Load Packages and Dataset
Packages used to import and analyse the data include
First step - Data Preparation
- we use as.matrix to convert the features of the data in wisc.df (col 3: 32) to matrix and store it.
wisc.data <- as.matrix(wisc.df[, 3:32])- assign the row names of wisc.data the values currently contained in the id column of wisc.df - helps track different observations throughout the modelling process. (note in last chapter we used “column_to_rownames) in dplyr to do the same). Here we are using the base function in R.
row.names(wisc.data) <- wisc.df$id- set a vector called diagnosis to be 1 if a diagnosis is malignant (“M”) and 0 if otherwise. here R coerces TRUE to 1 and FALSE to 0 by default
diagnosis <- as.numeric(wisc.df$diagnosis == "M")Second step - Exploratory data analysis
there are 569 observations in the dataset
10 variables/features are suffixed with _mean
212 observations have a malignant diagnosis
dim(wisc.data)## [1] 569 30colnames(wisc.data)## [1] "radius_mean" "texture_mean"
## [3] "perimeter_mean" "area_mean"
## [5] "smoothness_mean" "compactness_mean"
## [7] "concavity_mean" "concave.points_mean"
## [9] "symmetry_mean" "fractal_dimension_mean"
## [11] "radius_se" "texture_se"
## [13] "perimeter_se" "area_se"
## [15] "smoothness_se" "compactness_se"
## [17] "concavity_se" "concave.points_se"
## [19] "symmetry_se" "fractal_dimension_se"
## [21] "radius_worst" "texture_worst"
## [23] "perimeter_worst" "area_worst"
## [25] "smoothness_worst" "compactness_worst"
## [27] "concavity_worst" "concave.points_worst"
## [29] "symmetry_worst" "fractal_dimension_worst"table(diagnosis)## diagnosis
## 0 1
## 357 212- a bit visualization to explore the dataset
dev.off()## null device
## 1ggplot(wisc.df, aes(radius_mean, texture_mean, color = diagnosis)) +
geom_point(alpha = 0.5)Third step - Performing PCA
- check if mean is materially different from standard deviation - if true, then we need to scale the data before performing PCA analysis - need to scale
colMeans(wisc.data)## radius_mean texture_mean perimeter_mean
## 1.412729e+01 1.928965e+01 9.196903e+01
## area_mean smoothness_mean compactness_mean
## 6.548891e+02 9.636028e-02 1.043410e-01
## concavity_mean concave.points_mean symmetry_mean
## 8.879932e-02 4.891915e-02 1.811619e-01
## fractal_dimension_mean radius_se texture_se
## 6.279761e-02 4.051721e-01 1.216853e+00
## perimeter_se area_se smoothness_se
## 2.866059e+00 4.033708e+01 7.040979e-03
## compactness_se concavity_se concave.points_se
## 2.547814e-02 3.189372e-02 1.179614e-02
## symmetry_se fractal_dimension_se radius_worst
## 2.054230e-02 3.794904e-03 1.626919e+01
## texture_worst perimeter_worst area_worst
## 2.567722e+01 1.072612e+02 8.805831e+02
## smoothness_worst compactness_worst concavity_worst
## 1.323686e-01 2.542650e-01 2.721885e-01
## concave.points_worst symmetry_worst fractal_dimension_worst
## 1.146062e-01 2.900756e-01 8.394582e-02apply(wisc.data, 2, sd)## radius_mean texture_mean perimeter_mean
## 3.524049e+00 4.301036e+00 2.429898e+01
## area_mean smoothness_mean compactness_mean
## 3.519141e+02 1.406413e-02 5.281276e-02
## concavity_mean concave.points_mean symmetry_mean
## 7.971981e-02 3.880284e-02 2.741428e-02
## fractal_dimension_mean radius_se texture_se
## 7.060363e-03 2.773127e-01 5.516484e-01
## perimeter_se area_se smoothness_se
## 2.021855e+00 4.549101e+01 3.002518e-03
## compactness_se concavity_se concave.points_se
## 1.790818e-02 3.018606e-02 6.170285e-03
## symmetry_se fractal_dimension_se radius_worst
## 8.266372e-03 2.646071e-03 4.833242e+00
## texture_worst perimeter_worst area_worst
## 6.146258e+00 3.360254e+01 5.693570e+02
## smoothness_worst compactness_worst concavity_worst
## 2.283243e-02 1.573365e-01 2.086243e-01
## concave.points_worst symmetry_worst fractal_dimension_worst
## 6.573234e-02 6.186747e-02 1.806127e-02- perform pca analysis and save it
wisc.pr <- prcomp(wisc.data, center = TRUE, scale = TRUE)- inspect the summary of the results
summary(wisc.pr)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 3.6444 2.3857 1.67867 1.40735 1.28403 1.09880 0.82172
## Proportion of Variance 0.4427 0.1897 0.09393 0.06602 0.05496 0.04025 0.02251
## Cumulative Proportion 0.4427 0.6324 0.72636 0.79239 0.84734 0.88759 0.91010
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.69037 0.6457 0.59219 0.5421 0.51104 0.49128 0.39624
## Proportion of Variance 0.01589 0.0139 0.01169 0.0098 0.00871 0.00805 0.00523
## Cumulative Proportion 0.92598 0.9399 0.95157 0.9614 0.97007 0.97812 0.98335
## PC15 PC16 PC17 PC18 PC19 PC20 PC21
## Standard deviation 0.30681 0.28260 0.24372 0.22939 0.22244 0.17652 0.1731
## Proportion of Variance 0.00314 0.00266 0.00198 0.00175 0.00165 0.00104 0.0010
## Cumulative Proportion 0.98649 0.98915 0.99113 0.99288 0.99453 0.99557 0.9966
## PC22 PC23 PC24 PC25 PC26 PC27 PC28
## Standard deviation 0.16565 0.15602 0.1344 0.12442 0.09043 0.08307 0.03987
## Proportion of Variance 0.00091 0.00081 0.0006 0.00052 0.00027 0.00023 0.00005
## Cumulative Proportion 0.99749 0.99830 0.9989 0.99942 0.99969 0.99992 0.99997
## PC29 PC30
## Standard deviation 0.02736 0.01153
## Proportion of Variance 0.00002 0.00000
## Cumulative Proportion 1.00000 1.00000wisc.pr$rotation## PC1 PC2 PC3 PC4
## radius_mean -0.21890244 0.233857132 -0.008531243 0.041408962
## texture_mean -0.10372458 0.059706088 0.064549903 -0.603050001
## perimeter_mean -0.22753729 0.215181361 -0.009314220 0.041983099
## area_mean -0.22099499 0.231076711 0.028699526 0.053433795
## smoothness_mean -0.14258969 -0.186113023 -0.104291904 0.159382765
## compactness_mean -0.23928535 -0.151891610 -0.074091571 0.031794581
## concavity_mean -0.25840048 -0.060165363 0.002733838 0.019122753
## concave.points_mean -0.26085376 0.034767500 -0.025563541 0.065335944
## symmetry_mean -0.13816696 -0.190348770 -0.040239936 0.067124984
## fractal_dimension_mean -0.06436335 -0.366575471 -0.022574090 0.048586765
## radius_se -0.20597878 0.105552152 0.268481387 0.097941242
## texture_se -0.01742803 -0.089979682 0.374633665 -0.359855528
## perimeter_se -0.21132592 0.089457234 0.266645367 0.088992415
## area_se -0.20286964 0.152292628 0.216006528 0.108205039
## smoothness_se -0.01453145 -0.204430453 0.308838979 0.044664180
## compactness_se -0.17039345 -0.232715896 0.154779718 -0.027469363
## concavity_se -0.15358979 -0.197207283 0.176463743 0.001316880
## concave.points_se -0.18341740 -0.130321560 0.224657567 0.074067335
## symmetry_se -0.04249842 -0.183848000 0.288584292 0.044073351
## fractal_dimension_se -0.10256832 -0.280092027 0.211503764 0.015304750
## radius_worst -0.22799663 0.219866379 -0.047506990 0.015417240
## texture_worst -0.10446933 0.045467298 -0.042297823 -0.632807885
## perimeter_worst -0.23663968 0.199878428 -0.048546508 0.013802794
## area_worst -0.22487053 0.219351858 -0.011902318 0.025894749
## smoothness_worst -0.12795256 -0.172304352 -0.259797613 0.017652216
## compactness_worst -0.21009588 -0.143593173 -0.236075625 -0.091328415
## concavity_worst -0.22876753 -0.097964114 -0.173057335 -0.073951180
## concave.points_worst -0.25088597 0.008257235 -0.170344076 0.006006996
## symmetry_worst -0.12290456 -0.141883349 -0.271312642 -0.036250695
## fractal_dimension_worst -0.13178394 -0.275339469 -0.232791313 -0.077053470
## PC5 PC6 PC7 PC8
## radius_mean -0.037786354 0.0187407904 -0.1240883403 0.007452296
## texture_mean 0.049468850 -0.0321788366 