555216 50 30
## 67 1460 -1.358972e+00 -13.04916481 8.538453e-04 1.312321 50 30
## 68 1460 -1.854762e+00 -19.00474759 1.186887e-03 1.228241 50 30
## 69 1460 -1.600896e+01 6.76850500 6.052313e-04 1.196858 50 30
## 70 1460 -2.502587e+01 7.93620533 7.736814e-04 1.176920 50 30
## 71 1460 -1.760768e+00 -12.65743519 7.980831e-04 1.164909 50 30
## 72 1460 -9.611671e+00 7.21427195 1.164541e-03 1.155632 50 30
## 73 1460 1.958520e+01 13.47004709 6.768649e-04 1.148755 50 30
## 74 1460 -1.042616e+00 9.97945517 1.129621e-03 1.143827 50 30
## 75 1460 -2.902196e+01 -10.39267675 5.901708e-04 1.139748 50 30
## 76 1460 4.437559e+01 4.15370884 4.325591e-04 1.135437 50 30
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## 1245 1460 -2.540166e+01 5.14054193 4.846155e-04 71.037731 50 30
## 1246 1460 1.822073e+01 12.62852049 7.134899e-04 1.555216 50 30
## 1247 1460 3.059456e+01 4.26546151 4.838790e-04 1.312321 50 30
## 1248 1460 -3.884728e+00 0.52393439 6.720847e-04 1.228241 50 30
## 1249 1460 -2.652016e+01 7.27578547 7.951229e-04 1.196858 50 30
## 1250 1460 -2.734123e+00 8.74333801 7.943333e-04 1.176920 50 30
## 1251 1460 -7.047101e+00 -7.86275722 1.128152e-03 1.164909 50 30
## 1252 1460 1.268796e+01 -24.54415123 2.434529e-04 1.155632 50 30
## 1253 1460 -6.075204e+00 19.19902284 1.166881e-03 1.148755 50 30
## 1254 1460 1.095615e+01 6.11424815 1.171564e-03 1.143827 50 30
## 1255 1460 2.560167e+01 6.48476602 1.122767e-03 1.139748 50 30
## 1256 1460 -2.748764e+01 -1.86136962 1.131068e-03 1.135437 50 30
## 1257 1460 1.549194e+00 -18.77620954 6.145089e-04 1.131049 50 30
## 1258 1460 -1.714101e+01 7.83338498 2.365001e-04 1.127886 50 30
## 1259 1460 8.807345e+00 -20.01122653 1.837459e-03 1.125117 50 30
## 1260 1460 1.686083e+00 6.78015255 5.891155e-04 1.123256 50 30
## 1261 1460 2.650805e+01 8.79269085 3.557316e-04 73.771148 50 30
## 1262 1460 -1.224665e+01 4.58749803 1.519423e-03 71.150987 50 30
## 1263 1460 -2.301016e+01 -0.58319763 6.173417e-04 71.034367 50 30
## 1264 1460 -2.647977e+01 9.51812568 1.524213e-03 71.035404 50 30
## 1265 1460 1.335539e+01 -20.16209216 5.209157e-04 71.037731 50 30
## 1266 1460 3.804521e+01 -1.11009780 4.450407e-04 1.555216 50 30
## 1267 1460 -2.977194e+01 -9.99048355 4.511929e-04 1.312321 50 30
## 1268 1460 -8.546546e+00 -27.29141790 6.403968e-04 1.228241 50 30
## 1269 1460 1.315322e+01 16.03351545 1.596197e-03 1.196858 50 30
## 1270 1460 -2.079354e+01 1.53972731 2.011339e-03 1.176920 50 30
## 1271 1460 1.350818e+01 -10.08043664 9.514990e-04 1.164909 50 30
## 1272 1460 -1.140663e+01 -4.92229329 7.413112e-04 1.155632 50 30
## 1273 1460 -3.026996e+00 6.12620086 4.651014e-04 1.148755 50 30
## 1274 1460 4.900909e+00 -1.70005341 5.629987e-04 1.143827 50 30
## 1275 1460 -2.792041e+01 10.91173388 2.846806e-04 1.139748 50 30
## 1276 1460 -2.628841e+01 -12.58959628 6.336748e-04 1.135437 50 30
## 1277 1460 8.084532e+00 17.38720636 9.253381e-04 1.131049 50 30
## 1278 1460 -4.437983e+00 -1.00495019 7.486887e-04 1.127886 50 30
## 1279 1460 1.974963e+01 1.18861282 9.401900e-04 1.125117 50 30
## 1280 1460 -2.313806e+01 10.68184663 3.956677e-04 1.123256 50 30
## 1281 1460 -2.553256e+00 -18.28157578 8.377548e-04 73.771148 50 30
## 1282 1460 5.396652e+00 -0.33463111 6.964195e-04 71.150987 50 30
## 1283 1460 3.714374e+00 4.54991388 6.175788e-04 71.034367 50 30
## 1284 1460 -1.621096e+01 21.68983027 1.486470e-03 71.035404 50 30
## 1285 1460 -2.972198e+01 0.19433069 4.773389e-04 71.037731 50 30
## 1286 1460 -2.356292e+01 4.86935222 1.119647e-03 1.555216 50 30
## 1287 1460 1.529338e+00 3.31870083 8.585373e-04 1.312321 50 30
## 1288 1460 5.446334e+00 16.97106812 3.804077e-04 1.228241 50 30
## 1289 1460 1.250634e+01 -19.86023111 7.389092e-04 1.196858 50 30
## 1290 1460 2.749205e+01 -3.63065731 7.034816e-04 1.176920 50 30
## 1291 1460 -4.303314e+00 -0.20610935 5.811313e-04 1.164909 50 30
## 1292 1460 4.207010e+01 1.92191243 1.433816e-04 1.155632 50 30
## 1293 1460 -2.744753e+01 -11.35344998 4.411814e-04 1.148755 50 30
## 1294 1460 1.800078e+01 14.03130550 1.107602e-03 1.143827 50 30
## 1295 1460 -9.902561e+00 7.33933224 1.118413e-03 1.139748 50 30
## 1296 1460 -7.702431e+00 -0.47944687 3.341449e-04 1.135437 50 30
## 1297 1460 -6.533595e+00 -0.69021909 7.261761e-04 1.131049 50 30
## 1298 1460 2.054247e+01 -20.24396203 6.394960e-04 1.127886 50 30
## 1299 1460 1.176144e+01 -3.74954835 4.905038e-04 1.125117 50 30
## 1300 1460 -2.076496e-01 6.33577148 1.114348e-03 1.123256 50 30
## 1301 1460 2.123520e+01 0.38334018 7.094497e-04 73.771148 50 30
## 1302 1460 -2.731292e+01 -2.44252735 5.585333e-04 71.150987 50 30
## 1303 1460 2.052682e+01 -2.84287412 1.983558e-04 71.034367 50 30
## 1304 1460 -4.679950e+00 -26.44682402 5.531966e-04 71.035404 50 30
## 1305 1460 3.891173e+01 -3.89162125 5.901078e-04 71.037731 50 30
## 1306 1460 2.993982e+00 -19.08183295 1.795725e-04 1.555216 50 30
## 1307 1460 1.210126e+01 -24.62262605 6.037417e-04 1.312321 50 30
## 1308 1460 -1.261369e+01 -10.63398444 1.533238e-03 1.228241 50 30
## 1309 1460 -9.074730e-01 10.23020899 6.808699e-04 1.196858 50 30
## 1310 1460 -1.912910e+00 -15.86942742 1.029424e-03 1.176920 50 30
## 1311 1460 -7.686308e+00 -10.85756114 6.716461e-04 1.164909 50 30
## 1312 1460 -2.851621e+00 -18.77196002 2.266495e-04 1.155632 50 30
## 1313 1460 2.270620e+01 -2.53526167 6.592077e-04 1.148755 50 30
## 1314 1460 2.482795e+01 -2.04747028 5.244640e-04 1.143827 50 30
## 1315 1460 -1.191013e+01 8.10524631 1.300564e-03 1.139748 50 30
## 1316 1460 1.042493e+01 7.58144323 1.153833e-03 1.135437 50 30
## 1317 1460 -6.509026e+00 -28.67571521 9.103305e-04 1.131049 50 30
## 1318 1460 1.230147e+01 -25.57257527 7.496107e-04 1.127886 50 30
## 1319 1460 -3.301944e+00 -28.51996835 5.512957e-04 1.125117 50 30
## 1320 1460 -9.316102e+00 2.63327796 6.367968e-04 1.123256 50 30
## 1321 1460 4.951557e+00 4.72043121 5.022200e-04 73.771148 50 30
## 1322 1460 -2.007404e+01 27.99770980 1.867389e-04 71.150987 50 30
## 1323 1460 1.794273e+01 2.25681985 1.035978e-03 71.034367 50 30
## 1324 1460 -1.364476e+01 7.29529943 4.635868e-04 71.035404 50 30
## 1325 1460 -1.937071e+00 -25.39459310 1.798315e-04 71.037731 50 30
## 1326 1460 -2.028989e+01 15.28298993 6.660403e-04 1.555216 50 30
## 1327 1460 -1.602465e+01 14.85328847 2.948999e-04 1.312321 50 30
## 1328 1460 2.140701e+00 15.30602364 7.064330e-04 1.228241 50 30
## 1329 1460 -3.079910e+01 -2.87859875 1.576978e-03 1.196858 50 30
## 1330 1460 2.746870e+01 8.38715131 4.123686e-04 1.176920 50 30
## 1331 1460 -3.193789e+00 -27.99531387 4.237986e-04 1.164909 50 30
## 1332 1460 -1.379448e+00 -1.53323193 1.477692e-03 1.155632 50 30
## 1333 1460 -1.104080e+01 7.85451212 1.067980e-03 1.148755 50 30
## 1334 1460 -2.639026e+01 12.03696150 7.480435e-04 1.143827 50 30
## 1335 1460 4.313784e+01 2.67665727 3.102439e-04 1.139748 50 30
## 1336 1460 5.018972e+00 16.20276766 1.138778e-03 1.135437 50 30
## 1337 1460 -2.502603e+01 -13.33991386 3.055606e-04 1.131049 50 30
## 1338 1460 -1.675406e+01 10.10527106 4.260767e-04 1.127886 50 30
## 1339 1460 1.767987e+01 4.48867884 3.778574e-04 1.125117 50 30
## 1340 1460 -1.197186e+01 6.55698869 1.325789e-04 1.123256 50 30
## 1341 1460 -1.446913e+01 4.22400006 1.849201e-03 73.771148 50 30
## 1342 1460 -1.249353e+01 -11.01174687 1.456894e-03 71.150987 50 30
## 1343 1460 2.729598e+01 -1.16597113 1.898964e-03 71.034367 50 30
## 1344 1460 -2.356637e+01 5.37631394 7.713671e-04 71.035404 50 30
## 1345 1460 3.047090e+01 5.97558296 4.666967e-04 71.037731 