ML_Homework6: Topics on Support Vector
Andrew Zhang
Tuesday, April 07, 2015
R packages used in this assignment:
1. e1071: library for Support Vector Machine
2. randomForest: Breiman and Cutler’s random forests for classification and regression
3. glmnet: Lasso and Elastic-Net Regularized Generalized Linear Models
4. mlbench: Machine Learning Benchmark Problems
Question 1: In a past homework, you performed ridge regression on the wine quality data set. Now use a support vector machine to classify these data.
1a) First classify the data treating the last column as an ordered factor (the wine tasters score). Next treat the last column as a numeric. Which SVM implementation is better? Why do you think it is better?
1b) Using the best version choose two attributes and a slice through the data to plot. Choose a different set of attributes and another set of slices to plot.
1c) Compare and contrast the best version of the SVM with the ridge regression model.
rm(list=ls())
setwd("c:/Users/Andrew/SkyDrive/AGZ_Home/workspace_R/UCSC/MachinLearning/All_data")
wine<-read.csv("winequality-red.csv",header=TRUE,sep=";")
summary(wine)## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 4.60 Min. :0.1200 Min. :0.000 Min. : 0.900
## 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090 1st Qu.: 1.900
## Median : 7.90 Median :0.5200 Median :0.260 Median : 2.200
## Mean : 8.32 Mean :0.5278 Mean :0.271 Mean : 2.539
## 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420 3rd Qu.: 2.600
## Max. :15.90 Max. :1.5800 Max. :1.000 Max. :15.500
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :0.01200 Min. : 1.00 Min. : 6.00
## 1st Qu.:0.07000 1st Qu.: 7.00 1st Qu.: 22.00
## Median :0.07900 Median :14.00 Median : 38.00
## Mean :0.08747 Mean :15.87 Mean : 46.47
## 3rd Qu.:0.09000 3rd Qu.:21.00 3rd Qu.: 62.00
## Max. :0.61100 Max. :72.00 Max. :289.00
## density pH sulphates alcohol
## Min. :0.9901 Min. :2.740 Min. :0.3300 Min. : 8.40
## 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500 1st Qu.: 9.50
## Median :0.9968 Median :3.310 Median :0.6200 Median :10.20
## Mean :0.9967 Mean :3.311 Mean :0.6581 Mean :10.42
## 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300 3rd Qu.:11.10
## Max. :1.0037 Max. :4.010 Max. :2.0000 Max. :14.90
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.636
## 3rd Qu.:6.000
## Max. :8.000#library for Support Vector Machine
library(e1071)## Warning: package 'e1071' was built under R version 3.1.3str(wine$quality)## int [1:1599] 5 5 5 6 5 5 5 7 7 5 ...x <- subset(wine, select = -quality)
y <-as.numeric(wine$quality)