0.0113995382 -0.130674825
## perimeter_mean -0.037374663 0.0173084449 -0.1144770573 0.018687258
## area_mean -0.010331251 -0.0018877480 -0.0516534275 -0.034673604
## smoothness_mean 0.365088528 -0.2863744966 -0.1406689928 0.288974575
## compactness_mean -0.011703971 -0.0141309489 0.0309184960 0.151396350
## concavity_mean -0.086375412 -0.0093441809 -0.1075204434 0.072827285
## concave.points_mean 0.043861025 -0.0520499505 -0.1504822142 0.152322414
## symmetry_mean 0.305941428 0.3564584607 -0.0938911345 0.231530989
## fractal_dimension_mean 0.044424360 -0.1194306679 0.2957600240 0.177121441
## radius_se 0.154456496 -0.0256032561 0.3124900373 -0.022539967
## texture_se 0.191650506 -0.0287473145 -0.0907553556 0.475413139
## perimeter_se 0.120990220 0.0018107150 0.3146403902 0.011896690
## area_se 0.127574432 -0.0428639079 0.3466790028 -0.085805135
## smoothness_se 0.232065676 -0.3429173935 -0.2440240556 -0.573410232
## compactness_se -0.279968156 0.0691975186 0.0234635340 -0.117460157
## concavity_se -0.353982091 0.0563432386 -0.2088237897 -0.060566501
## concave.points_se -0.195548089 -0.0312244482 -0.3696459369 0.108319309
## symmetry_se 0.252868765 0.4902456426 -0.0803822539 -0.220149279
## fractal_dimension_se -0.263297438 -0.0531952674 0.1913949726 -0.011168188
## radius_worst 0.004406592 -0.0002906849 -0.0097099360 -0.042619416
## texture_worst 0.092883400 -0.0500080613 0.0098707439 -0.036251636
## perimeter_worst -0.007454151 0.0085009872 -0.0004457267 -0.030558534
## area_worst 0.027390903 -0.0251643821 0.0678316595 -0.079394246
## smoothness_worst 0.324435445 -0.3692553703 -0.1088308865 -0.205852191
## compactness_worst -0.121804107 0.0477057929 0.1404729381 -0.084019659
## concavity_worst -0.188518727 0.0283792555 -0.0604880561 -0.072467871
## concave.points_worst -0.043332069 -0.0308734498 -0.1679666187 0.036170795
## symmetry_worst 0.244558663 0.4989267845 -0.0184906298 -0.228225053
## fractal_dimension_worst -0.094423351 -0.0802235245 0.3746576261 -0.048360667
## PC9 PC10 PC11 PC12
## radius_mean -0.223109764 0.095486443 -0.04147149 0.051067457
## texture_mean 0.112699390 0.240934066 0.30224340 0.254896423
## perimeter_mean -0.223739213 0.086385615 -0.01678264 0.038926106
## area_mean -0.195586014 0.074956489 -0.11016964 0.065437508
## smoothness_mean 0.006424722 -0.069292681 0.13702184 0.316727211
## compactness_mean -0.167841425 0.012936200 0.30800963 -0.104017044
## concavity_mean 0.040591006 -0.135602298 -0.12419024 0.065653480
## concave.points_mean -0.111971106 0.008054528 0.07244603 0.042589267
## symmetry_mean 0.256040084 0.572069479 -0.16305408 -0.288865504
## fractal_dimension_mean -0.123740789 0.081103207 0.03804827 0.236358988
## radius_se 0.249985002 -0.049547594 0.02535702 -0.016687915
## texture_se -0.246645397 -0.289142742 -0.34494446 -0.306160423
## perimeter_se 0.227154024 -0.114508236 0.16731877 -0.101446828
## area_se 0.229160015 -0.091927889 -0.05161946 -0.017679218
## smoothness_se -0.141924890 0.160884609 -0.08420621 -0.294710053
## compactness_se -0.145322810 0.043504866 0.20688568 -0.263456509
## concavity_se 0.358107079 -0.141276243 -0.34951794 0.251146975
## concave.points_se 0.272519886 0.086240847 0.34237591 -0.006458751
## symmetry_se -0.304077200 -0.316529830 0.18784404 0.320571348
## fractal_dimension_se -0.213722716 0.367541918 -0.25062479 0.276165974
## radius_worst -0.112141463 0.077361643 -0.10506733 0.039679665
## texture_worst 0.103341204 0.029550941 -0.01315727 0.079797450
## perimeter_worst -0.109614364 0.050508334 -0.05107628 -0.008987738
## area_worst -0.080732461 0.069921152 -0.18459894 0.048088657
## smoothness_worst 0.112315904 -0.128304659 -0.14389035 0.056514866
## compactness_worst -0.100677822 -0.172133632 0.19742047 -0.371662503
## concavity_worst 0.161908621 -0.311638520 -0.18501676 -0.087034532
## concave.points_worst 0.060488462 -0.076648291 0.11777205 -0.068125354
## symmetry_worst 0.064637806 -0.029563075 -0.15756025 0.044033503
## fractal_dimension_worst -0.134174175 0.012609579 -0.11828355 -0.034731693
## PC13 PC14 PC15 PC16
## radius_mean 0.01196721 0.059506135 -0.051118775 -0.15058388
## texture_mean 0.20346133 -0.021560100 -0.107922421 -0.15784196
## perimeter_mean 0.04410950 0.048513812 -0.039902936 -0.11445396
## area_mean 0.06737574 0.010830829 0.013966907 -0.13244803
## smoothness_mean 0.04557360 0.445064860 -0.118143364 -0.20461325
## compactness_mean 0.22928130 0.008101057 0.230899962 0.17017837
## concavity_mean 0.38709081 -0.189358699 -0.128283732 0.26947021
## concave.points_mean 0.13213810 -0.244794768 -0.217099194 0.38046410
## symmetry_mean 0.18993367 0.030738856 -0.073961707 -0.16466159
## fractal_dimension_mean 0.10623908 -0.377078865 0.517975705 -0.04079279
## radius_se -0.06819523 0.010347413 -0.110050711 0.05890572
## texture_se -0.16822238 -0.010849347 0.032752721 -0.03450040
## perimeter_se -0.03784399 -0.045523718 -0.008268089 0.02651665
## area_se 0.05606493 0.083570718 -0.046024366 0.04115323
## smoothness_se 0.15044143 -0.201152530 0.018559465 -0.05803906
## compactness_se 0.01004017 0.491755932 0.168209315 0.18983090
## concavity_se 0.15878319 0.134586924 0.250471408 -0.12542065
## concave.points_se -0.49402674 -0.199666719 0.062079344 -0.19881035
## symmetry_se 0.01033274 -0.046864383 -0.113383199 -0.15771150
## fractal_dimension_se -0.24045832 0.145652466 -0.353232211 0.26855388
## radius_worst -0.13789053 0.023101281 0.166567074 -0.08156057
## texture_worst -0.08014543 0.053430792 0.101115399 0.18555785
## perimeter_worst -0.09696571 0.012219382 0.182755198 -0.05485705
## area_worst -0.10116061 -0.006685465 0.314993600 -0.09065339
## smoothness_worst -0.20513034 0.162235443 0.046125866 0.14555166
## compactness_worst 0.01227931 0.166470250 -0.049956014 -0.15373486
## concavity_worst 0.21798433 -0.066798931 -0.204835886 -0.21502195
## concave.points_worst -0.25438749 -0.276418891 -0.169499607 0.17814174
## symmetry_worst -0.25653491 0.005355574 0.139888394 0.25789401
## fractal_dimension_worst -0.17281424 -0.212104110 -0.256173195 -0.40555649
## PC17 PC18 PC19 PC20
## radius_mean 0.202924255 0.1467123385 0.22538466 -0.049698664
## texture_mean -0.038706119 -0.0411029851 0.02978864 -0.244134993
## perimeter_mean 0.194821310 0.1583174548 0.23959528 -0.017665012
## area_mean 0.255705763 0.2661681046 -0.02732219 -0.090143762
## smoothness_mean 0.167929914 -0.3522268017 -0.16456584 0.017100960
## compactness_mean -0.020307708 0.0077941384 0.28422236 0.488686329
## concavity_mean -0.001598353 -0.0269681105 0.00226636 -0.033387086
## concave.points_mean 0.034509509 -0.0828277367 -0.15497236 -0.235407606
## symmetry_mean -0.191737848 0.1733977905 -0.05881116 0.026069156
## fractal_dimension_mean 0.050225246 0.0878673570 -0.05815705 -0.175637222
## radius_se -0.139396866 -0.2362165319 0.17588331 -0.090800503
## texture_se 0.043963016 -0.0098586620 0.03600985 -0.071659988
## perimeter_se -0.024635639 -0.0259288003 0.36570154 -0.177250625
## area_se 0.334418173 0.3049069032 -0.41657231 0.274201148
## smoothness_se 0.139595006 -0.2312599432 -0.01326009 0.090061477
## compactness_se -0.008246477 0.1004742346 -0.24244818 -0.461098220
## concavity_se 0.084616716 -0.0001954852 0.12638102 0.066946174
## concave.points_se 0.108132263 0.0460549116 -0.01216430 0.068868294
## symmetry_se -0.274059129 0.1870147640 -0.08903929 0.107385289
## fractal_dimension_se -0.122733398 -0.0598230982 0.08660084 