50 30
## 1346 1460 -2.190837e+01 13.97418251 8.189207e-04 1.555216 50 30
## 1347 1460 6.762327e+00 -10.50273444 1.322443e-04 1.312321 50 30
## 1348 1460 4.318283e-01 -22.51522626 2.532287e-04 1.228241 50 30
## 1349 1460 -3.656722e+00 -16.62937037 1.278241e-03 1.196858 50 30
## 1350 1460 -3.702042e+01 5.17766375 2.694002e-04 1.176920 50 30
## 1351 1460 -2.584654e+01 -14.72906381 5.283051e-04 1.164909 50 30
## 1352 1460 1.701152e+01 13.87875352 1.497029e-03 1.155632 50 30
## 1353 1460 -1.961894e+01 9.07431859 9.310188e-04 1.148755 50 30
## 1354 1460 1.880640e+01 -5.27069659 4.004588e-04 1.143827 50 30
## 1355 1460 1.942626e+01 2.44647447 8.521893e-04 1.139748 50 30
## 1356 1460 1.515471e+01 11.29349565 5.487230e-04 1.135437 50 30
## 1357 1460 -9.867016e+00 0.77479541 9.631889e-04 1.131049 50 30
## 1358 1460 -6.964562e+00 8.84894628 9.500521e-04 1.127886 50 30
## 1359 1460 3.764908e+01 -0.34270177 4.035667e-04 1.125117 50 30
## 1360 1460 1.989695e+00 -19.84011817 5.314296e-04 1.123256 50 30
## 1361 1460 -2.919856e+01 9.65331295 3.336737e-04 73.771148 50 30
## 1362 1460 3.187539e-01 -17.76952879 6.637997e-04 71.150987 50 30
## 1363 1460 -2.174909e+01 -1.02780931 8.458363e-04 71.034367 50 30
## 1364 1460 3.013531e+01 6.10894286 4.053416e-04 71.035404 50 30
## 1365 1460 3.459583e+01 -3.96961758 6.101300e-04 71.037731 50 30
## 1366 1460 2.070526e+01 2.67537288 3.730291e-04 1.555216 50 30
## 1367 1460 2.000883e+01 0.32907817 8.719287e-04 1.312321 50 30
## 1368 1460 4.067834e+01 5.00298494 1.340106e-03 1.228241 50 30
## 1369 1460 1.824514e+01 -18.74733841 5.184798e-04 1.196858 50 30
## 1370 1460 -4.590964e+00 -13.73293333 8.141778e-04 1.176920 50 30
## 1371 1460 -2.399639e+01 9.66807337 4.438865e-04 1.164909 50 30
## 1372 1460 4.998440e+00 -1.82405653 1.209042e-03 1.155632 50 30
## 1373 1460 1.751266e+01 4.57877052 3.443515e-04 1.148755 50 30
## 1374 1460 2.916348e+00 -21.91188529 2.690864e-04 1.143827 50 30
## 1375 1460 2.906671e+01 1.57611099 7.561695e-04 1.139748 50 30
## 1376 1460 -2.366398e+00 -27.64143362 4.422657e-04 1.135437 50 30
## 1377 1460 -1.542553e+01 10.21345837 7.706226e-04 1.131049 50 30
## 1378 1460 -1.866683e+01 -1.05064069 1.516564e-03 1.127886 50 30
## 1379 1460 4.310220e+01 1.35819238 1.725718e-04 1.125117 50 30
## 1380 1460 2.622680e+01 6.10666584 3.817043e-04 1.123256 50 30
## 1381 1460 -1.895693e+01 15.72106196 7.224166e-04 73.771148 50 30
## 1382 1460 -7.306908e+00 -7.54582628 8.661589e-04 71.150987 50 30
## 1383 1460 -2.696610e+01 9.97051628 1.283917e-04 71.034367 50 30
## 1384 1460 -2.598000e+01 15.73877384 1.166908e-03 71.035404 50 30
## 1385 1460 -1.878012e+01 3.19652685 1.779332e-03 71.037731 50 30
## 1386 1460 -1.861003e+01 5.42054716 8.674972e-04 1.555216 50 30
## 1387 1460 1.135432e+01 -3.12270130 2.958409e-04 1.312321 50 30
## 1388 1460 -1.789877e+01 -1.58739302 9.518334e-04 1.228241 50 30
## 1389 1460 3.223137e+00 -18.76080570 1.670713e-04 1.196858 50 30
## 1390 1460 -2.826381e+01 3.99850850 1.621857e-03 1.176920 50 30
## 1391 1460 -1.942626e+00 -19.58142467 6.960169e-04 1.164909 50 30
## 1392 1460 -2.508929e+01 -12.95259306 3.634438e-04 1.155632 50 30
## 1393 1460 -3.217513e+00 -3.99328407 8.343260e-04 1.148755 50 30
## 1394 1460 -2.910464e+01 -9.66275390 7.397813e-04 1.143827 50 30
## 1395 1460 1.082041e+01 -20.99354492 6.115731e-04 1.139748 50 30
## 1396 1460 2.584270e+01 -1.61483855 6.766643e-04 1.135437 50 30
## 1397 1460 3.090891e+00 8.95257883 7.130339e-04 1.131049 50 30
## 1398 1460 -2.819301e+01 11.88027754 4.380803e-04 1.127886 50 30
## 1399 1460 -1.750433e+01 0.92893274 1.026517e-03 1.125117 50 30
## 1400 1460 -2.295668e+01 4.02285008 1.137997e-03 1.123256 50 30
## 1401 1460 -2.550102e+01 10.97773251 1.289437e-03 73.771148 50 30
## 1402 1460 1.906586e+01 5.92726893 6.251599e-04 71.150987 50 30
## 1403 1460 -6.030812e+00 -24.70304990 5.400615e-04 71.034367 50 30
## 1404 1460 -1.038455e+00 -19.29325654 9.850615e-05 71.035404 50 30
## 1405 1460 -2.386656e+01 11.36117545 8.398040e-05 71.037731 50 30
## 1406 1460 9.230135e+00 -17.38942026 5.442093e-04 1.555216 50 30
## 1407 1460 -9.327454e-01 -0.14965968 1.155527e-03 1.312321 50 30
## 1408 1460 -8.854525e+00 6.70130812 8.467396e-04 1.228241 50 30
## 1409 1460 -2.899469e+01 -0.85822727 4.657984e-04 1.196858 50 30
## 1410 1460 2.268907e+01 9.64053484 9.739213e-04 1.176920 50 30
## 1411 1460 2.006537e+01 2.54681089 9.351594e-04 1.164909 50 30
## 1412 1460 -2.078524e+01 3.16538571 6.392506e-04 1.155632 50 30
## 1413 1460 -2.179679e+01 30.22033195 1.942632e-04 1.148755 50 30
## 1414 1460 1.277761e+00 -18.70173162 3.241941e-04 1.143827 50 30
## 1415 1460 -2.830772e+01 -0.16233698 1.168225e-03 1.139748 50 30
## 1416 1460 1.580743e+01 -23.78245187 6.510689e-04 1.135437 50 30
## 1417 1460 -2.889879e+01 -10.13346604 7.792210e-04 1.131049 50 30
## 1418 1460 2.096871e+01 -4.48546571 3.990922e-04 1.127886 50 30
## 1419 1460 -2.770916e+00 8.40843064 1.196091e-03 1.125117 50 30
## 1420 1460 -6.531665e+00 -9.51499605 1.223070e-03 1.123256 50 30
## 1421 1460 1.716970e+01 13.71371564 5.184436e-04 73.771148 50 30
## 1422 1460 4.742453e+00 -4.95434696 9.666950e-04 71.150987 50 30
## 1423 1460 1.847358e+01 -19.11311497 3.802887e-04 71.034367 50 30
## 1424 1460 1.124661e+01 -3.27266249 5.747808e-04 71.035404 50 30
## 1425 1460 4.712412e-01 8.16717441 9.501021e-04 71.037731 50 30
## 1426 1460 -1.183659e+01 -1.05178630 4.994076e-04 1.555216 50 30
## 1427 1460 1.975865e+01 -2.33915744 1.054720e-03 1.312321 50 30
## 1428 1460 -2.033919e+01 1.81794261 1.478647e-03 1.228241 50 30
## 1429 1460 -1.087534e+01 11.77413812 6.370088e-04 1.196858 50 30
## 1430 1460 -8.826696e+00 -8.80315052 9.085545e-04 1.176920 50 30
## 1431 1460 2.810761e+01 6.71918546 1.235895e-05 1.164909 50 30
## 1432 1460 3.868118e+00 -5.37952424 6.288693e-04 1.155632 50 30
## 1433 1460 -1.661957e+01 5.17810626 1.096805e-03 1.148755 50 30
## 1434 1460 2.535641e+01 9.06612780 4.559541e-04 1.143827 50 30
## 1435 1460 -4.935467e+00 -4.11613447 1.539246e-03 1.139748 50 30
## 1436 1460 -6.494504e+00 10.44968801 6.199137e-04 1.135437 50 30
## 1437 1460 -1.050849e+01 5.68464705 1.963096e-03 1.131049 50 30
## 1438 1460 7.103009e+00 -11.60549147 2.151471e-04 1.127886 50 30
## 1439 1460 -9.786456e+00 13.71638794 6.997396e-04 1.125117 50 30
## 1440 1460 1.337203e+01 12.78608475 9.893252e-04 1.123256 50 30
## 1441 1460 -3.824934e+01 5.20511904 6.129777e-04 73.771148 50 30
## 1442 1460 1.791757e+01 -18.96874872 4.387507e-04 71.150987 50 30
## 1443 1460 2.088602e+01 -6.26097887 4.572060e-04 71.034367 50 30
## 1444 1460 -1.621145e+01 10.50017360 4.934299e-04 71.035404 50 30
## 1445 1460 -4.787609e+00 -27.51355008 4.254095e-04 71.037731 50 30
## 1446 1460 -1.659919e+00 5.01261706 6.946730e-04 1.555216 50 30
## 1447 1460 -8.850115e+00 0.23989059 3.445671e-04 1.312321 50 30
## 1448 1460 2.029528e+01 -1.74577380 4.550161e-04 1.228241 50 30
## 1449 1460 -2.112497e+01 7.39873074 8.625991e-04 1.196858 50 30
## 1450 1460 4.543679e+01 4.46023390 6.728958e-04 1.176920 50 30
## 1451 1460 -1.623457e+01 21.62679191 1.708126e-03 1.164909 50 30
## 1452 1460 -2.317150e+00 -25.15562445 3.244397e-04 1.155632 50 30
## 1453 1460 2.044313e+01 -20.20933600 9.929341e-04 1.148755 50 30
## 1454 1460 -1.486533e+01 -10.55844168 6.205043e-04 1.143827 50 30
## 1455 1460 -5.134882e+00 -19.33441084 9.290986e-04 1.139748 50 30
## 1456 1460 2.816420e+01 8.06133960 1.117811e-03 1.135437 50 30
## 1457 1460 -1.921733e+00 -12.02716207 8.692068e-04 1.131049 50 30
## 1458 1460 5.645777e+00 26.29267797 1.536823e-03 1.127886 50 30
## 1459 1460 -5.443215e-01 6.01642272 4.247624e-04 1.125117 50 30
## 1460 1460 5.800857e-01 7.68324594 8.081546e-04 1.123256 50 30
## theta max_iter stop_lying_iter mom_switch_iter momentum final_momentum eta
## 1 0.5 1000 250 250 0.5 0.8 200
## 2 0.5 1000 250 250 0.5 0.8 200
## 3 0.5 1000 250 250 0.5 0.8 200
## 4 0.5 1000 250 250 0.5 0.8 200
## 5 0.5 1000 250 250 0.5 0.8 200
## 6 0.5 1000 250 250 0.5 0.8 200
## 7 0.5 1000 250 250 0.5 0.8 200
## 8 0.5 1000 250 250 0.5 0.8 200
## 9 0.5 1000 250 250 0.5 0.8 200
## 10 0.5 1000 250 250 0.5 0.8 200
## 11 0.5 1000 250 250 0.5 0.8 200
## 12 0.5 1000 250 250 0.5 0.8 200
## 13 0.5 1000 250 250 0.5 0.8 200
## 14 0.5 1000 250 250 0.5 0.8 200
## 15 0.5 1000 250 250 0.5 0.8 200
## 16 0.5 1000 250 250 0.5 0.8 200
## 17 0.5 1000 250 250 0.5 0.8 200
## 18 0.5 1000 250 250 0.5 0.8 200
## 19 0.5 1000 250 250 0.5 0.8 200
## 20 0.5 1000 250 250 0.5 0.8 200
## 21 0.5 1000 250 250 0.5 0.8 200
## 22 0.5 1000 250 250 0.5 0.8 200
## 23 0.5 1000 250 250 0.5 0.8 200
## 24 0.5 1000 250 250 0.5 0.8 200
## 25 0.5 1000 250 250 0.5 0.8 200
## 26 0.5 1000 250 250 0.5 0.8 200
## 27 0.5 1000 250 250 0.5 0.8 200
## 28 0.5 1000 250 250 0.5 0.8 200
## 29 0.5 1000 250 250 0.5 0.8 200
## 30 0.5 1000 250 250 0.5 0.8 200
## 31 0.5 1000 250 250 0.5 0.8 200
## 32 0.5 1000 250 250 0.5 0.8 200
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## 1423 0.5 1000 250 250 0.5 0.8 200
## 1424 0.5 1000 250 250 0.5 0.8 200
## 1425 0.5 1000 250 250 0.5 0.8 200
## 1426 0.5 1000 250 250 0.5 0.8 200
## 1427 0.5 1000 250 250 0.5 0.8 200
## 1428 0.5 1000 250 250 0.5 0.8 200
## 1429 0.5 1000 250 250 0.5 0.8 200
## 1430 0.5 1000 250 250 0.5 0.8 200
## 1431 0.5 1000 250 250 0.5 0.8 200
## 1432 0.5 1000 250 250 0.5 0.8 200
## 1433 0.5 1000 250 250 0.5 0.8 200
## 1434 0.5 1000 250 250 0.5 0.8 200
## 1435 0.5 1000 250 250 0.5 0.8 200
## 1436 0.5 1000 250 250 0.5 0.8 200
## 1437 0.5 1000 250 250 0.5 0.8 200
## 1438 0.5 1000 250 250 0.5 0.8 200
## 1439 0.5 1000 250 250 0.5 0.8 200
## 1440 0.5 1000 250 250 0.5 0.8 200
## 1441 0.5 1000 250 250 0.5 0.8 200
## 1442 0.5 1000 250 250 0.5 0.8 200
## 1443 0.5 1000 250 250 0.5 0.8 200
## 1444 0.5 1000 250 250 0.5 0.8 200
## 1445 0.5 1000 250 250 0.5 0.8 200
## 1446 0.5 1000 250 250 0.5 0.8 200
## 1447 0.5 1000 250 250 0.5 0.8 200
## 1448 0.5 1000 250 250 0.5 0.8 200
## 1449 0.5 1000 250 250 0.5 0.8 200
## 1450 0.5 1000 250 250 0.5 0.8 200
## 1451 0.5 1000 250 250 0.5 0.8 200
## 1452 0.5 1000 250 250 0.5 0.8 200
## 1453 0.5 1000 250 250 0.5 0.8 200
## 1454 0.5 1000 250 250 0.5 0.8 200
## 1455 0.5 1000 250 250 0.5 0.8 200
## 1456 0.5 1000 250 250 0.5 0.8 200
## 1457 0.5 1000 250 250 0.5 0.8 200
## 1458 0.5 1000 250 250 0.5 0.8 200
## 1459 0.5 1000 250 250 0.5 0.8 200
## 1460 0.5 1000 250 250 0.5 0.8 200
## exaggeration_factor cluster
## 1 12 1
## 2 12 2
## 3 12 1
## 4 12 3
## 5 12 1
## 6 12 4
## 7 12 5
## 8 12 2
## 9 12 6
## 10 12 7
## 11 12 8
## 12 12 1
## 13 12 9
## 14 12 5
## 15 12 7
## 16 12 3
## 17 12 10
## 18 12 11
## 19 12 7
## 20 12 8
## 21 12 1
## 22 12 3
## 23 12 5
## 24 12 4
## 25 12 9
## 26 12 5
## 27 12 2
## 28 12 5
## 29 12 7
## 30 12 3
## 31 12 3
## 32 12 7
## 33 12 5
## 34 12 2
## 35 12 12
## 36 12 1
## 37 12 7
## 38 12 2
## 39 12 8
## 40 12 11
## 41 12 7
## 42 12 2
## 43 12 9
## 44 12 9
## 45 12 9
## 46 12 12
## 47 12 4
## 48 12 5
## 49 12 6
## 50 12 8
## 51 12 2
## 52 12 13
## 53 12 9
## 54 12 4
## 55 12 7
## 56 12 4
## 57 12 14
## 58 12 1
## 59 12 1
## 60 12 8
## 61 12 7
## 62 12 3
## 63 12 12
## 64 12 3
## 65 12 1
## 66 12 1
## 67 12 7
## 68 12 5
## 69 12 3
## 70 12 3
## 71 12 7
## 72 12 8
## 73 12 15
## 74 12 9
## 75 12 6
## 76 12 14
## 77 12 8
## 78 12 3
## 79 12 6
## 80 12 3
## 81 12 15
## 82 12 12
## 83 12 5
## 84 12 7
## 85 12 2
## 86 12 1
## 87 12 1
## 88 12 14
## 89 12 13
## 90 12 7
## 91 12 11
## 92 12 7
## 93 12 3
## 94 12 6
## 95 12 1
## 96 12 2
## 97 12 5
## 98 12 7
## 99 12 10
## 100 12 10
## 101 12 5
## 102 12 1
## 103 12 11
## 104 12 5
## 105 12 3
## 106 12 1
## 107 12 10
## 108 12 9
## 109 12 3
## 110 12 7
## 111 12 3
## 112 12 1
## 113 12 1
## 114 12 7
## 115 12 15
## 116 12 14
## 117 12 2
## 118 12 7
## 119 12 1
## 120 12 1
## 121 12 4
## 122 12 3
## 123 12 9
## 124 12 12
## 125 12 7
## 126 12 13
## 127 12 4
## 128 12 3
## 129 12 15
## 130 12 4
## 131 12 15
## 132 12 1
## 133 12 8
## 134 12 5
## 135 12 7
## 136 12 7
## 137 12 7
## 138 12 6
## 139 12 1
## 140 12 1
## 141 12 8
## 142 12 5
## 143 12 3
## 144 12 5
## 145 12 6
## 146 12 14
## 147 12 3
## 148 12 1
## 149 12 7
## 150 12 3
## 151 12 8
## 152 12 5
## 153 12 15
## 154 12 9
## 155 12 3
## 156 12 3
## 157 12 11
## 158 12 1
## 159 12 1
## 160 12 4
## 161 12 7
## 162 12 1
## 163 12 5
## 164 12 3
## 165 12 3
## 166 12 6
## 167 12 9
## 168 12 1
## 169 12 1
## 170 12 5
## 171 12 13
## 172 12 7
## 173 12 1
## 174 12 9
## 175 12 7
## 176 12 7
## 177 12 2
## 178 12 3
## 179 12 5
## 180 12 3
## 181 12 14
## 182 12 3
## 183 12 11
## 184 12 1
## 185 12 3
## 186 12 13
## 187 12 7
## 188 12 13
## 189 12 10
## 190 12 4
## 191 12 10
## 192 12 15
## 193 12 5
## 194 12 14
## 195 12 8
## 196 12 14
## 197 12 5
## 198 12 9
## 199 12 13
## 200 12 5
## 201 12 5
## 202 12 2
## 203 12 3
## 204 12 12
## 205 12 3
## 206 12 4
## 207 12 7
## 208 12 9
## 209 12 1
## 210 12 7
## 211 12 3
## 212 12 5
## 213 12 1
## 214 12 2
## 215 12 2
## 216 12 2
## 217 12 5
## 218 12 3
## 219 12 2
## 220 12 12
## 221 12 5
## 222 12 1
## 223 12 1
## 224 12 9
## 225 12 5
## 226 12 14
## 227 12 1
## 228 12 14
## 229 12 8
## 230 12 12
## 231 12 9
## 232 12 1
## 233 12 14
## 234 12 9
## 235 12 1
## 236 12 14
## 237 12 5
## 238 12 4
## 239 12 5
## 240 12 3
## 241 12 5
## 242 12 3
## 243 12 3
## 244 12 1
## 245 12 1
## 246 12 2
## 247 12 6
## 248 12 7
## 249 12 1
## 250 12 2
## 251 12 10
## 252 12 12
## 253 12 1
## 254 12 2
## 255 12 8
## 256 12 1
## 257 12 1
## 258 12 5
## 259 12 4
## 260 12 11
## 261 12 9
## 262 12 1
## 263 12 7
## 264 12 13
## 265 12 3
## 266 12 7
## 267 12 1
## 268 12 13
## 269 12 9
## 270 12 7
## 271 12 1
## 272 12 9
## 273 12 1
## 274 12 7
## 275 12 8
## 276 12 3
## 277 12 5
## 278 12 8
## 279 12 5
## 280 12 15
## 281 12 4
## 282 12 5
## 283 12 12
## 284 12 5
## 285 12 12
## 286 12 14
## 287 12 3
## 288 12 8
## 289 12 8
## 290 12 3
## 291 12 1
## 292 12 3
## 293 12 3
## 294 12 15
## 295 12 7
## 296 12 7
## 297 12 3
## 298 12 15
## 299 12 2
## 300 12 2
## 301 12 7
## 302 12 1
## 303 12 5
## 304 12 8
## 305 12 10
## 306 12 5
## 307 12 1
## 308 12 3
## 309 12 8
## 310 12 5
## 311 12 1
## 312 12 8
## 313 12 3
## 314 12 9
## 315 12 3
## 316 12 1
## 317 12 15
## 318 12 1
## 319 12 1
## 320 12 7
## 321 12 1
## 322 12 1
## 323 12 15
## 324 12 3
## 325 12 1
## 326 12 3
## 327 12 12
## 328 12 7
## 329 12 3
## 330 12 3
## 331 12 6
## 332 12 8
## 333 12 5
## 334 12 12
## 335 12 1
## 336 12 9
## 337 12 5
## 338 12 5
## 339 12 7
## 340 12 9
## 341 12 1
## 342 12 3
## 343 12 11
## 344 12 12
## 345 12 14
## 346 12 3
## 347 12 10
## 348 12 7
## 349 12 14
## 350 12 1
## 351 12 12
## 352 12 4
## 353 12 2
## 354 12 3
## 355 12 3
## 356 12 5
## 357 12 5
## 358 12 4
## 359 12 2
## 360 12 1
## 361 12 9
## 362 12 3
## 363 12 11
## 364 12 14
## 365 12 1
## 366 12 3
## 367 12 9
## 368 12 2
## 369 12 7
## 370 12 9
## 371 12 1
## 372 12 11
## 373 12 9
## 374 12 9
## 375 12 1
## 376 12 3
## 377 12 7
## 378 12 1
## 379 12 5
## 380 12 1