# 1a) First classify the data treating the last column as an ordered factor
# (the wine tasters score).
wine_factor<-cbind(x, quality=as.factor(y))
str(wine_factor)## 'data.frame': 1599 obs. of 12 variables:
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : Factor w/ 6 levels "3","4","5","6",..: 3 3 3 4 3 3 3 5 5 3 ...wineTrain<-wine_factor[1:1400,]
wineTest<-wine_factor[1401:1599,]
x_factor <- subset(wineTest, select = -quality)
y_factor <- wineTest$quality
wine_svm <- svm(quality ~ ., data = wineTrain)
summary(wine_svm)##
## Call:
## svm(formula = quality ~ ., data = wineTrain)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: radial
## cost: 1
## gamma: 0.09090909
##
## Number of Support Vectors: 1166
##
## ( 430 496 172 46 15 7 )
##
##
## Number of Classes: 6
##
## Levels:
## 3 4 5 6 7 8# gamma: 0.0909 cost: 1
wine_factor_predict <- predict(wine_svm, x_factor);
1-sum(wine_factor_predict == y_factor)/length(y_factor)## [1] 0.4371859## tune `svm' for classification with RBF-kernel (default in svm),
## using one split for training/validation set
# gamma = 0.06 0.07 0.08 0.09 0.10 0.11; cost = 1.0 1.5 2.0 2.5 3.0 3.5
wine_svm_tuned <- tune(svm, quality~., data = wineTrain,
ranges = list(gamma = seq(.05,.11,.01), cost = seq(1,4,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
summary(wine_svm_tuned)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## gamma cost
## 0.1 1.5
##
## - best performance: 0.3621429
##
## - Detailed performance results:
## gamma cost error dispersion
## 1 0.05 1.0 0.3764286 0.03595948
## 2 0.06 1.0 0.3742857 0.03353679
## 3 0.07 1.0 0.3728571 0.03363806
## 4 0.08 1.0 0.3735714 0.03384807
## 5 0.09 1.0 0.3735714 0.04041312
## 6 0.10 1.0 0.3678571 0.04127366
## 7 0.11 1.0 0.3678571 0.03842860
## 8 0.05 1.5 0.3771429 0.03746503
## 9 0.06 1.5 0.3757143 0.03502510
## 10 0.07 1.5 0.3714286 0.03779645
## 11 0.08 1.5 0.3642857 0.03897787
## 12 0.09 1.5 0.3628571 0.03981249
## 13 0.10 1.5 0.3621429 0.03810268
## 14 0.11 1.5 0.3628571 0.03850965
## 15 0.05 2.0 0.3750000 0.03661561
## 16 0.06 2.0 0.3707143 0.03649154
## 17 0.07 2.0 0.3692857 0.03719929
## 18 0.08 2.0 0.3678571 0.03722975
## 19 0.09 2.0 0.3635714 0.03904326
## 20 0.10 2.0 0.3628571 0.03512207
## 21 0.11 2.0 0.3650000 0.03554723
## 22 0.05 2.5 0.3757143 0.03598312
## 23 0.06 2.5 0.3721429 0.03756325
## 24 0.07 2.5 0.3700000 0.03654587
## 25 0.08 2.5 0.3642857 0.03955535
## 26 0.09 2.5 0.3671429 0.03486287
## 27 0.10 2.5 0.3664286 0.03532326
## 28 0.11 2.5 0.3657143 0.03607752
## 29 0.05 3.0 0.3714286 0.03688556
## 30 0.06 3.0 0.3728571 0.03761603
## 31 0.07 3.0 0.3692857 0.03970555
## 32 0.08 3.0 0.3664286 0.03467537
## 33 0.09 3.0 0.3671429 0.03598312
## 34 0.10 3.0 0.3685714 0.03566663
## 35 0.11 3.0 0.3657143 0.03821410
## 36 0.05 3.5 0.3742857 0.03782643
## 37 0.06 3.5 0.3728571 0.03670066
## 38 0.07 3.5 0.3700000 0.03607752
## 39 0.08 3.5 0.3671429 0.03453612
## 40 0.09 3.5 0.3700000 0.03654587
## 41 0.10 3.5 0.3685714 0.03767627
## 42 0.11 3.5 0.3721429 0.03875178
## 43 0.05 4.0 0.3728571 0.03731341
## 44 0.06 4.0 0.3692857 0.04027260
## 45 0.07 4.0 0.3707143 0.03602248
## 46 0.08 4.0 0.3700000 0.03463447
## 47 0.09 4.0 0.3692857 0.03689324
## 48 0.10 4.0 0.3707143 0.03933258
## 49 0.11 4.0 0.3714286 0.04123930plot(wine_svm_tuned)
# took long time ...
wine_svm_tuned$best.parameters## gamma cost
## 13 0.1 1.5# using gamma = 0.07 cost = 1.5
wine_svm <- svm(quality ~ ., data = wineTrain, gamma = 0.07, cost = 1.5)
wine_factor_predict <- predict(wine_svm, x_factor);
1-sum(wine_factor_predict == y_factor)/length(y_factor)## [1] 0.4371859# Next treat the last column as a numeric.