0.222345297
## radius_worst -0.240049982 -0.2161013526 0.01366130 -0.005626909
## texture_worst 0.069365185 0.0583984505 -0.07586693 0.300599798
## perimeter_worst -0.234164147 -0.1885435919 0.09081325 0.011003858
## area_worst -0.273399584 -0.1420648558 -0.41004720 0.060047387
## smoothness_worst -0.278030197 0.5015516751 0.23451384 -0.129723903
## compactness_worst -0.004037123 -0.0735745143 0.02020070 0.229280589
## concavity_worst -0.191313419 -0.1039079796 -0.04578612 -0.046482792
## concave.points_worst -0.075485316 0.0758138963 -0.26022962 0.033022340
## symmetry_worst 0.430658116 -0.2787138431 0.11725053 -0.116759236
## fractal_dimension_worst 0.159394300 0.0235647497 -0.01149448 -0.104991974
## PC21 PC22 PC23 PC24
## radius_mean -0.0685700057 -0.07292890 -0.0985526942 -0.18257944
## texture_mean 0.4483694667 -0.09480063 -0.0005549975 0.09878679
## perimeter_mean -0.0697690429 -0.07516048 -0.0402447050 -0.11664888
## area_mean -0.0184432785 -0.09756578 0.0077772734 0.06984834
## smoothness_mean -0.1194917473 -0.06382295 -0.0206657211 0.06869742
## compactness_mean 0.1926213963 0.09807756 0.0523603957 -0.10413552
## concavity_mean 0.0055717533 0.18521200 0.3248703785 0.04474106
## concave.points_mean -0.0094238187 0.31185243 -0.0514087968 0.08402770
## symmetry_mean -0.0869384844 0.01840673 -0.0512005770 0.01933947
## fractal_dimension_mean -0.0762718362 -0.28786888 -0.0846898562 -0.13326055
## radius_se 0.0863867747 0.15027468 -0.2641253170 -0.55870157
## texture_se 0.2170719674 -0.04845693 -0.0008738805 0.02426730
## perimeter_se -0.3049501584 -0.15935280 0.0900742110 0.51675039
## area_se 0.1925877857 -0.06423262 0.0982150746 -0.02246072
## smoothness_se -0.0720987261 -0.05054490 -0.0598177179 0.01563119
## compactness_se -0.1403865724 0.04528769 0.0091038710 -0.12177779
## concavity_se 0.0630479298 0.20521269 -0.3875423290 0.18820504
## concave.points_se 0.0343753236 0.07254538 0.3517550738 -0.10966898
## symmetry_se -0.0976995265 0.08465443 -0.0423628949 0.00322620
## fractal_dimension_se 0.0628432814 -0.24470508 0.0857810992 0.07519442
## radius_worst 0.0072938995 0.09629821 -0.0556767923 -0.15683037
## texture_worst -0.5944401434 0.11111202 -0.0089228997 -0.11848460
## perimeter_worst -0.0920235990 -0.01722163 0.0633448296 0.23711317
## area_worst 0.1467901315 0.09695982 0.1908896250 0.14406303
## smoothness_worst 0.1648492374 0.06825409 0.0936901494 -0.01099014
## compactness_worst 0.1813748671 -0.02967641 -0.1479209247 0.18674995
## concavity_worst -0.1321005945 -0.46042619 0.2864331353 -0.28885257
## concave.points_worst 0.0008860815 -0.29984056 -0.5675277966 0.10734024
## symmetry_worst 0.1627085487 -0.09714484 0.1213434508 -0.01438181
## fractal_dimension_worst -0.0923439434 0.46947115 0.0076253382 0.03782545
## PC25 PC26 PC27 PC28
## radius_mean -0.01922650 -0.129476396 -0.131526670 2.111940e-01
## texture_mean 0.08474593 -0.024556664 -0.017357309 -6.581146e-05
## perimeter_mean 0.02701541 -0.125255946 -0.115415423 8.433827e-02
## area_mean -0.21004078 0.362727403 0.466612477 -2.725083e-01
## smoothness_mean 0.02895489 -0.037003686 0.069689923 1.479269e-03
## compactness_mean 0.39662323 0.262808474 0.097748705 -5.462767e-03
## concavity_mean -0.09697732 -0.548876170 0.364808397 4.553864e-02
## concave.points_mean -0.18645160 0.387643377 -0.454699351 -8.883097e-03
## symmetry_mean -0.02458369 -0.016044038 -0.015164835 1.433026e-03
## fractal_dimension_mean -0.20722186 -0.097404839 -0.101244946 -6.311687e-03
## radius_se -0.17493043 0.049977080 0.212982901 -1.922239e-01
## texture_se 0.05698648 -0.011237242 -0.010092889 -5.622611e-03
## perimeter_se 0.07292764 0.103653282 0.041691553 2.631919e-01
## area_se 0.13185041 -0.155304589 -0.313358657 -4.206811e-02
## smoothness_se 0.03121070 -0.007717557 -0.009052154 9.792963e-03
## compactness_se 0.17316455 -0.049727632 0.046536088 -1.539555e-02
## concavity_se 0.01593998 0.091454968 -0.084224797 5.820978e-03
## concave.points_se -0.12954655 -0.017941919 -0.011165509 -2.900930e-02
## symmetry_se -0.01951493 -0.017267849 -0.019975983 -7.636526e-03
## fractal_dimension_se -0.08417120 0.035488974 -0.012036564 1.975646e-02
## radius_worst 0.07070972 -0.197054744 -0.178666740 4.126396e-01
## texture_worst -0.11818972 0.036469433 0.021410694 -3.902509e-04
## perimeter_worst 0.11803403 -0.244103670 -0.241031046 -7.286809e-01
## area_worst -0.03828995 0.231359525 0.237162466 2.389603e-01
## smoothness_worst -0.04796476 0.012602464 -0.040853568 -1.535248e-03
## compactness_worst -0.62438494 -0.100463424 -0.070505414 4.869182e-02
## concavity_worst 0.11577034 0.266853781 -0.142905801 -1.764090e-02
## concave.points_worst 0.26319634 -0.133574507 0.230901389 2.247567e-02
## symmetry_worst 0.04529962 0.028184296 0.022790444 4.920481e-03
## fractal_dimension_worst 0.28013348 0.004520482 0.059985998 -2.356214e-02
## PC29 PC30
## radius_mean 2.114605e-01 0.7024140910
## texture_mean -1.053393e-02 0.0002736610
## perimeter_mean 3.838261e-01 -0.6898969685
## area_mean -4.227949e-01 -0.0329473482
## smoothness_mean -3.434667e-03 -0.0048474577
## compactness_mean -4.101677e-02 0.0446741863
## concavity_mean -1.001479e-02 0.0251386661
## concave.points_mean -4.206949e-03 -0.0010772653
## symmetry_mean -7.569862e-03 -0.0012803794
## fractal_dimension_mean 7.301433e-03 -0.0047556848
## radius_se 1.184421e-01 -0.0087110937
## texture_se -8.776279e-03 -0.0010710392
## perimeter_se -6.100219e-03 0.0137293906
## area_se -8.592591e-02 0.0011053260
## smoothness_se 1.776386e-03 -0.0016082109
## compactness_se 3.158134e-03 0.0019156224
## concavity_se 1.607852e-02 -0.0089265265
## concave.points_se -2.393779e-02 -0.0021601973
## symmetry_se -5.223292e-03 0.0003293898
## fractal_dimension_se -8.341912e-03 0.0017989568
## radius_worst -6.357249e-01 -0.1356430561
## texture_worst 1.723549e-02 0.0010205360
## perimeter_worst 2.292180e-02 0.0797438536
## area_worst 4.449359e-01 0.0397422838
## smoothness_worst 7.385492e-03 0.0045832773
## compactness_worst 3.566904e-06 -0.0128415624
## concavity_worst -1.267572e-02 0.0004021392
## concave.points_worst 3.524045e-02 -0.0022884418
## symmetry_worst 1.340423e-02 0.0003954435
## fractal_dimension_worst 1.147766e-02 0.0018942925- plots of PCA results - biplot is hard to see because there are many principal components plotted
biplot(wisc.pr)
- plot selected PCA components - scatter plot each observation by principal components 1 and 2, coloring the points by the diagnosis. principal components are contained in the x component of wisc.pr
plot(wisc.pr$x[, c(1,2)],
col = (diagnosis + 1),
xlab = "PC1", ylab = "PC2")
- scatter plot each observation by principal components 1 and 3, coloring the points by the diagnosis
plot(wisc.pr$x[, c(1,3)],
col = (diagnosis + 1),
xlab = "PC1", ylab = "PC3")
visually, first selected plot has a cleaner cut separating the two subgroups then the second plot as principal component 2 explains more variance in the original data than principal component 3.
variance explained
par(mfrow = c(1,2))- observe PCA contributions
pr.var <- wisc.pr$sdev ^ 2
pve <- pr.var/sum(pr.var)plot(pve, xlab = "Principal Component",
ylab = "Proportion of Variance Explained",
ylim = c(0, 1), type = "b")
plot(cumsum(pve), xlab = "Principal Component",
ylab = "Proportion of Variance Explained",
ylim = c(0, 1), type = "b")
we need five number of principal components to explain 80% of variance in the data.