## 381 12 3
## 382 12 5
## 383 12 1
## 384 12 3
## 385 12 1
## 386 12 12
## 387 12 3
## 388 12 7
## 389 12 5
## 390 12 1
## 391 12 3
## 392 12 1
## 393 12 11
## 394 12 8
## 395 12 3
## 396 12 8
## 397 12 8
## 398 12 15
## 399 12 3
## 400 12 1
## 401 12 4
## 402 12 5
## 403 12 3
## 404 12 1
## 405 12 1
## 406 12 7
## 407 12 13
## 408 12 3
## 409 12 1
## 410 12 1
## 411 12 8
## 412 12 7
## 413 12 5
## 414 12 3
## 415 12 2
## 416 12 5
## 417 12 15
## 418 12 10
## 419 12 3
## 420 12 8
## 421 12 6
## 422 12 2
## 423 12 8
## 424 12 1
## 425 12 7
## 426 12 3
## 427 12 12
## 428 12 8
## 429 12 5
## 430 12 7
## 431 12 14
## 432 12 3
## 433 12 14
## 434 12 1
## 435 12 14
## 436 12 1
## 437 12 3
## 438 12 3
## 439 12 3
## 440 12 10
## 441 12 5
## 442 12 6
## 443 12 3
## 444 12 12
## 445 12 1
## 446 12 7
## 447 12 7
## 448 12 1
## 449 12 3
## 450 12 3
## 451 12 3
## 452 12 7
## 453 12 1
## 454 12 1
## 455 12 6
## 456 12 7
## 457 12 3
## 458 12 7
## 459 12 3
## 460 12 3
## 461 12 1
## 462 12 7
## 463 12 9
## 464 12 3
## 465 12 7
## 466 12 12
## 467 12 9
## 468 12 15
## 469 12 5
## 470 12 1
## 471 12 4
## 472 12 15
## 473 12 12
## 474 12 5
## 475 12 12
## 476 12 9
## 477 12 5
## 478 12 1
## 479 12 5
## 480 12 8
## 481 12 5
## 482 12 5
## 483 12 3
## 484 12 12
## 485 12 8
## 486 12 8
## 487 12 7
## 488 12 9
## 489 12 6
## 490 12 14
## 491 12 14
## 492 12 3
## 493 12 1
## 494 12 9
## 495 12 3
## 496 12 3
## 497 12 5
## 498 12 3
## 499 12 7
## 500 12 2
## 501 12 14
## 502 12 1
## 503 12 10
## 504 12 9
## 505 12 14
## 506 12 6
## 507 12 1
## 508 12 5
## 509 12 3
## 510 12 7
## 511 12 10
## 512 12 12
## 513 12 9
## 514 12 8
## 515 12 3
## 516 12 5
## 517 12 15
## 518 12 1
## 519 12 1
## 520 12 3
## 521 12 11
## 522 12 7
## 523 12 3
## 524 12 1
## 525 12 1
## 526 12 5
## 527 12 8
## 528 12 1
## 529 12 3
## 530 12 5
## 531 12 7
## 532 12 3
## 533 12 11
## 534 12 11
## 535 12 1
## 536 12 3
## 537 12 1
## 538 12 8
## 539 12 7
## 540 12 7
## 541 12 5
## 542 12 1
## 543 12 5
## 544 12 12
## 545 12 1
## 546 12 1
## 547 12 4
## 548 12 7
## 549 12 9
## 550 12 1
## 551 12 4
## 552 12 8
## 553 12 5
## 554 12 11
## 555 12 1
## 556 12 3
## 557 12 9
## 558 12 3
## 559 12 2
## 560 12 12
## 561 12 9
## 562 12 9
## 563 12 8
## 564 12 3
## 565 12 1
## 566 12 3
## 567 12 1
## 568 12 5
## 569 12 4
## 570 12 7
## 571 12 6
## 572 12 7
## 573 12 1
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## 578 12 9
## 579 12 14
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## 581 12 2
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## 583 12 7
## 584 12 10
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## 588 12 7
## 589 12 9
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## 591 12 1
## 592 12 1
## 593 12 8
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## 595 12 8
## 596 12 5
## 597 12 3
## 598 12 12
## 599 12 7
## 600 12 14
## 601 12 1
## 602 12 3
## 603 12 1
## 604 12 14
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## 606 12 15
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## 612 12 2
## 613 12 1
## 614 12 7
## 615 12 14
## 616 12 7
## 617 12 1
## 618 12 8
## 619 12 5
## 620 12 1
## 621 12 3
## 622 12 15
## 623 12 7
## 624 12 14
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## 626 12 9
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## 629 12 2
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## 631 12 3
## 632 12 12
## 633 12 7
## 634 12 2
## 635 12 10
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## 639 12 3
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## 641 12 12
## 642 12 1
## 643 12 1
## 644 12 15
## 645 12 5
## 646 12 9
## 647 12 11
## 648 12 9
## 649 12 15
## 650 12 14
## 651 12 1
## 652 12 3
## 653 12 1
## 654 12 3
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## 656 12 14
## 657 12 8
## 658 12 3
## 659 12 3
## 660 12 8
## 661 12 15
## 662 12 1
## 663 12 7
## 664 12 9
## 665 12 5
## 666 12 1
## 667 12 15
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## 669 12 8
## 670 12 3
## 671 12 1
## 672 12 3
## 673 12 7
## 674 12 9
## 675 12 8
## 676 12 14
## 677 12 6
## 678 12 3
## 679 12 5
## 680 12 7
## 681 12 4
## 682 12 3
## 683 12 12
## 684 12 5
## 685 12 1
## 686 12 1
## 687 12 1
## 688 12 14
## 689 12 5
## 690 12 12
## 691 12 12
## 692 12 1
## 693 12 1
## 694 12 3
## 695 12 3
## 696 12 7
## 697 12 3
## 698 12 2
## 699 12 9
## 700 12 12
## 701 12 5
## 702 12 7
## 703 12 1
## 704 12 6
## 705 12 4
## 706 12 11
## 707 12 7
## 708 12 12
## 709 12 1
## 710 12 7
## 711 12 3
## 712 12 3
## 713 12 12
## 714 12 7
## 715 12 15
## 716 12 7
## 717 12 3
## 718 12 2
## 719 12 1
## 720 12 8
## 721 12 12
## 722 12 12
## 723 12 8
## 724 12 3
## 725 12 5
## 726 12 10
## 727 12 4
## 728 12 5
## 729 12 6
## 730 12 13
## 731 12 12
## 732 12 12
## 733 12 1
## 734 12 10
## 735 12 8
## 736 12 3
## 737 12 11
## 738 12 1
## 739 12 6
## 740 12 1
## 741 12 3
## 742 12 2
## 743 12 5
## 744 12 2
## 745 12 4
## 746 12 2
## 747 12 1
## 748 12 3
## 749 12 5
## 750 12 11
## 751 12 3
## 752 12 1
## 753 12 5
## 754 12 1
## 755 12 9
## 756 12 14
## 757 12 1
## 758 12 15
## 759 12 14
## 760 12 1
## 761 12 10
## 762 12 8
## 763 12 1
## 764 12 1
## 765 12 4
## 766 12 5
## 767 12 2
## 768 12 2
## 769 12 5
## 770 12 1
## 771 12 7
## 772 12 7
## 773 12 9
## 774 12 8
## 775 12 5
## 776 12 12
## 777 12 5
## 778 12 8
## 779 12 11
## 780 12 7
## 781 12 5
## 782 12 1
## 783 12 5
## 784 12 7
## 785 12 3
## 786 12 9
## 787 12 3
## 788 12 1
## 789 12 3
## 790 12 15
## 791 12 12
## 792 12 7
## 793 12 1
## 794 12 5
## 795 12 2
## 796 12 15
## 797 12 7
## 798 12 8
## 799 12 1
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## 804 12 1
## 805 12 8
## 806 12 5
## 807 12 9
## 808 12 1
## 809 12 9
## 810 12 6
## 811 12 9
## 812 12 12
## 813 12 10
## 814 12 10
## 815 12 3
## 816 12 5
## 817 12 8
## 818 12 5
## 819 12 7
## 820 12 12
## 821 12 1
## 822 12 3
## 823 12 1
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## 830 12 14
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## 833 12 1
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## 835 12 7
## 836 12 8
## 837 12 8
## 838 12 14
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## 847 12 1
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## 849 12 3
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## 858 12 1
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## 1021 12 7
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## 1162 12 4
## 1163 12 8
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## 1460 12 9ggplot(tsne_df, aes(x=Y.1, y=Y.2, color=y)) +
geom_point() +
scale_color_gradientn(colours = heat.colors(10))
ggplot(data.frame(table(tsne_df$cluster)), aes(x=Var1, y=Freq)) +
geom_bar(stat = "identity") +
coord_flip()
ggplot(tsne_df, aes(x=Y.1, y=Y.2, color=cluster)) +
geom_point() +
scale_color_viridis() +
scale_fill_viridis(discrete = T) +
geom_point(data = data.frame(centroids), aes(x=X1, y=X2), color="black", fill="white", shape=21, size=8) +
geom_text(data = data.frame(centroids), aes(x=X1, y=X2, label=1:k), color="black")
fviz_silhouette(silhouette(cutree(hclust_avg, k = k), dist_mat))## cluster size ave.sil.width
## 1 1 241 0.32
## 2 2 71 0.48
## 3 3 240 0.19
## 4 4 39 0.50
## 5 5 175 0.52
## 6 6 42 0.83
## 7 7 152 0.17
## 8 8 104 0.52
## 9 9 105 0.32
## 10 10 35 0.57
## 11 11 37 0.85
## 12 12 77 0.60
## 13 13 21 0.90
## 14 14 66 0.72
## 15 15 55 0.56
Baselines
baselines_rmse <- list()
baselines_rmse_test <- list()