wine_numeric<-cbind(x, quality=y)
str(wine_numeric)## 'data.frame': 1599 obs. of 12 variables:
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : num 5 5 5 6 5 5 5 7 7 5 ...wineTrain<-wine_numeric[1:1400,]
wineTest<-wine_numeric[1401:1599,]
x_factor <- subset(wineTest, select = -quality)
y_factor <- wineTest$quality
wine_svm <- svm(quality ~ ., data = wineTrain)
summary(wine_svm)##
## Call:
## svm(formula = quality ~ ., data = wineTrain)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 1
## gamma: 0.09090909
## epsilon: 0.1
##
##
## Number of Support Vectors: 1162# gamma: 0.0909 cost: 1
wine_factor_predict <- predict(wine_svm, x_factor);
sqrt( sum((wineTest$quality-wine_factor_predict)^2))/length(wine_factor_predict)## [1] 0.04847373#[1] 0.04847373
## tune `svm' for classification with RBF-kernel (default in svm),
## using one split for training/validation set
# gamma = 0.06 0.07 0.08 0.09 0.10 0.11; cost = 1.0 1.5 2.0 2.5 3.0 3.5
wine_svm_tuned <- tune(svm, quality~., data = wineTrain,
ranges = list(gamma = seq(.05,.11,.01), cost = seq(1,4,0.5)),
tunecontrol = tune.control(sampling = "cross")
) # This took a long time also.
summary(wine_svm_tuned)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## gamma cost
## 0.11 1.5
##
## - best performance: 0.3779477
##
## - Detailed performance results:
## gamma cost error dispersion
## 1 0.05 1.0 0.3933767 0.03111975
## 2 0.06 1.0 0.3894143 0.03040395
## 3 0.07 1.0 0.3859173 0.02794516
## 4 0.08 1.0 0.3836139 0.02557613
## 5 0.09 1.0 0.3820125 0.02484204
## 6 0.10 1.0 0.3806449 0.02437718
## 7 0.11 1.0 0.3798551 0.02417274
## 8 0.05 1.5 0.3887931 0.02951885
## 9 0.06 1.5 0.3860247 0.02670351
## 10 0.07 1.5 0.3827143 0.02435098
## 11 0.08 1.5 0.3805294 0.02319417
## 12 0.09 1.5 0.3789467 0.02276341
## 13 0.10 1.5 0.3781318 0.02331553
## 14 0.11 1.5 0.3779477 0.02422690
## 15 0.05 2.0 0.3876178 0.02826725
## 16 0.06 2.0 0.3834809 0.02450302
## 17 0.07 2.0 0.3809698 0.02302295
## 18 0.08 2.0 0.3788462 0.02231663
## 19 0.09 2.0 0.3783697 0.02356869
## 20 0.10 2.0 0.3786191 0.02504706
## 21 0.11 2.0 0.3797492 0.02677891
## 22 0.05 2.5 0.3860613 0.02628725
## 23 0.06 2.5 0.3824666 0.02356673
## 24 0.07 2.5 0.3795438 0.02291436
## 25 0.08 2.5 0.3787625 0.02406585
## 26 0.09 2.5 0.3791854 0.02545808
## 27 0.10 2.5 0.3804509 0.02705919
## 28 0.11 2.5 0.3820752 0.02840122
## 29 0.05 3.0 0.3845686 0.02497025
## 30 0.06 3.0 0.3809081 0.02367164
## 31 0.07 3.0 0.3790676 0.02372830
## 32 0.08 3.0 0.3790282 0.02550304
## 33 0.09 3.0 0.3804384 0.02712539
## 34 0.10 3.0 0.3824476 0.02829878
## 35 0.11 3.0 0.3835673 0.02974205
## 36 0.05 3.5 0.3835795 0.02423519
## 37 0.06 3.5 0.3802913 0.02390804
## 38 0.07 3.5 0.3786601 0.02483396
## 39 0.08 3.5 0.3800767 0.02652691
## 40 0.09 3.5 0.3820321 0.02776698
## 41 0.10 3.5 0.3831677 0.02949035
## 42 0.11 3.5 0.3854873 0.03128188
## 43 0.05 4.0 0.3822812 0.02415505
## 44 0.06 4.0 0.3797801 0.02470262
## 45 0.07 4.0 0.3792003 0.02592417
## 46 0.08 4.0 0.3811046 0.02724750
## 47 0.09 4.0 0.3829279 0.02873294
## 48 0.10 4.0 0.3847974 0.03081793
## 49 0.11 4.0 0.3886604 0.03264213plot(wine_svm_tuned)
wine_svm_tuned$best.parameters## gamma cost
## 14 0.11 1.5# using gamma = 0.1 cost = 2
wine_svm <- svm(quality ~ ., data = wineTrain, gamma = 0.1, cost = 2)
wine_factor_predict <- predict(wine_svm, x_factor);
sqrt(sum((wineTest$quality-wine_factor_predict)^2))/length(wine_factor_predict)## [1] 0.04952251#[1] 0.04952251