Fourth step - hierarchical clustering
here we do not assume in advance the number of natural groups that exist in the data
- scale the wisc.data and assign the results
data.scaled <- scale(wisc.data)- calculate the euclidean distances between all paris of observations in the new scaled dataset.
data.dist <- dist(data.scaled)- create a hierarchical clustering model, using method with “complete” linkage. From the plot we can see at height of 20 the clustering model has 4 clusters
wisc.hclust <- hclust(data.dist, method = "complete")
plot(wisc.hclust)
- cut tree so that it only has 4 clusters
wisc.hclust.clusters <- cutree(wisc.hclust, k = 4)- compare cluster membership to diagnosis
table(wisc.hclust.clusters, diagnosis)## diagnosis
## wisc.hclust.clusters 0 1
## 1 12 165
## 2 2 5
## 3 343 40
## 4 0 2- kmeans - 2 clusters corresponding to the actual number of diagnosis. scale the data, repeat the algorithm 20 times.
wisc.km <- kmeans(scale(wisc.data), centers = 2, nstart = 20)- table to compare k means results to actual diagnosis
table(wisc.km$cluster, diagnosis)## diagnosis
## 0 1
## 1 343 37
## 2 14 175str(wisc.km$cluster)## Named int [1:569] 2 2 2 2 2 2 2 2 2 2 ...
## - attr(*, "names")= chr [1:569] "842302" "842517" "84300903" "84348301" ...- compare k means to hierarchical clustering - looks like clusters 1, 2, and 4 from the hierarchical clustering model can be interpreted as the cluster 1 equivalent from the k-means algorithm.
table(wisc.km$cluster, wisc.hclust.clusters)## wisc.hclust.clusters
## 1 2 3 4
## 1 17 0 363 0
## 2 160 7 20 2wisc.pr$x[, 1:7]## PC1 PC2 PC3 PC4 PC5
## 842302 -9.18475521 -1.946870030 -1.122178766 3.630536408 1.1940594778
## 842517 -2.38570263 3.764859063 -0.528827374 1.117280773 -0.6212283647
## 84300903 -5.72885549 1.074228589 -0.551262540 0.911280840 0.1769302185
## 84348301 -7.11669126 -10.266555635 -3.229947535 0.152412923 2.9582754313
## 84358402 -3.93184247 1.946358977 1.388544953 2.938054169 -0.5462667446
## 843786 -2.37815462 -3.946456430 -2.932296681 0.940209586 1.0551135428
## 844359 -2.23691506 2.687666414 -1.638471247 0.149208600 -0.0403240371
## 84458202 -2.14141428 -2.338186649 -0.871180715 -0.126931171 1.4261817833
## 844981 -3.17213315 -3.388831138 -3.117243065 -0.600768440 1.5209521144
## 84501001 -6.34616284 -7.720380945 -4.338098744 -3.372234369 -1.7087596141
## 845636 0.80970132 2.656937673 -0.488400053 -1.671096176 -0.2755690974
## 84610002 -2.64876984 -0.066509405 -1.525113359 0.051216497 -0.3316592904
## 846226 -8.17783882 -2.698602007 5.725193241 -1.111278747 -1.0425531111
## 846381 -0.34182514 0.967428026 1.715661982 -0.594479872 -0.4675990720
## 84667401 -4.33856172 -4.856809832 -2.813639832 -1.453278303 -1.2889287269
## 84799002 -4.07207318 -2.974443983 -3.122526655 -2.455909915 0.4079831402
## 848406 -0.22985277 1.563382114 -0.801813642 -0.650010973 0.4942761390
## 84862001 -4.41412695 -1.417423150 -2.268323145 -0.186108659 1.4226094459
## 849014 -4.94435304 4.110716528 -0.314472408 -0.088128974 0.0566653163
## 8510426 1.23597583 0.188049490 -0.592761930 1.594942716 0.4417655273
## 8510653 1.57677384 -0.572304625 -1.799863016 1.124286473 0.3949222435
## 8510824 3.55420904 -1.661487969 0.450790799 2.071941593 0.4903150736
## 8511133 -4.72904972 -3.302058265 -1.465247427 2.039355666 0.0261970715
## 851509 -4.20482441 5.123858059 -0.751740573 -0.861951843 0.4705538779
## 852552 -4.94528075 1.542395143 -1.711687827 0.046718059 1.7377012054
## 852631 -7.09232236 -2.016835734 -0.028984132 2.585675482 2.0375470912
## 852763 -3.50717666 -2.169715994 -3.891122637 -1.294620549 0.0681580703
## 852781 -3.06136021 1.874902631 2.579478032 0.128371462 0.1165625639
## 852973 -4.00374127 -0.536769860 -2.759197831 -1.896718595 0.5252107652
## 853201 -1.71380176 1.522365502 0.146058578 1.909706071 -0.5356519265
## 853401 -6.05411853 0.756511800 -0.348932376 -1.063281958 0.7454493340
## 853612 -2.89968469 -4.001774373 -2.998823809 -0.325030387 0.8546038749
## 85382601 -4.55077848 -0.337239419 -0.753637681 -0.699714306 1.5471839770
## 854002 -4.98621538 1.131593223 -2.575118337 -1.216191663 -0.6693259394
## 854039 -2.98271631 -0.757756497 -3.490690279 0.054212589 -0.1669530505
## 854253 -2.76393718 0.354044421 -1.895295337 -0.533786198 0.8832432812
## 854268 -1.29505925 -0.912393466 -1.574383382 -1.042249570 -0.4143571251
## 854941 3.74601730 1.412230504 1.730784885 -0.564945456 -0.0802687991
## 855133 0.99719148 3.348346731 4.301788720 -0.560716245 0.4639645611
## 855138 -0.76459136 -0.885464837 -2.702540362 -0.274538185 -0.8097169787
## 855167 2.14906252 1.922300194 -1.179446370 -1.112219391 -0.4480774771
## 855563 0.09324934 -2.258764532 -1.903051997 -1.441039161 1.7038647386
## 855625 -9.08001023 -2.016898441 2.139343894 -1.068304028 -0.7972299505
## 856106 -0.98958304 -0.984064148 -2.308702241 -0.276582144 0.6399478981
## 85638502 0.29328849 0.136978564 -3.299029123 -1.008898141 0.0224910920
## 857010 -5.37620991 0.134758404 -1.677366657 1.506369463 -0.1518645822
## 85713702 4.57790860 -1.482915508 0.042037623 0.295968708 0.7132249498
## 85715 -1.69851237 -2.350203862 -3.075383081 -0.065962912 1.0555376469
## 857155 2.13456708 -0.095745364 -1.491099878 1.120077655 0.0679774156
## 857156 1.56610099 1.207370855 -0.368834570 -1.474331566 -0.1725985690
## 857343 3.53979091 1.281368110 1.017315805 -0.607621596 0.2194428358
## 857373 3.15503795 1.687473796 -0.495857416 0.193841543 -1.4386516886
## 857374 3.44745515 0.497780720 -0.152383875 0.574980496 0.0522688899
## 857392 -3.29964761 1.129943574 0.825666100 0.981853085 1.1942122234
## 857438 0.67402621 2.114549137 -1.394992302 -1.042221635 -0.2416042153
## 85759902 2.85564577 -0.152588874 0.428557855 0.482635650 1.5092086632
## 857637 -4.64465207 2.308301508 -0.728168145 0.639379104 1.1573061797
## 857793 -2.17494916 -0.971261438 -1.942179421 -0.736670095 0.3954358798
## 857810 3.71818738 1.786070097 1.278807604 0.115464169 0.5258196576
## 858477 4.13232693 -2.401679261 -1.241865694 2.046545722 1.1646276518
## 858970 2.38373822 -2.755233814 1.213018303 1.792911568 3.3352233901
## 858981 2.57661610 -3.135912650 1.399049169 -0.763194998 2.7816479152
## 858986 -4.75492832 -3.009032875 -0.166094576 -0.605295233 -1.1406976712
## 859196 2.31209785 -3.265116721 2.793766025 0.565229094 0.3814984103
## 85922302 -1.69012080 -1.539322116 -1.798262954 -1.389367072 1.2116088977
## 859283 -1.81071217 -0.722104815 -1.464960560 -1.197676214 1.4267861675
## 859464 2.78347559 -2.308617372 0.472309720 -1.605747397 1.6114402596
## 859465 3.51555502 0.657730736 0.590855071 -0.010793189 -0.0205709988
## 859471 -4.32619605 -9.194435552 1.491650337 0.319666023 -4.7240139158
## 859487 3.25841241 0.937013647 0.204949679 1.089113223 0.4599452518
## 859575 -2.70221851 4.433240985 0.307075192 0.488263229 -0.3721675732
## 859711 0.30758513 -7.381317396 3.815728542 2.131680166 -2.7083196796
## 859717 -5.49886689 -0.937500513 -2.208188675 -1.522456429 -0.9240784393
## 859983 0.36139121 -0.119633821 -2.039161544 1.057953093 -0.7564437850
## 8610175 2.62766457 0.696696349 -0.583428281 0.337884296 -0.4671344130
## 8610404 -1.42691206 1.965372092 1.110961327 0.752248984 0.5394071070
## 8610629 0.83378424 -1.963876860 0.789737653 3.434609101 2.3524809639
## 8610637 -6.22541880 -0.919260690 0.089748341 2.536926544 -0.0620812262
## 8610862 -11.65845644 -4.744442593 2.004115633 0.318768543 3.3883795562
## 8610908 2.01980045 0.254675746 -0.647302452 0.059199217 0.0547996477
## 861103 1.63694460 -1.714440587 0.433824539 -1.526622964 1.7678261507
## 8611161 -1.16643527 -2.512305286 -1.904043397 0.637750373 -0.2359734956
## 8611555 -10.75977535 2.255997858 0.038801648 -0.389043228 -1.1862447821
## 8611792 -5.03038488 -0.773728357 2.679979922 -1.665039071 0.3113456414
## 8612080 2.17255269 -0.496441169 -0.948257444 0.207037052 0.8845677371
## 8612399 -3.28534463 1.666770480 0.146802675 0.437108401 1.3673667927
## 86135501 -0.60707378 -0.162071919 1.635935419 -1.113531850 0.5403198078
## 86135502 -3.58041324 2.204721916 -1.703037100 -0.800589442 -0.3650009185
## 861597 0.93333687 -0.926885919 -0.040128345 -1.352209082 -0.0648850467
## 861598 -1.25849730 -1.014684255 -0.080521995 2.049531496 -0.1373994614
## 861648 1.58686770 1.618232954 0.309726682 -1.091038889 -0.0537268234
## 861799 -0.25227559 0.530884425 0.588809736 -0.110441165 -0.4283042881
## 861853 2.84492835 2.891103732 0.527524677 0.598290300 -1.4344348070
## 862009 1.96322268 0.964308498 -0.081136715 -0.093998029 0.5495403920
## 862028 -2.77342525 -0.557509977 -0.605238702 0.499390598 -0.4994662006
## 86208 -4.39236314 2.121640892 0.579000549 -0.776729960 0.3035669597
## 86211 2.58980407 -0.213446120 1.034701089 0.661423462 0.5402889624
## 862261 3.90090576 -1.189020421 1.550616806 -0.934952821 0.7074978792
## 862485 2.81575365 -0.367560567 -1.350247556 1.736886645 -0.2840715251
## 862548 -0.61573908 -0.638349988 -0.199743121 -1.096533937 -0.1185853914
## 862717 0.43247968 1.390820523 -0.082646762 -1.933578565 0.0344302397
## 862722 4.55102442 -3.525683788 -0.215074716 1.090925794 2.7559240651
## 862965 3.44515217 1.423370040 -0.088646005 -1.709223842 0.1065229834
## 862980 2.11410008 -1.847747782 -0.556184595 -0.463948150 0.4744968363
## 862989 2.68898618 -1.418813334 0.968298772 -0.002857011 1.2554137475
## 863030 -3.21109134 -4.043198634 -2.712997305 1.327457319 0.2214783192
## 863031 0.74861266 -1.796058175 -0.567866143 -0.560006237 0.9322757208
## 863270 3.15622889 1.034838878 -1.489373670 -0.592646911 -0.5136339075
## 86355 -13.04464395 -0.980650357 0.598286247 1.471636087 0.5993856696
## 864018 2.22672053 -0.666823902 -1.090600727 -1.077353762 0.2988661489
## 864033 2.49063954 -2.596401708 1.668257671 0.632929090 1.1557305724
## 86408 0.10325957 -2.278139015 2.107708229 -0.351536677 -0.6219347413
## 86409 -3.58813694 -3.922881433 2.045207163 -0.231562584 -5.4604591892
## 864292 1.34776279 -3.553098748 1.730668471 -0.046949434 0.3449474850
## 864496 2.50791098 -3.248461200 -1.686140767 1.188915291 0.4551865326
## 864685 2.04423086 -0.304616836 -0.533369397 -0.489411120 0.0678524055
## 864726 2.09522559 -3.663872062 3.629007335 1.538433194 -2.2345636748
## 864729 -3.10779316 -1.568009873 -2.611638159 0.617924024 1.1807403791
## 864877 -4.95236801 -2.382749650 -1.933405900 -0.610304229 0.1480794337
## 865128 -0.85026612 2.304707468 0.566963050 -0.043586897 2.0922055990
## 865137 2.96339173 -0.371179883 -2.064716427 2.070684315 -0.1628943517
## 86517 -3.33120209 1.324392029 0.727373652 1.002316780 0.9328861016
## 865423 -12.88327621 -2.314585873 6.323133317 1.940496559 3.1574494112
## 865432 0.77006610 0.064052860 -1.133411514 2.508256103 -0.0202192366
## 865468 2.20057925 0.734958544 0.266845303 -0.037586447 -2.9314571580
## 86561 3.14064881 1.875758557 -0.669779705 0.303065257 -0.4077106627
## 866083 0.63831885 0.910564828 -2.140840449 -2.139033534 0.4287624850
## 866203 -1.91744627 3.534971966 1.253821297 0.335703696 -0.5885511025
## 866458 -1.40762980 -1.303782215 0.640864876 1.885297508 0.0362201276
## 866674 -4.63960895 1.480714297 -1.169651383 -1.217534223 -0.1779160105
## 866714 1.87581684 -1.421979452 -1.069870821 1.707830258 0.8837714798
## 8670 -1.43081046 1.048681220 -1.260901861 0.532720319 0.6261456617
## 86730502 -1.35143790 1.153126842 -1.208729712 -0.827378497 0.9859398192
## 867387 0.70849143 1.566853657 -0.669405084 1.685780647 -0.3390165106
## 867739 -2.16950708 2.823776101 -0.561613332 -0.660250673 0.4745525764
## 868202 1.97510247 0.419018755 -0.380240597 -1.737931013 0.3083668329
## 868223 2.59850310 0.481911436 1.870726668 -0.437633248 -0.0160686443
## 868682 3.25514318 0.417953651 -0.691197447 0.659273518 -0.1214593563
## 868826 -3.77870160 -0.859625218 3.667773435 2.046019895 2.1818702714
## 868871 1.99028348 -1.328186508 1.134246527 2.044634146 0.2519061287
## 868999 5.01059989 -0.574194748 -0.841697543 2.167755281 0.8812268193
## 869104 -1.34383800 1.273650278 0.555354894 0.574366142 0.4704353120
## 869218 2.45380972 -0.897665441 0.352823033 -0.367668079 1.1033160270
## 869224 1.83566648 0.090946742 -1.444010288 0.671957291 0.1360791853
## 869254 4.34266862 0.892786708 0.638694049 0.425252734 -0.9556015217
## 869476 0.73216868 -3.698927716 0.657926113 2.234161633 0.3361716375
## 869691 -2.39788795 -4.833735642 -1.027253164 0.342615376 2.3897699977
## 86973701 -0.39275308 -1.082115915 2.245629588 -0.461452569 -1.6901413981
## 86973702 0.41196533 0.389288784 -1.044851048 1.365044596 -0.8627479982
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## 894047 3.76210430 -4.394333943 3.946735131 -0.306998155 4.7854456445
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## 898690 3.32315522 -0.474753848 -0.897496041 0.812772706 0.5848648524
## 899147 1.92709976 -1.460184989 -0.100554033 1.819163615 1.9342391900
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## 901041 2.48373073 1.187894183 0.348470172 -1.255187427 0.1292803966
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## 9010872 0.77892982 2.122475872 0.320506876 0.079179253 0.0857346246