actual_metrics_test <- list()
metrics_fusion <- function(y_pred, y) {
y_pred_inv <- expm1(y_pred)
y_inv <- expm1(y)
a <- mae(y_pred_inv, y_inv)
b <- mape(y_pred_inv, y_inv)
c <- rmse(y_pred_inv, y_inv)
d <- mse(y_pred_inv, y_inv)
e <- R2(y_pred_inv, y_inv)
return(c("mae" = a, "mape" = b, "rmse" = c, "mse" = d, "r2" = e))
}Linear Regression
linreg_tc <- trainControl(method = "cv", number = 5)
linreg_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = linreg_tc,
method = "lm"
)## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading# Validation predictions and metrics
score_val <- linreg_cv$results$RMSE
baselines_rmse$linear_regression <- score_val
# Test predictions and metrics
linreg <- lm(SalePrice ~ ., data = cbind(X_train_val, SalePrice = y_train_val))
y_pred_test <- predict(linreg, newdata = X_test)## Warning in predict.lm(linreg, newdata = X_test): prediction from a
## rank-deficient fit may be misleadingscore_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$linear_regression <- score_test
actual_metrics_test$linear_regression <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.1407635score_test## [1] 0.1350529Lasso Regression
lasso <- cv.glmnet(x = as.matrix(X_train_val), y = y_train_val, alpha = 1)
# Validation predictions and metrics
score_val <- mean(sqrt(lasso$cvm))
baselines_rmse$lasso <- score_val
# Test predictions and metrics
y_pred_test <- predict(lasso, newx = as.matrix(X_test))
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$lasso <- score_test
actual_metrics_test$lasso <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.1654072score_test## [1] 0.1360549Ridge Regression
ridge <- cv.glmnet(x = as.matrix(X_train_val), y = y_train_val, alpha = 0)
# Validation predictions and metrics
score_val <- mean(sqrt(ridge$cvm))
baselines_rmse$ridge <- score_val
# Test predictions and metrics
y_pred_test <- predict(ridge, newx = as.matrix(X_test))
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$ridge <- score_test
actual_metrics_test$ridge <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.2432459score_test## [1] 0.1434131Elastic Net
results <- data.frame()
for (i in 0:20) {
elasticnet <- cv.glmnet(x = as.matrix(X_train_val), y = y_train_val, alpha = i/20)
row <- data.frame(alpha = i/20, rmse_val = mean(sqrt(elasticnet$cvm)))
results <- rbind(results, row)
}
best_alpha <- results$alpha[which.min(results$rmse_val)]
# Validation predictions and metrics
score_val <- min(results$rmse_val)
baselines_rmse$elasticnet <- score_val
# Test predictions and metrics
elasticnet <- cv.glmnet(x = as.matrix(X_train_val), y = y_train_val, alpha = best_alpha)
y_pred_test <- predict(elasticnet, newx = as.matrix(X_test))
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$elasticnet <- score_test
actual_metrics_test$elasticnet <- metrics_fusion(y_pred_test, y_test)
# Display scores
best_alpha## [1] 0.7score_val## [1] 0.1639068score_test## [1] 0.1356406K-Nearest Neighbors Regression
knn_tc <- trainControl(method = "cv", number = 5)
knn_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = knn_tc,
method = "knn"
)
# Validation predictions and metrics
score_val <- mean(knn_cv$results$RMSE)
baselines_rmse$knn <- score_val
# Test predictions and metrics
knn <- knnreg(x = X_train_val, y = y_train_val)
y_pred_test <- predict(knn, newdata = X_test)
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$knn <- score_test
actual_metrics_test$knn <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.1832128score_test## [1] 0.1880515Support Vector Regression
svr_tc <- trainControl(method = "cv", number = 5)
svr_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = svr_tc,
method = "svmLinear2"
)## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlRoll' and 'Exterior1stBrkComm' and 'Exterior1stCBlock' and
## 'Exterior1stStone' and 'ExterCondEx' and 'FoundationWood' and 'HeatingFloor'
## and 'HeatingOthW' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlRoll' and 'Exterior1stBrkComm' and 'Exterior1stCBlock' and
## 'Exterior1stStone' and 'ExterCondEx' and 'FoundationWood' and 'HeatingFloor'
## and 'HeatingOthW' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlRoll' and 'Exterior1stBrkComm' and 'Exterior1stCBlock' and
## 'Exterior1stStone' and 'ExterCondEx' and 'FoundationWood' and 'HeatingFloor'
## and 'HeatingOthW' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlMembran' and 'RoofMatlMetal' and 'RoofMatlRoll' and
## 'RoofMatlWdShngl' and 'Exterior1stCBlock' and 'ExterCondEx' and 'BsmtCondPo'
## and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlMembran' and 'RoofMatlMetal' and 'RoofMatlRoll' and
## 'RoofMatlWdShngl' and 'Exterior1stCBlock' and 'ExterCondEx' and 'BsmtCondPo'
## and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlMembran' and 'RoofMatlMetal' and 'RoofMatlRoll' and
## 'RoofMatlWdShngl' and 'Exterior1stCBlock' and 'ExterCondEx' and 'BsmtCondPo'
## and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn'
## and 'RoofStyleShed' and 'RoofMatlRoll' and 'Exterior1stCBlock' and
## 'Exterior1stImStucc' and 'ExterCondEx' and 'HeatingFloor' and 'HeatingQCPo' and
## 'ElectricalFuseP' and 'ElectricalMix' and 'FunctionalSev' and 'GarageQualEx'
## and 'GarageQualPo' and 'GarageCondEx' and 'SaleConditionAdjLand' constant.
## Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn'
## and 'RoofStyleShed' and 'RoofMatlRoll' and 'Exterior1stCBlock' and
## 'Exterior1stImStucc' and 'ExterCondEx' and 'HeatingFloor' and 'HeatingQCPo' and
## 'ElectricalFuseP' and 'ElectricalMix' and 'FunctionalSev' and 'GarageQualEx'
## and 'GarageQualPo' and 'GarageCondEx' and 'SaleConditionAdjLand' constant.
## Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2PosN' and 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn'
## and 'RoofStyleShed' and 'RoofMatlRoll' and 'Exterior1stCBlock' and
## 'Exterior1stImStucc' and 'ExterCondEx' and 'HeatingFloor' and 'HeatingQCPo' and
## 'ElectricalFuseP' and 'ElectricalMix' and 'FunctionalSev' and 'GarageQualEx'
## and 'GarageQualPo' and 'GarageCondEx' and 'SaleConditionAdjLand' constant.
## Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlRoll' and 'Exterior1stCBlock' and 'ExterCondEx' and 'ExterCondPo'
## and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and 'GarageCondPo'
## and 'SaleTypeConLw' and 'SaleConditionAdjLand' constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlRoll' and 'Exterior1stCBlock' and 'ExterCondEx' and 'ExterCondPo'
## and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and 'GarageCondPo'
## and 'SaleTypeConLw' and 'SaleConditionAdjLand' constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlRoll' and 'Exterior1stCBlock' and 'ExterCondEx' and 'ExterCondPo'
## and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and 'GarageCondPo'
## and 'SaleTypeConLw' and 'SaleConditionAdjLand' constant. Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'RoofMatlRoll' and 'Exterior1stCBlock' and
## 'ExterCondEx' and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'RoofMatlRoll' and 'Exterior1stCBlock' and
## 'ExterCondEx' and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.
## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlClyTile' and 'RoofMatlRoll' and 'Exterior1stCBlock' and
## 'ExterCondEx' and 'HeatingFloor' and 'ElectricalMix' and 'GarageQualPo' and
## 'SaleConditionAdjLand' constant. Cannot scale data.## Warning in svm.default(x = as.matrix(x), y = y, kernel = "linear", cost =
## param$cost, : Variable(s) 'Condition1RRNe' and 'Condition2PosA' and
## 'Condition2RRAe' and 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed'
## and 'RoofMatlRoll' and 'Exterior1stCBlock' and 'ExterCondEx' and 'HeatingFloor'
## and 'ElectricalMix' and 'GarageQualPo' and 'SaleConditionAdjLand' constant.
## Cannot scale data.# Validation predictions and metrics
score_val <- mean(svr_cv$results$RMSE)
baselines_rmse$svr <- score_val
# Test predictions and metrics
svr <- e1071::svm(SalePrice ~ ., data = cbind(X_train_val, SalePrice = y_train_val))## Warning in svm.default(x, y, scale = scale, ..., na.action = na.action):
## Variable(s) 'Condition1RRNe' and 'Condition2PosA' and 'Condition2RRAe' and
## 'Condition2RRAn' and 'Condition2RRNn' and 'RoofStyleShed' and 'RoofMatlRoll'
## and 'Exterior1stCBlock' and 'ExterCondEx' and 'HeatingFloor' and
## 'ElectricalMix' and 'GarageQualPo' and 'SaleConditionAdjLand' constant. Cannot
## scale data.y_pred_test <- predict(svr, newdata = X_test)
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$svr <- score_test
actual_metrics_test$svr <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.1419871score_test## [1] 0.1327052Decision Tree
dt_tc <- trainControl(method = "cv", number = 5)
dt_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = dt_tc,
method = "rpart"
)## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.# Validation predictions and metrics
score_val <- mean(dt_cv$results$RMSE, na.rm = TRUE)
baselines_rmse$decision_tree <- score_val
# Test predictions and metrics
dt <- caret::train(x = X_train_val, y = y_train_val, method = "rpart")## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.y_pred_test <- predict(dt, newdata = X_test)
score_test <- rmse(y_pred_test, y_test)
baselines_rmse_test$decision_tree <- score_test
actual_metrics_test$decision_tree <- metrics_fusion(y_pred_test, y_test)
# Display scores
score_val## [1] 0.299904score_test## [1] 0.2722831Ensemble Learning
ensemble_rmse <- list()
ensemble_actual_metrics <- list()
ensemble_rmse_test <- list()
ensemble_actual_metrics_test <- list()Random Forest
rf_tc <- trainControl(method = "cv", number = 5)
rf_cv <- caret::train(
SalePrice ~ .,
data = cbind(X_train_val, SalePrice = y_train_val),
trControl = rf_tc,
method = "rf"
)
# Validation predictions and metrics
score_val <- mean(rf_cv$results$RMSE)
ensemble_rmse$random_forest <- score_val
# Test predictions and metrics
rf <- randomForest(x = X_train_val, y = y_train_val, proximity = T)
y_pred_test_rf <- predict(rf, newdata = X_test)
score_test <- rmse(y_pred_test_rf, y_test)
ensemble_rmse_test$random_forest <- score_test
ensemble_actual_metrics_test$random_forest <- metrics_fusion(y_pred_test_rf, y_test)
y_pred_train_rf <- predict(rf, newdata = X_train_val)
# Display scores
score_val## [1] 0.1713973score_test## [1] 0.1357491rf_df <- data.frame(rf$importance) %>%
mutate(Feature = rownames(rf$importance)) %>%
arrange(desc(IncNodePurity)) %>%
head(30)
rf_df## IncNodePurity Feature
## OverallQual 39.7209019 OverallQual
## GrLivArea 24.5983039 GrLivArea
## YearBuilt 11.6601697 YearBuilt
## X1stFlrSF 7.5297066 X1stFlrSF
## GarageArea 6.9206338 GarageArea
## ExterQualTA 6.7091022 ExterQualTA
## FullBath 5.1375729 FullBath
## TotalBsmtSF 5.1111876 TotalBsmtSF
## YearRemodAdd 3.8569232 YearRemodAdd
## BsmtFinSF1 3.7129777 BsmtFinSF1
## X2ndFlrSF 3.2530535 X2ndFlrSF
## Fireplaces 3.0204553 Fireplaces
## LotArea 2.8762806 LotArea
## GarageFinishUnf 2.7743017 GarageFinishUnf
## KitchenQualTA 2.4958733 KitchenQualTA
## BsmtQualEx 2.4798451 BsmtQualEx
## OverallCond 1.5845403 OverallCond
## LotFrontage 1.5414618 LotFrontage
## CentralAirY 1.4865066 CentralAirY
## CentralAirN 1.4743146 CentralAirN
## FoundationPConc 1.0694477 FoundationPConc
## BsmtUnfSF 1.0666151 BsmtUnfSF
## OpenPorchSF 0.6653111 OpenPorchSF
## BsmtQualTA 0.6469899 BsmtQualTA
## MoSold 0.5691623 MoSold
## MasVnrArea 0.5445010 MasVnrArea
## BsmtQualGd 0.5343642 BsmtQualGd
## BedroomAbvGr 0.5102979 BedroomAbvGr
## MSSubClass 0.4899512 MSSubClass
## WoodDeckSF 0.4754511 WoodDeckSFggplot(data = rf_df, aes(x = reorder(Feature, IncNodePurity), y = IncNodePurity)) +
geom_bar(stat = "identity") +
coord_flip()
Gradient-Boosted Trees
dtrain_val <- xgb.DMatrix(data = as.matrix(X_train_val), label = y_train_val)
dtest <- xgb.DMatrix(data = as.matrix(X_test), label = y_test)
xgb_params = list(
eta = 0.01,
gamma = 0.0468,
max_depth = 6,
min_child_weight = 1.41,
subsample = 0.769,
colsample_bytree = 0.283
)
xgb_cv <- xgb.cv(
params = xgb_params,
data = dtrain_val,
nround = 10000,
nfold = 5,
prediction = F,
showsd = T,
metrics = "rmse",
verbose = 1,
print_every_n = 500,
early_stopping_rounds = 25
)## [1] train-rmse:11.421870+0.002228 test-rmse:11.421845+0.008812
## Multiple eval metrics are present. Will use test_rmse for early stopping.
## Will train until test_rmse hasn't improved in 25 rounds.
##
## [501] train-rmse:0.123310+0.001267 test-rmse:0.158822+0.014159
## [1001] train-rmse:0.066385+0.000492 test-rmse:0.125945+0.014985
## [1501] train-rmse:0.062994+0.000387 test-rmse:0.124761+0.015229
## Stopping. Best iteration:
## [1735] train-rmse:0.062190+0.000412 test-rmse:0.124509+0.015267# Validation predictions and metrics
score_val <- xgb_cv$evaluation_log$test_rmse_mean %>% min
ensemble_rmse$xgboost <- score_val
# Test predictions and metrics
xgb <- xgboost(
params = xgb_params,
data = dtrain_val,
nround = 10000,
eval_metric = "rmse",
verbose = 1,
print_every_n = 500,
early_stopping_rounds = 25
)## [1] train-rmse:11.421799
## Will train until train_rmse hasn't improved in 25 rounds.
##
## [501] train-rmse:0.121796
## [1001] train-rmse:0.065984
## [1501] train-rmse:0.062528
## [2001] train-rmse:0.060477
## Stopping. Best iteration:
## [2385] train-rmse:0.059566y_pred_test_xgb <- predict(xgb, newdata = dtest)
score_test <- rmse(y_pred_test_xgb, y_test)
ensemble_rmse_test$xgboost_test <- score_test
ensemble_actual_metrics_test$xgboost_test <- metrics_fusion(y_pred_test_xgb, y_test)
y_pred_train_xgb <- predict(xgb, newdata = dtrain_val)
# Display scores
score_val## [1] 0.1245088score_test## [1] 0.1244002xgb_df <- xgb.importance(model = xgb) %>% head(30)
xgb_df## Feature Gain Cover Frequency
## 1: OverallQual 0.219915277 0.045360040 0.032951459
## 2: GrLivArea 0.181955425 0.087390449 0.066257234
## 3: GarageArea 0.060513800 0.047418051 0.047360340
## 4: X1stFlrSF 0.059266543 0.030578246 0.039329160
## 5: TotalBsmtSF 0.052725009 0.040237936 0.043699067
## 6: Fireplaces 0.038946145 0.009199863 0.006732018
## 7: YearBuilt 0.037675189 0.033309176 0.032715247
## 8: BsmtFinSF1 0.029308536 0.041645129 0.036022204
## 9: YearRemodAdd 0.028532563 0.034051037 0.030235030
## 10: LotArea 0.026724925 0.056808245 0.055509626
## 11: GarageFinishUnf 0.023168899 0.008557950 0.006495807
## 12: OverallCond 0.020560107 0.051620499 0.037675682
## 13: BsmtQualEx 0.018100201 0.005172243 0.003779379
## 14: X2ndFlrSF 0.016061987 0.030427498 0.024565962
## 15: ExterQualTA 0.011281210 0.001924417 0.001653478
## 16: FullBath 0.010100371 0.005709918 0.005669068
## 17: KitchenQualTA 0.008496994 0.001953115 0.002007795
## 18: CentralAirN 0.008365267 0.003944825 0.004488012
## 19: LotFrontage 0.007479454 0.012298920 0.018660683
## 20: SaleConditionAbnorml 0.006871704 0.015901677 0.016889099
## 21: MSZoningRM 0.006198449 0.007454561 0.008503602
## 22: BsmtUnfSF 0.005889369 0.022203369 0.030116925
## 23: CentralAirY 0.005650806 0.002989873 0.002834534
## 24: NeighborhoodCrawfor 0.005282940 0.019267923 0.012637298
## 25: MSZoningC..all. 0.004798593 0.003262339 0.006259596
## 26: OpenPorchSF 0.004389543 0.020511504 0.018306366
## 27: Exterior1stBrkFace 0.003929712 0.021602030 0.013109720
## 28: FoundationPConc 0.003606362 0.001231376 0.001535373
## 29: SaleConditionFamily 0.003466460 0.008905296 0.010629503
## 30: KitchenQualEx 0.003458514 0.003924043 0.002952640
## Feature Gain Cover Frequencyggplot(data = xgb_df, aes(x = reorder(Feature, Gain), y = Gain)) +
geom_bar(stat = "identity") +
coord_flip()
objective_fn <- makeSingleObjectiveFunction(
fn = function(x) {
params = list(
booster = "gbtree",
eta = x["eta"],
gamma = x["gamma"],
max_depth = x["max_depth"],
min_child_weight = x["min_child_weight"],
subsample = x["subsample"],
colsample_bytree = x["colsample_bytree"],
max_delta_step = x["max_delta_step"]
)
cv <- xgb.cv(
params = params,
data = dtrain_val,
nround = 10000,
nfold = 5,
prediction = F,
showsd = T,
metrics = "rmse",
verbose = 1,
print_every_n = 500,
early_stopping_rounds = 25
)
cv$evaluation_log$test_rmse_mean %>% min
},
par.set = makeParamSet(
makeNumericParam("eta", lower = 0.005, upper = 0.01),
makeNumericParam("gamma", lower = 0.01, upper = 5),
makeIntegerParam("max_depth", lower = 2, upper = 10),
makeIntegerParam("min_child_weight", lower = 1, upper = 2000),
makeNumericParam("subsample", lower = 0.20, upper = 0.8),
makeNumericParam("colsample_bytree", lower = 0.20, upper = 0.8),
makeNumericParam("max_delta_step", lower = 0, upper = 5)
),
minimize = TRUE
)
#Train model
design <- generateDesign(n = 1000, par.set = getParamSet(objective_fn), fun = lhs::randomLHS)
control <- makeMBOControl() %>% setMBOControlTermination(., iters = 10)
#run <- mbo(
# fun = objective_fn,
# design = design,
# learner = makeLearner("regr.km", predict.type = "se", covtype = "matern3_2", control = list(trace = FALSE)),
# control = control,
# show.info = TRUE
#)# Best parameters
#run$xlgb_train_val <- lgb.Dataset(data = as.matrix(X_train_val), label = y_train_val)
lgb_test <- lgb.Dataset(data = as.matrix(X_test), label = y_test)
params <- list(
objective = "regression",
metric = "rmse",
boosting_type = "gbdt",
num_boost_round = 100,
num_leaves = 15,
learning_rate = 0.1,
feature_fraction = 0.9,
bagging_fraction = 0.8,
bagging_freq = 5
)
lgb_cv <- lgb.cv(
params = params,
data = lgb_train_val,
early_stopping_rounds = 25,
verbose = 0
)## [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000572 seconds.
## You can set `force_row_wise=true` to remove the overhead.
## And if memory is not enough, you can set `force_col_wise=true`.
## [LightGBM] [Warning] Auto-choosing col-wise multi-threading, the overhead of testing was 0.001091 seconds.
## You can set `force_col_wise=true` to remove the overhead.
## [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000819 seconds.
## You can set `force_row_wise=true` to remove the overhead.
## And if memory is not enough, you can set `force_col_wise=true`.
## [LightGBM] [Info] Start training from score 12.031745
## [LightGBM] [Info] Start training from score 12.029589
## [LightGBM] [Info] Start training from score 12.028376# Validation predictions and metrics
score_val <- min(unlist(lgb_cv$record_evals$valid$rmse$eval))
ensemble_rmse$lightgbm <- score_val
# Test predictions and metrics
lgb <- lgb.train(
params = params,
data = lgb_train_val,
verbose = 0
)## [LightGBM] [Warning] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000794 seconds.