## 9010877 3.13722800 1.486714010 -1.197824530 0.453050754 -0.8401627046
## 901088 -2.73260737 3.941699950 -0.017154393 0.299846924 -0.2830181364
## 9011494 -6.22155168 1.388887616 2.731833465 -1.092200460 0.5821459417
## 9011495 2.22182078 0.356846723 -1.100713817 0.186058986 0.2390645934
## 9011971 -5.30247440 6.717504288 1.484358772 1.774948969 1.0726100091
## 9012000 -7.24162919 3.652255530 -0.155565119 1.225750236 -0.2973284171
## 9012315 -4.20352196 -1.175208822 -1.588620367 -0.977982825 0.1174778025
## 9012568 2.49743889 2.016761090 -0.730631718 1.983278202 -1.1349569236
## 9012795 -3.63181933 1.954720962 -0.828046542 1.378539602 -0.9935467144
## 901288 -3.51615443 3.855214937 -1.021630135 1.382926471 -0.3203822623
## 9013005 2.61264945 1.101505251 -1.239645246 0.908676936 -0.3781480185
## 901303 0.09602363 0.129733431 -1.669994689 1.526133855 -0.4027131208
## 901315 -2.04305926 -6.421169887 1.273001142 -0.109645013 -4.5986701548
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## 9013594 1.60217670 -0.292338995 -1.584830948 0.908898609 -1.2347827015
## 9013838 -3.76262144 -5.980033549 -4.876070721 -1.119887331 0.5637410178
## 901549 0.92475292 -2.300457270 -1.594708683 1.674764766 1.4257318574
## 901836 3.28545874 -0.201134359 -0.627204410 0.612295926 -0.1706180435
## 90250 1.55348525 -0.978996316 1.195507876 -1.773616381 -3.4960491469
## 90251 0.39842934 -2.159312724 -0.944773717 0.372153562 -1.0117604959
## 902727 2.29854534 0.931258175 -1.128959899 1.451099756 -1.5542727004
## 90291 0.54242409 1.315910048 0.994879134 -1.483570015 -0.2027995563
## 902975 2.05700950 -0.320153445 -0.122350756 1.019962435 -2.0773397982
## 902976 3.42150749 2.443368505 0.045009146 0.785450794 -1.6017729103
## 903011 0.47199125 -3.699574203 1.952067274 0.995440694 -3.8110426797
## 90312 -4.69936579 0.195783486 3.753730061 -1.003344863 -0.3283619127
## 90317302 3.64017727 -0.786168171 -1.161124120 2.097029762 0.4236952100
## 903483 3.59152918 -2.602797030 1.850401478 0.089806410 2.4403924824
## 903507 -4.14544978 -0.766814129 -0.887194062 -0.008362190 0.6044479220
## 903516 -7.66539681 0.859727681 -2.151756805 0.254499442 0.2362625219
## 903554 2.00861205 -0.429311811 -0.103997306 -0.160151144 1.5081790902
## 903811 2.91826573 1.698977554 0.295467269 -0.413812779 -0.3635999269
## 90401601 0.50029759 -0.106637635 -1.027843564 -0.304616687 -0.1389987468
## 90401602 1.90981814 0.650821226 1.449013512 0.400350786 -2.0611887662
## 904302 3.78177167 0.325859645 -1.057150017 0.605475000 -1.5248138903
## 904357 2.70601296 0.219472629 -0.314228262 0.055204339 0.0482116178
## 90439701 -6.28414409 -2.034757025 -3.179284831 0.155406788 -0.2023110488
## 904647 3.42775463 0.991737410 -0.731051348 1.342541631 -0.2356318119
## 904689 1.99962900 0.293068594 0.618659534 -0.352201845 -1.1637958353
## 9047 2.47111877 0.334752480 -1.481058853 0.464828450 -0.0489496329
## 904969 3.64405137 1.240273815 1.385405524 1.612540488 0.1728393129
## 904971 2.34412427 -0.682141105 1.131738080 -0.302837266 0.5411994776
## 905189 1.14199209 1.960446508 -1.239628958 1.477776286 -0.4837568556
## 905190 1.34966974 -0.369249002 2.484489568 -1.139714833 -1.9041890533
## 90524101 -2.76094145 1.077685260 -1.178586912 0.413794976 0.1644668356
## 905501 1.96759233 0.175693916 0.420361503 -0.785620740 0.8604953761
## 905502 2.92861019 0.494421191 -1.016176763 -1.684940447 0.5652328718
## 905520 2.92380175 -0.377000536 -0.886014238 -0.115243469 0.9848137147
## 905539 3.99267514 -0.959012260 0.204224433 -1.508902626 -1.7077458028
## 905557 -0.15500167 0.437623166 -0.461040030 -1.453254393 -0.8550878945
## 905680 0.93326963 2.104094210 1.431657320 -2.891717258 1.2742945854
## 905686 1.92792536 -0.891682104 0.042307522 -0.558392976 1.2792046734
## 905978 2.62003325 -2.499901968 2.432858840 -1.876362157 3.1480466996
## 90602302 -5.99833869 0.090949196 1.709697317 0.946542059 1.1740030698
## 906024 2.91930912 0.009204582 -0.900511128 1.789753754 -0.5764724361
## 906290 3.33900683 0.022205192 0.502858739 -1.141258134 1.5633857813
## 906539 2.01314368 -0.777767778 0.125468395 -0.659155792 0.0219104429
## 906564 -1.98671401 -2.314011967 1.235217081 1.768220225 -0.1438692164
## 906616 1.66813615 -0.861560770 -1.009417991 1.322731355 0.2813203167
## 906878 0.37085180 -0.113512779 -0.997485893 -0.155233295 -1.4746581730
## 907145 1.84733447 -2.538995601 2.003584668 0.483946194 3.5055609223
## 907367 4.69890766 0.431922385 0.005300424 -1.369403704 0.0850247711
## 907409 1.28205907 -2.548666752 -0.083786622 0.770833997 -0.5564209652
## 90745 2.31221232 -0.401678043 0.274381769 -1.668994639 0.5362392557
## 90769601 4.65498928 0.781611021 0.191953023 0.493247906 -0.5356508029
## 90769602 3.94000659 2.028231657 0.691127602 0.512954900 -0.3398155529
## 907914 -4.94550694 -3.003421435 -1.752529645 -0.671769430 -2.8622552978
## 907915 0.91499842 -2.476833776 0.362287911 0.261736218 -0.1383500423
## 908194 -4.54511193 0.815283142 -0.518299038 0.915534201 0.0714231738
## 908445 -4.43843746 0.991566424 1.441051113 -0.574529073 0.3572756344
## 908469 2.19305464 1.803766114 -0.434726892 0.953104432 -0.5533135626
## 908489 -0.66385679 -0.436476802 -2.678425146 -0.728585540 0.0277629459
## 908916 2.23890605 0.454189872 -0.465118333 0.188558748 0.8275650396
## 909220 2.12331215 1.193746541 0.489940891 0.854644353 0.1058427332
## 909231 2.61301823 1.830449830 0.763657618 -0.822442197 0.3005228170
## 909410 3.20814515 2.233177743 -0.166078298 1.129064342 -1.2590809462
## 909411 0.30648073 -2.183077955 0.039251705 -0.486027975 -2.0876130896
## 909445 -2.47018342 1.498506224 0.590933256 -2.265358224 -1.4046042766
## 90944601 3.45168126 2.134583340 0.196989342 1.532828161 -0.9420463979
## 909777 3.89709781 -0.730133530 2.134193239 -0.780486142 0.8318195830
## 9110127 -0.98086448 2.208486712 -1.698424795 0.970118413 -1.1822180725
## 9110720 1.25614629 -1.066752885 0.259247160 -1.240660490 0.3928701037
## 9110732 -3.24256054 1.776795240 -1.791577273 -2.482874793 -0.5498682865
## 9110944 1.55585043 1.037014643 -1.300101127 0.621126067 0.3790198963
## 911150 1.24815985 1.587442008 -0.326126484 -0.924508658 -1.5340001134
## 911157302 -4.32784530 4.045772565 -0.192336290 -0.290357973 -0.6103038017
## 9111596 1.07650412 -1.802032564 1.779475879 -1.627520204 -3.7384644652
## 9111805 -2.50954497 2.526584455 0.797500590 -0.822950476 0.4288865709
## 9111843 2.21514321 -0.029865010 0.635900610 -3.373732618 -0.4795727546
## 911201 1.17279871 0.474422064 -0.481147553 2.142074589 0.2430866392
## 911202 2.83380799 1.017230750 -1.485323075 0.456004436 -0.1146041549
## 9112085 1.85545330 1.570011674 0.825756166 -3.926794310 0.2206325260
## 9112366 1.32744636 -0.776412499 1.255653387 -3.782215661 1.2439684480
## 9112367 2.80030738 1.664836753 -0.193847761 -2.231144249 0.2050662449
## 9112594 3.17177797 2.073908798 0.074834422 -1.868185223 0.2091427763
## 9112712 4.08348433 0.484283961 0.630808963 -3.399741429 0.0182086861
## 911296201 -3.47243837 1.671413723 0.856073545 -1.155750941 1.3813559853
## 911296202 -16.30488665 7.769016888 6.229933870 2.326026514 1.7079531344
## 9113156 2.55786437 2.491852880 0.170162861 -2.107901855 -0.9783779753
## 911320501 2.96627878 