## You can set `force_row_wise=true` to remove the overhead.
## And if memory is not enough, you can set `force_col_wise=true`.y_pred_test_lgb <- predict(lgb, data = as.matrix(X_test))
score_test <- rmse(y_pred_test_lgb, y_test)
ensemble_rmse_test$lightgbm <- score_test
ensemble_actual_metrics_test$lightgbm <- metrics_fusion(y_pred_test_lgb, y_test)
y_pred_train_lgb <- predict(lgb, data = as.matrix(X_train_val))
# Display scores
score_val## [1] 0.1302412score_test## [1] 0.1376078lgb_df <- lgb.importance(model = lgb) %>% head(30)
lgb_df## Feature Gain Cover Frequency
## 1: OverallQual 0.448797848 0.0608210473 0.0464285714
## 2: GrLivArea 0.172172339 0.0797923563 0.0907142857
## 3: GarageArea 0.041167164 0.0739122523 0.0671428571
## 4: TotalBsmtSF 0.039537635 0.0458549970 0.0500000000
## 5: BsmtFinSF1 0.035684857 0.0290979274 0.0364285714
## 6: YearBuilt 0.031577184 0.0444728863 0.0535714286
## 7: YearRemodAdd 0.026329128 0.0381716066 0.0471428571
## 8: X1stFlrSF 0.023588562 0.0332381258 0.0378571429
## 9: LotArea 0.019733055 0.0406046121 0.0492857143
## 10: BsmtQualEx 0.019494303 0.0018094200 0.0014285714
## 11: OverallCond 0.014241708 0.0389076419 0.0314285714
## 12: Fireplaces 0.013110956 0.0056040907 0.0057142857
## 13: CentralAirN 0.011964934 0.0080534525 0.0057142857
## 14: ExterQualTA 0.008407335 0.0006338081 0.0007142857
## 15: CentralAirY 0.008154943 0.0019198253 0.0014285714
## 16: X2ndFlrSF 0.007339136 0.0175155947 0.0207142857
## 17: FullBath 0.006563982 0.0027274196 0.0042857143
## 18: BsmtUnfSF 0.005110355 0.0364746364 0.0478571429
## 19: LotFrontage 0.004669221 0.0303164747 0.0300000000
## 20: OpenPorchSF 0.003863542 0.0456852999 0.0328571429
## 21: MSZoningRM 0.003835061 0.0039234769 0.0057142857
## 22: KitchenQualEx 0.002896801 0.0018298654 0.0021428571
## 23: LotShapeReg 0.002610447 0.0015661195 0.0035714286
## 24: SaleConditionAbnorml 0.002499404 0.0192555003 0.0121428571
## 25: SaleConditionNormal 0.002244475 0.0083703566 0.0114285714
## 26: MoSold 0.002179210 0.0192779903 0.0214285714
## 27: GarageFinishUnf 0.002144017 0.0005683828 0.0028571429
## 28: NeighborhoodCrawfor 0.002110246 0.0090491447 0.0078571429
## 29: GarageTypeDetchd 0.002057353 0.0090409665 0.0071428571
## 30: WoodDeckSF 0.001994714 0.0178877015 0.0221428571
## Feature Gain Cover Frequencyggplot(data = xgb_df, aes(x = reorder(Feature, Gain), y = Gain)) +
geom_bar(stat = "identity") +
coord_flip()
train_val_pool <- catboost.load_pool(data = X_train_val, label = y_train_val)
test_pool <- catboost.load_pool(data = X_test, label = y_test)
params <- list(
loss_function = "RMSE",
iterations = 10000,
learning_rate = 0.01,
metric_period = 1000
)
catb_cv <- catboost.cv(
train_val_pool,
params = params,
fold_count = 5,
early_stopping_rounds = 25
)## Warning: Overfitting detector is active, thus evaluation metric is calculated on every iteration. 'metric_period' is ignored for evaluation metric.
## 0: learn: 11.9184021 test: 11.9183456 best: 11.9183456 (0) total: 126ms remaining: 20m 59s
## 1000: learn: 0.1244250 test: 0.2320500 best: 0.2320500 (1000) total: 38.6s remaining: 5m 47s
## 2000: learn: 0.0705784 test: 0.2061964 best: 0.2061964 (2000) total: 1m 16s remaining: 5m 5s
## 3000: learn: 0.0477268 test: 0.1987054 best: 0.1987054 (3000) total: 1m 53s remaining: 4m 24s
## 4000: learn: 0.0342460 test: 0.1954636 best: 0.1954636 (4000) total: 2m 29s remaining: 3m 44s
## 5000: learn: 0.0250191 test: 0.1938556 best: 0.1938556 (5000) total: 3m 8s remaining: 3m 8s
## 6000: learn: 0.0184365 test: 0.1929067 best: 0.1929060 (5999) total: 3m 49s remaining: 2m 33s
## 7000: learn: 0.0138769 test: 0.1923543 best: 0.1923543 (7000) total: 4m 30s remaining: 1m 55s
## 8000: learn: 0.0105367 test: 0.1920651 best: 0.1920648 (7995) total: 5m 6s remaining: 1m 16s
## 9000: learn: 0.0080681 test: 0.1918585 best: 0.1918559 (8995) total: 5m 42s remaining: 38s
## Stopped by overfitting detector (25 iterations wait)# Validation predictions and metrics
score_val <- min(catb_cv$test.RMSE.mean)
ensemble_rmse$catboost <- score_val
# Test predictions and metrics
catb <- catboost.train(
params = params,
learn_pool = train_val_pool
)## 0: learn: 0.3990236 total: 9.34ms remaining: 1m 33s
## 1000: learn: 0.0815022 total: 4.78s remaining: 43s
## 2000: learn: 0.0521736 total: 8.97s remaining: 35.9s
## 3000: learn: 0.0374963 total: 13.9s remaining: 32.3s
## 4000: learn: 0.0272295 total: 18.3s remaining: 27.5s
## 5000: learn: 0.0201268 total: 22.7s remaining: 22.7s
## 6000: learn: 0.0153246 total: 26.9s remaining: 17.9s
## 7000: learn: 0.0119705 total: 31.7s remaining: 13.6s
## 8000: learn: 0.0094310 total: 36.2s remaining: 9.04s
## 9000: learn: 0.0076078 total: 40.3s remaining: 4.47s
## 9999: learn: 0.0061117 total: 46s remaining: 0usy_pred_test_catboost <- catboost.predict(catb, test_pool)
score_test <- rmse(y_pred_test_catboost, y_test)
ensemble_rmse_test$catboost <- score_test
ensemble_actual_metrics_test$catboost <- metrics_fusion(y_pred_test_catboost, y_test)
y_pred_train_catboost <- catboost.predict(catb, train_val_pool)
# Display scores
score_val## [1] 0.1918585score_test## [1] 0.1245417catb_df <- data.frame(catboost.get_feature_importance(catb))
catb_df <- catb_df %>%
mutate(Feature = rownames(catb_df)) %>%
rename(Importance = catboost.get_feature_importance.catb.) %>%
arrange(desc(Importance)) %>%
head(30)
catb_df## Importance Feature
## OverallQual 21.3708169 OverallQual
## GrLivArea 13.2941599 GrLivArea
## GarageArea 4.2996937 GarageArea
## TotalBsmtSF 4.2248298 TotalBsmtSF
## X1stFlrSF 4.1532465 X1stFlrSF
## Fireplaces 3.6382169 Fireplaces
## YearRemodAdd 3.2718445 YearRemodAdd
## BsmtFinSF1 3.2528029 BsmtFinSF1
## LotArea 2.9909552 LotArea
## OverallCond 2.6934004 OverallCond
## YearBuilt 2.6535442 YearBuilt
## X2ndFlrSF 2.2081448 X2ndFlrSF
## FullBath 1.5628649 FullBath
## CentralAirN 1.4773335 CentralAirN
## LotFrontage 1.2242371 LotFrontage
## ExterQualTA 1.2221691 ExterQualTA
## BsmtQualEx 1.1670156 BsmtQualEx
## BsmtUnfSF 0.9903617 BsmtUnfSF
## HalfBath 0.9478941 HalfBath
## SaleConditionAbnorml 0.8230171 SaleConditionAbnorml
## OpenPorchSF 0.7818386 OpenPorchSF
## MSZoningRL 0.7047584 MSZoningRL
## KitchenQualGd 0.6986101 KitchenQualGd
## GarageFinishUnf 0.6937182 GarageFinishUnf
## BsmtFinType1Unf 0.6828694 BsmtFinType1Unf
## MoSold 0.6708278 MoSold
## KitchenQualTA 0.6656939 KitchenQualTA
## MSSubClass 0.6627088 MSSubClass
## NeighborhoodCrawfor 0.6209431 NeighborhoodCrawfor
## CentralAirY 0.5923854 CentralAirYggplot(data = catb_df, aes(x = reorder(Feature, Importance), y = Importance)) +
geom_bar(stat = "identity") +
coord_flip()
Association Rule Mining on Housing Characteristics
transactions <- transactions(categorical_data)## Warning: Column(s) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
## 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37
## not logical or factor. Applying default discretization (see '? discretizeDF').summary(transactions)## transactions as itemMatrix in sparse format with
## 1460 rows (elements/itemsets/transactions) and
## 218 columns (items) and a density of 0.1697248
##
## most frequent items:
## Utilities=AllPub Street=Pave Condition2=Norm RoofMatl=CompShg
## 1459 1454 1445 1434
## Heating=GasA (Other)
## 1428 46800
##
## element (itemset/transaction) length distribution:
## sizes
## 37
## 1460
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 37 37 37 37 37 37
##
## includes extended item information - examples:
## labels variables levels
## 1 MSZoning=C (all) MSZoning C (all)
## 2 MSZoning=FV MSZoning FV
## 3 MSZoning=RH MSZoning RH
##
## includes extended transaction information - examples:
## transactionID
## 1 1
## 2 2
## 3 3inspect(head(transactions, n = 1))## items transactionID
## [1] {MSZoning=RL,
## Street=Pave,
## LotShape=Reg,
## LandContour=Lvl,
## Utilities=AllPub,
## LotConfig=Inside,
## LandSlope=Gtl,
## Neighborhood=CollgCr,
## Condition1=Norm,
## Condition2=Norm,
## BldgType=1Fam,
## HouseStyle=2Story,
## RoofStyle=Gable,
## RoofMatl=CompShg,
## Exterior1st=VinylSd,
## MasVnrType=BrkFace,
## ExterQual=Gd,
## ExterCond=TA,
## Foundation=PConc,
## BsmtQual=Gd,
## BsmtCond=TA,
## BsmtExposure=No,
## BsmtFinType1=GLQ,
## BsmtFinType2=Unf,
## Heating=GasA,
## HeatingQC=Ex,
## CentralAir=Y,
## Electrical=SBrkr,
## KitchenQual=Gd,
## Functional=Typ,
## GarageType=Attchd,
## GarageFinish=RFn,
## GarageQual=TA,
## GarageCond=TA,
## PavedDrive=Y,
## SaleType=WD,
## SaleCondition=Normal} 1rules <- apriori(transactions, parameter = list(support = 0.95, confidence = 0.95))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.95 0.1 1 none FALSE TRUE 5 0.95 1
## maxlen target ext
## 10 rules TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 1387
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[218 item(s), 1460 transaction(s)] done [0.01s].
## sorting and recoding items ... [7 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [94 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].summary(rules)## set of 94 rules
##
## rule length distribution (lhs + rhs):sizes
## 1 2 3 4
## 7 28 39 20
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 2.000 3.000 2.766 3.000 4.000
##
## summary of quality measures:
## support confidence coverage lift
## Min. :0.9500 Min. :0.9534 Min. :0.9507 Min. :0.9996
## 1st Qu.:0.9562 1st Qu.:0.9793 1st Qu.:0.9678 1st Qu.:0.9998
## Median :0.9637 Median :0.9895 Median :0.9781 Median :1.0000
## Mean :0.9664 Mean :0.9871 Mean :0.9791 Mean :1.0000
## 3rd Qu.:0.9740 3rd Qu.:0.9958 3rd Qu.:0.9897 3rd Qu.:1.0000
## Max. :0.9993 Max. :0.9993 Max. :1.0000 Max. :1.0010
## count
## Min. :1387
## 1st Qu.:1396
## Median :1407
## Mean :1411
## 3rd Qu.:1422
## Max. :1459
##
## mining info:
## data ntransactions support confidence
## transactions 1460 0.95 0.95
## call
## apriori(data = transactions, parameter = list(support = 0.95, confidence = 0.95))con <- file("data_description.txt", open = "r")
column_dictionary <- list()
value_dictionary <- list()
repeat {
line <- readLines(con, n = 1)
if (length(line) == 0) {
break
}
first_character <- substr(line, 1, 1)
if (first_character == "") {
next
}
if (first_character != " ") {
column_name <- sub(":.*", "", line)
column_description <- trimws(sub(".*:", "", line))
column_dictionary[[column_name]] <- column_description
value_dictionary[[column_name]] <- list()
} else {
pairs <- unlist(strsplit(line, "\t"))
key <- trimws(pairs[1])
value <- trimws(pairs[2])
value_dictionary[[column_name]][[key]] <- value
}
}
close(con)rules_top_ten_df <- data.frame(
lhs = labels(lhs(rules)),
rhs = labels(rhs(rules)),
rules@quality
) %>% arrange(desc(lift)) %>% head(n = 20)for (i in 1:nrow(rules_top_ten_df)) {
row <- rules_top_ten_df[i, ]
explanation <- ""
lhs <- unlist(strsplit(gsub('^.|.$', '', row["lhs"]), ","))
for (i in 1:length(lhs)) {
pair <- unlist(strsplit(lhs[i], "="))
key <- pair[1]
value <- pair[2]
key_t <- column_dictionary[[key]]
value_t <- value_dictionary[[key]][[value]]
if (i == 1) {
explanation <- paste("IF", key_t, "=", value_t)
} else {
explanation <- paste(explanation, "AND", key_t, "=", value_t)
}
}
rhs <- unlist(strsplit(gsub('^.|.$', '', row["rhs"]), "="))
key <- rhs[1]
value <- rhs[2]
key_t <- column_dictionary[[key]]
value_t <- value_dictionary[[key]][[value]]
confidence_pct <- format(round(row["confidence"] * 100, 2), 2)
explanation <- paste(explanation, "THEN", key_t, "=", value_t, "(Confidence:", paste0(confidence_pct, "%)"))
print(explanation)
cat("\n")
}## [1] "IF Proximity to various conditions (if more than one is present) = Normal THEN Garage condition = Typical/Average (Confidence: 96.47%)"
##
## [1] "IF Garage condition = Typical/Average THEN Proximity to various conditions (if more than one is present) = Normal (Confidence: 99.08%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Garage condition = Typical/Average THEN Proximity to various conditions (if more than one is present) = Normal (Confidence: 99.08%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Proximity to various conditions (if more than one is present) = Normal THEN Garage condition = Typical/Average (Confidence: 96.47%)"
##
## [1] "IF Type of road access to property = Paved AND Garage condition = Typical/Average THEN Proximity to various conditions (if more than one is present) = Normal (Confidence: 99.07%)"
##
## [1] "IF Type of road access to property = Paved AND Type of utilities available = All public Utilities (E,G,W,& S) AND Garage condition = Typical/Average THEN Proximity to various conditions (if more than one is present) = Normal (Confidence: 99.07%)"
##
## [1] "IF Type of road access to property = Paved AND Proximity to various conditions (if more than one is present) = Normal THEN Garage condition = Typical/Average (Confidence: 96.46%)"
##
## [1] "IF Type of road access to property = Paved AND Type of utilities available = All public Utilities (E,G,W,& S) AND Proximity to various conditions (if more than one is present) = Normal THEN Garage condition = Typical/Average (Confidence: 96.45%)"
##
## [1] "IF Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.25%)"
##
## [1] "IF Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.84%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.25%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.84%)"
##
## [1] "IF Type of road access to property = Paved AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.24%)"
##
## [1] "IF Type of road access to property = Paved AND Type of utilities available = All public Utilities (E,G,W,& S) AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.24%)"
##
## [1] "IF Type of road access to property = Paved AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.83%)"
##
## [1] "IF Type of road access to property = Paved AND Type of utilities available = All public Utilities (E,G,W,& S) AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.83%)"
##
## [1] "IF Proximity to various conditions (if more than one is present) = Normal AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.23%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Proximity to various conditions (if more than one is present) = Normal AND Type of heating = Gas forced warm air furnace THEN Roof material = Standard (Composite) Shingle (Confidence: 98.23%)"
##
## [1] "IF Proximity to various conditions (if more than one is present) = Normal AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.82%)"
##
## [1] "IF Type of utilities available = All public Utilities (E,G,W,& S) AND Proximity to various conditions (if more than one is present) = Normal AND Roof material = Standard (Composite) Shingle THEN Type of heating = Gas forced warm air furnace (Confidence: 97.81%)"Stacking
stacked_data <- data.frame(y = y_train_val, prediction_rf = y_pred_train_rf, prediction_xgb = y_pred_train_xgb, prediction_lgb = y_pred_train_lgb, prediction_catboost = y_pred_train_catboost)
stacked_data_test <- data.frame(y = y_test, prediction_rf = y_pred_test_rf, prediction_xgb = y_pred_test_xgb, prediction_lgb = y_pred_test_lgb, prediction_catboost = y_pred_test_catboost)
model_meta <- caret::train(y ~ ., data = stacked_data, method = "lm")
predictions_meta <- predict(model_meta, newdata = stacked_data_test)
ensemble_rmse_test$stacking_score <- rmse(predictions_meta, y_test)
ensemble_actual_metrics_test$stacking <- metrics_fusion(predictions_meta, y_test)Comparison
# Plot RMSE for baseline models
df <- data.frame(models = names(baselines_rmse), rmse = unlist(baselines_rmse))
df## models rmse
## linear_regression linear_regression 0.1407635
## lasso lasso 0.1654072
## ridge ridge 0.2432459
## elasticnet elasticnet 0.1639068
## knn knn 0.1832128
## svr svr 0.1419871
## decision_tree decision_tree 0.2999040ggplot(df, aes(x = models, y = rmse)) +
geom_bar(stat = "identity", fill = "steelblue") +
xlab("Models") +
ylab("RMSE") +
ylim(0, 0.35) +
ggtitle("Baseline RMSE") +
theme_minimal()
# Plot RMSE for ensemble models
df <- data.frame(models = names(ensemble_rmse), rmse = unlist(ensemble_rmse))
df## models rmse
## random_forest random_forest 0.1713973
## xgboost xgboost 0.1245088
## lightgbm lightgbm 0.1302412
## catboost catboost 0.1918585ggplot(df, aes(x = models, y = rmse)) +
geom_bar(stat = "identity", fill = "steelblue") +
xlab("Models") +
ylab("RMSE") +
ylim(0, 0.35) +
ggtitle("Ensemble RMSE") +
theme_minimal()
# Plot RMSE for baseline models on the test set
df <- data.frame(models = names(baselines_rmse_test), rmse = unlist(baselines_rmse_test))
df## models rmse
## linear_regression linear_regression 0.1350529
## lasso lasso 0.1360549
## ridge ridge 0.1434131
## elasticnet elasticnet 0.1356406
## knn knn 0.1880515
## svr svr 0.1327052
## decision_tree decision_tree 0.2722831ggplot(df, aes(x = models, y = rmse)) +
geom_bar(stat = "identity", fill = "steelblue") +
xlab("Models") +
ylab("RMSE") +
ylim(0, 0.35) +
ggtitle("Baseline RMSE") +
theme_minimal()
# Plot RMSE for ensemble models on the test set
df <- data.frame(models = names(ensemble_rmse_test), rmse = unlist(ensemble_rmse_test))
df## models rmse
## random_forest random_forest 0.1357491
## xgboost_test xgboost_test 0.1244002
## lightgbm lightgbm 0.1376078
## catboost catboost 0.1245417
## stacking_score stacking_score 0.1248171ggplot(df, aes(x = models, y = rmse)) +
geom_bar(stat = "identity", fill = "steelblue") +
xlab("Models") +
ylab("RMSE") +
ylim(0, 0.35) +
ggtitle("Ensemble RMSE") +
theme_minimal()
data.frame(t(data.frame(actual_metrics_test))) %>% arrange(desc(r2))## mae mape rmse mse r2
## linear_regression 16056.05 0.09045067 29117.05 847802651 0.8733346
## elasticnet 17289.46 0.09193298 32702.94 1069482248 0.8441074
## ridge 19094.63 0.10052425 34361.77 1180731262 0.8437131
## lasso 17272.65 0.09204278 32792.67 1075359017 0.8422404
## svr 16614.60 0.09025399 33192.63 1101750749 0.8350740
## knn 23965.75 0.13568260 42242.53 1784431556 0.7565352
## decision_tree 37014.43 0.20984270 54080.44 2924693697 0.5608676data.frame(t(data.frame(ensemble_actual_metrics_test))) %>% arrange(desc(r2))## mae mape rmse mse r2
## xgboost_test 15254.32 0.08386270 27981.27 782951571 0.8849246
## catboost 15316.05 0.08374207 28646.92 820646116 0.8805195
## stacking 15381.62 0.08394283 28771.87 827820452 0.8796489
## lightgbm 17119.48 0.09717112 29105.29 847118182 0.8727715
## random_forest 17074.57 0.09237490 30152.65 909182292 0.8705999save(list=ls(), file="assignment_modell")