0.068786611 -0.777727248 -0.046625788 -0.2280062503
## 911320502 2.75500634 1.792341696 -0.757147909 0.024097077 -1.2827836689
## 9113239 -1.36913518 -2.108156394 -0.852969723 -0.723132156 -3.8210171185
## 9113455 0.41729731 -0.116417262 -0.535671262 -0.363878888 -1.5121265752
## 9113514 3.83502421 -0.898388162 0.699948069 -0.219746414 1.3359873635
## 9113538 -5.92575082 -1.227216861 1.720074272 -0.473165926 -2.8810043579
## 911366 -0.64491119 -3.422999542 0.607750202 0.234280083 1.2086350824
## 9113778 2.68148698 -1.442286469 0.339105123 -0.244601788 0.7919949893
## 9113816 2.03986918 0.902461858 2.840741857 -2.883294431 1.0158156443
## 911384 1.39806620 1.770668244 -1.478260847 1.306959009 -1.8037276563
## 9113846 3.53330636 1.245758018 3.382434941 -4.661948944 1.8740788308
## 911391 1.98877953 -1.897792693 -2.029212586 0.911103793 -1.2304717877
## 911408 1.99642872 0.206189711 -1.639882150 1.038296903 -0.9034160493
## 911654 0.52020039 0.972512103 -0.323850426 -0.543521127 -1.4281800593
## 911673 3.16958159 2.087215768 -0.977945244 0.386756799 -1.4182276802
## 911685 2.20077374 -1.284908734 -0.886619084 0.700486694 -0.1796630638
## 911916 -3.82107090 -2.303209735 0.027521977 0.669669644 -1.2886313605
## 912193 2.98286009 0.672747298 -0.589970772 -0.593827781 -0.4615631694
## 91227 2.47887396 2.361880555 -0.432234246 -0.383132558 -1.0372087673
## 912519 1.27099312 -0.509385643 -2.237023334 1.670906156 0.1175030515
## 912558 2.23319191 1.297562775 -0.900644424 0.433712494 -0.1827652155
## 912600 0.05613371 0.227183495 -2.253532782 2.708217480 -0.8010805172
## 913063 -2.31535334 -4.385275755 1.776847691 0.968563355 -2.6430509823
## 913102 2.28232306 2.464672105 -0.820466562 -0.040767325 -1.0918206156
## 913505 -4.75043499 1.488114177 -1.252648906 -0.052540766 0.0965398306
## 913512 1.72479328 -0.997300316 -0.080167877 1.063711106 1.4343549437
## 913535 0.74112965 2.449879331 -1.995953713 -0.457537180 -0.2610613824
## 91376701 2.89176621 0.977084588 -0.804935982 -1.719266485 0.0289580691
## 91376702 1.65306732 4.551659142 0.751661685 1.646873743 -1.4018393993
## 914062 -3.10079133 1.235066483 1.286223339 0.608113830 1.1212732858
## 914101 4.06069761 0.560461075 2.174771231 1.374658804 -0.1992898120
## 914102 2.79087498 1.076940539 0.843799658 -1.109231547 -0.0048653882
## 914333 1.47362330 1.589695437 0.319710133 -0.798129881 -0.1579186103
## 914366 0.22919297 -1.514570755 -2.214334625 0.555081328 -0.2509810467
## 914580 2.55101378 0.763228924 -1.607988258 0.059875184 -0.5054003068
## 914769 -3.71243855 1.057755506 0.521494703 1.395773631 -0.3682903454
## 91485 -5.09036286 2.017432706 -0.708746074 -0.082722167 -0.3834794788
## 914862 0.60008810 0.837717560 -0.686437977 1.154318132 -0.9815689274
## 91504 -2.78794673 -3.382584454 -0.752414277 -1.332009710 1.5841377430
## 91505 1.40753273 -1.504446838 -0.353584900 1.120754558 1.8100776146
## 915143 -7.25279714 5.490904302 1.909245947 1.894050092 -0.3960294570
## 915186 -1.29772469 -7.723057325 -0.688309017 2.890184346 2.0135831354
## 915276 -1.07574673 -8.287483337 0.433810751 1.952471847 1.3946448821
## 91544001 1.24866183 -1.594281055 -1.355282076 0.126156474 -0.0233994859
## 91544002 1.25582341 -4.113567176 -0.412366931 1.053246923 1.1385251781
## 915452 1.16550969 1.664229389 -0.737229323 1.760617958 -0.7377031703
## 915460 -4.09054331 -2.800463137 -0.506987325 -1.975580106 -0.1327084112
## 91550 1.88597978 -1.670721680 0.119692299 1.217144238 -2.5658122684
## 915664 2.76500279 2.159148972 -0.021077623 1.608860107 -0.7157489170
## 915691 -2.22503669 -1.939927827 -2.283594176 -0.339561903 0.5363853531
## 915940 1.13058210 1.409761524 -0.564556376 1.993206904 -0.5280229629
## 91594602 0.73312738 1.941988438 -0.274994234 -0.337526159 -0.6604100570
## 916221 2.33161916 -0.789451973 -0.349735677 0.440471990 1.4212995780
## 916799 -2.69485257 1.942001189 -0.959719996 0.459104689 0.5839845732
## 916838 -3.37604410 2.331377578 -1.200875536 0.553126259 -0.5274167311
## 917062 0.19969487 -1.075413752 -0.672557052 0.627893020 0.8395117260
## 917080 1.17499204 -1.010481061 -0.711142576 1.065131254 1.4206509043
## 917092 1.29150016 -4.959860548 0.345622908 2.238565182 3.8371535988
## 91762702 -8.62316838 3.456410638 -0.178899380 1.176129200 0.0228851505
## 91789 4.42556234 0.785345015 -0.473002900 -0.696004578 -0.1037131678
## 917896 0.61929383 -0.635789842 -0.488421490 -0.015141135 0.1063131129
## 917897 3.24945659 -1.284794677 -0.218284421 0.307537632 0.0993416275
## 91805 3.34997942 -2.670950443 -1.777523046 1.388364375 0.3541295063
## 91813701 0.85904712 -0.096763381 -2.811570840 0.184161855 0.6295214724
## 91813702 3.15384692 0.870776432 -2.193784489 1.448593014 -0.4310565911
## 918192 -0.34622347 -1.539870352 2.843951628 1.908132516 0.5713316529
## 918465 2.45924278 -0.600319751 -1.170435277 2.209110148 0.6913036191
## 91858 1.52875558 -0.404861554 0.603933344 -0.346866279 0.7853562456
## 91903901 1.77202587 -0.803503014 -2.026135257 -0.686728928 0.6155504122
## 91903902 2.67808519 1.483403662 -1.740162222 1.022590841 -0.2972072410
## 91930402 -4.02489378 2.938844225 1.658026507 0.224969353 0.5131432277
## 919537 2.13447312 -1.517245623 0.178807901 -0.500336469 -0.6824469628
## 919555 -5.16086993 2.380108987 -0.421906048 0.882650977 0.2092240560
## 91979701 -0.53546080 -0.380380451 -0.442745212 -1.877719723 -0.2266699710
## 919812 -0.34282174 -3.531373815 0.069607554 -1.549307121 1.9552004887
## 921092 4.19339024 -2.365311059 1.325978010 -2.037710987 1.7603677988
## 921362 1.14182718 -5.594535868 1.299893249 -2.186325923 -0.7649016389
## 921385 1.66401100 -2.387517361 1.500928782 0.875181074 -0.4841195986
## 921386 -1.01082308 -1.091429307 -0.632142163 -1.756972472 -1.0459061568
## 921644 1.29978604 1.819814057 0.372979316 -1.846544182 -0.1994515741
## 922296 2.37134219 1.680097929 0.384190094 -3.014076570 0.0382130321
## 922297 1.66440651 0.213774641 -0.147942249 -0.196878516 -0.5559910407
## 922576 1.92598353 1.136739705 0.477781900 -1.156482818 0.2021640255
## 922577 4.23349159 -0.184110499 -0.326131445 0.587786142 0.7040073381
## 922840 2.67551655 -2.313756961 -0.053800867 0.340150357 -0.4502519824
## 923169 3.83312511 -0.495813665 0.922428047 -0.551386509 -0.0799652223
## 923465 2.54919727 -0.228129228 1.412934778 -1.969057256 1.4550448383
## 923748 4.69079604 0.766803238 1.542607509 -0.778334167 0.7842069600
## 923780 2.02325691 -1.260133116 0.504482203 -1.134529125 0.1141621816
## 924084 2.89340232 1.450359601 0.779859803 -2.967836815 0.3568359788
## 924342 3.49912218 -1.799249342 2.764024589 -0.865545694 0.6248149194
## 924632 2.15201013 0.829339088 0.564300199 -3.009108230 -0.5653278607
## 924934 2.05327740 -1.615038205 1.837342797 -3.110797801 -0.2108571316
## 924964 3.87388097 -1.083301553 1.858308794 -0.433358360 1.6859553304
## 925236 4.06028949 -0.122061034 3.235925374 -3.466133119 2.2399371646
## 925277 0.09858059 0.213372093 0.388587548 -1.011820230 -2.9864399976
## 925291 1.08841850 -1.291711328 1.428122289 -3.369171941 -0.9465087393
## 925292 0.48134743 0.177863190 1.031200235 -2.008512908 -0.3268156112
## 925311 4.86602793 2.129232607 3.411187296 -5.129474909 0.4884909563
## 925622 -5.91241029 -3.479575000 -3.259923297 -3.914141413 -1.7148732547
## 926125 -8.73365338 0.573350185 0.896301447 0.384811315 -0.6784463175
## 926424 -6.43365455 3.573672989 2.457324373 1.176279049 0.0747585153
## 926682 -3.79004753 3.580897052 2.086640366 -2.503824654 0.5102735378
## 926954 -1.25507494 1.900624364 0.562235817 -2.087390339 -1.8084001296
## 927241 -10.36567336 -1.670540206 -1.875379194 -2.353959892 0.0337122683
## 92751 5.47042990 0.670047220 1.489132801 -2.297135901 0.1845409324
## PC6 PC7
## 842302 1.410183639 2.1574715203
## 842517 0.028631162 0.0133463502
## 84300903 0.540976145 -0.6675790845
## 84348301 3.050737497 1.4286536346
## 84358402 -1.225416405 -0.9353895017
## 843786 -0.450642134 0.4900139551
## 844359 -0.128835073 -0.3013023315
## 84458202 -1.255934103 0.9732434974
## 844981 0.559052820 -0.2149145974
## 84501001 -0.723272337 2.5176245802
## 845636 0.127219899 0.6244628561
## 84610002 0.764194227 0.6655068738
## 846226 2.592290301 0.9406696600
## 846381 1.006774257 -1.7974995418
## 84667401 -0.349408795 0.7422274132
## 84799002 0.495342130 0.9142524133
## 848406 -0.761520960 -0.0867706702
## 84862001 -0.751827782 0.4415962916
## 849014 -1.136688687 -0.2510619539
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## 9110127 0.143526659 -0.4567092765
## 9110720 -0.699155425 -0.4977435511
## 9110732 -0.598086185 -0.4691884880
## 9110944 1.534348384 -0.2905432068
## 911150 0.012054627 -0.1010876325
## 911157302 -1.422336801 -0.6695517414
## 9111596 0.342133611 0.9291469178
## 9111805 -1.829924638 -2.4021852235
## 9111843 -0.484220288 0.0429605111
## 911201 -0.482435963 -0.5070647518
## 911202 0.972979646 -0.1503289773
## 9112085 -1.198785425 0.3364916499
## 9112366 -0.225426032 -0.7491044280
## 9112367 -0.571668797 -0.3612489115
## 9112594 -0.482141691 -0.1794272022
## 9112712 -0.309548924 0.2304236421
## 911296201 -0.999041862 1.1146528459
## 911296202 -1.123832614 4.9581336925
## 9113156 0.488325468 -0.0462299464
## 911320501 0.344589192 -0.0765341769
## 911320502 -0.658253511 -0.3129584449
## 9113239 0.223223930 1.4700860059
## 9113455 -0.555212156 -0.2170958245
## 9113514 0.076677038 0.6404792504
## 9113538 -1.099270464 2.0225405128
## 911366 -2.425717007 -0.9408861129
## 9113778 0.924815954 0.4955679709
## 9113816 0.104368624 0.3193046533
## 911384 0.614923390 0.2799737367
## 9113846 0.889614864 0.9246961441
## 911391 -0.419258899 1.2867603886
## 911408 0.367305570 -0.3444775333
## 911654 -0.049155752 0.2225068454
## 911673 1.337188809 0.5365858519
## 911685 -0.024030956 0.2726963978
## 911916 0.808383394 -1.5668970121
## 912193 -0.544923618 0.6168567753
## 91227 -0.020448924 0.5596010017
## 912519 -0.015465239 0.0341998123
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## 913063 1.555748208 -0.0074068986
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## 913535 3.200742182 0.1681848622
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## 914062 0.929231997 -0.1972060738
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## 915143 0.066333057 1.1529703725
## 915186 -2.200919526 1.0250951989
## 915276 -3.508790828 0.6042606963
## 91544001 -0.484723076 -0.1359505647
## 91544002 -1.947329468 0.4881934312
## 915452 -0.833977551 -1.4088879023
## 915460 -1.602111794 -1.0533691956
## 91550 0.253668588 0.5472551225
## 915664 0.032979942 -0.8752970956
## 915691 -0.136700223 0.3929176231
## 915940 0.072494321 -0.1758143289
## 91594602 -0.773624515 -0.1454686759
## 916221 0.046608047 -1.0005231004
## 916799 -0.491293222 -0.5167539200
## 916838 -1.017677377 -0.0261084918
## 917062 -1.286369931 0.7480548590
## 917080 -0.265206232 0.1942744924
## 917092 -0.548135411 -0.8140726857
## 91762702 -0.006685146 0.9611743974
## 91789 0.097095633 0.7218828231
## 917896 -0.600188263 0.1391868086
## 917897 -1.401965911 0.9527774834
## 91805 -1.210209018 0.8160391133
## 91813701 -0.364718273 -0.0462160782
## 91813702 0.325770470 -0.0944504391
## 918192 -1.686010994 -1.7109061685
## 918465 -0.851940525 -0.0288485824
## 91858 -1.101161685 0.0869517853
## 91903901 -0.289073515 0.4730366470
## 91903902 -0.197903630 0.4337496082
## 91930402 1.934520374 -0.7275859760
## 919537 -1.550311718 -0.7176961616
## 919555 0.578720770 -0.5430102167
## 91979701 -0.523378449 -1.1495594767
## 919812 -2.337461193 -0.4830815304
## 921092 0.042391707 2.1668488112
## 921362 -1.158207647 0.1913668076
## 921385 -1.188472456 -0.6771595730
## 921386 0.425520296 0.3979358310
## 921644 0.765081147 -0.4663049042
## 922296 0.068753051 -0.4148574879
## 922297 -0.930763180 0.5238585798
## 922576 0.114797260 -0.1161527345
## 922577 -0.145962831 0.2596286888
## 922840 -0.677751360 0.0640445882
## 923169 -0.112569772 0.4740694793
## 923465 0.854769667 1.0210226174
## 923748 0.850625097 0.7520064103
## 923780 1.783207929 0.3901520318
## 924084 -0.582689902 -0.6178681677
## 924342 0.411907169 -0.3073955477
## 924632 -0.549918834 -0.4839795902
## 924934 -1.640362885 -1.0878956916
## 924964 -0.814176294 -0.4706597676
## 925236 0.174755382 1.0763071056
## 925277 0.012441261 -0.2900018002
## 925291 -1.724352624 -0.3536636324
## 925292 -0.991190143 -0.0485030055
## 925311 -1.109815814 0.4879418774
## 925622 1.012707855 0.2712037562
## 926125 -0.300488375 0.0947410215
## 926424 -2.373104852 -0.5956056075
## 926682 -0.246493221 -0.7156966020
## 926954 -0.533977345 -0.1925887705
## 927241 0.567437190 0.2228855560
## 92751 1.616415088 1.6974579729Final - clustering on PCA results
- Using the minimum number of principal components required to describe at least 90% of the variability in the data, create a hierarchical clustering model with complete linkage. Assign the results to
wisc.pr.hclust. recall check on previous output it requires 5 to achieve 80% and 7 to achieve 90%
wisc.pr.hclust <- hclust(dist(wisc.pr$x[, 1:7]), method = "complete")- cut the model into 4 clusters
wisc.pr.hclust.clusters <- cutree(wisc.pr.hclust, k = 4)- compare results
# Compare to actual diagnoses
table(wisc.pr.hclust.clusters, diagnosis)## diagnosis
## wisc.pr.hclust.clusters 0 1
## 1 5 113
## 2 350 97
## 3 2 0
## 4 0 2# Compare to k-means and hierarchical
table(diagnosis, wisc.hclust.clusters)## wisc.hclust.clusters
## diagnosis 1 2 3 4
## 0 12 2 343 0
## 1 165 5 40 2table(diagnosis, wisc.km$cluster)##
## diagnosis 1 2
## 0 343 14
## 1 37 175