# Which SVM implementation is better? Why do you think it is better?
print("quality as factor had error = 0.437 but numeric quality had small error = 0.0495")## [1] "quality as factor had error = 0.437 but numeric quality had small error = 0.0495"print("Regression is better than classification")## [1] "Regression is better than classification"Quesiton 2: Classify the sonar data set.
2a) Use a support vector machine to classify the sonar data set. First tune an SVM employing radial basis function (default). Next tune an SVM employing a linear kernel. Compare the results.
setwd("c:/Users/Andrew/SkyDrive/AGZ_Home/workspace_R/UCSC/MachinLearning/All_data")
sonarTest<-read.csv("sonar_test.csv",header=FALSE)
sonarTest$V61[sonarTest$V61 == -1]<-0
sonarTrain<-read.csv("sonar_train.csv",header=FALSE)
sonarTrain$V61[sonarTrain$V61 == -1]<-0
x <- subset(sonarTest, select = -V61)
y <- sonarTest$V61
sonar_svm <- svm(V61 ~ ., data = sonarTrain)
summary(sonar_svm)##
## Call:
## svm(formula = V61 ~ ., data = sonarTrain)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 1
## gamma: 0.01666667
## epsilon: 0.1
##
##
## Number of Support Vectors: 111# cost: 1 gamma: 0.01666667
sonar_predict <- predict(sonar_svm, x);
sqrt(sum((y-sonar_predict)^2))/length(sonarTest)## [1] 0.05062342#[1] 0.05062342
## tune `svm' for classification with RBF-kernel (default in svm),
## using one split for training/validation set
# gamma = 0.0 0.01 0.02 0.03 0.04 0.05; cost = 1.0 1.5 2.0 2.5 3.0 3.5
sonar_svm_tuned <- tune(svm, V61~., data = sonarTrain,
ranges = list(gamma = seq(0,.05,.01), cost = seq(1,4,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
summary(sonar_svm_tuned)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## gamma cost
## 0.02 4
##
## - best performance: 0.1170109
##
## - Detailed performance results:
## gamma cost error dispersion
## 1 0.00 1.0 0.5007608 0.06359573
## 2 0.01 1.0 0.1544112 0.05267355
## 3 0.02 1.0 0.1407517 0.05224512
## 4 0.03 1.0 0.1395238 0.04443672
## 5 0.04 1.0 0.1448254 0.03794580
## 6 0.05 1.0 0.1523087 0.03336457
## 7 0.00 1.5 0.5007608 0.06359573
## 8 0.01 1.5 0.1484291 0.05476681
## 9 0.02 1.5 0.1327762 0.04671820
## 10 0.03 1.5 0.1307349 0.03825207
## 11 0.04 1.5 0.1382642 0.03405481
## 12 0.05 1.5 0.1484242 0.03128048
## 13 0.00 2.0 0.5007608 0.06359573
## 14 0.01 2.0 0.1445690 0.05426878
## 15 0.02 2.0 0.1256375 0.04116307
## 16 0.03 2.0 0.1267979 0.03552814
## 17 0.04 2.0 0.1372200 0.03343265
## 18 0.05 2.0 0.1484109 0.03130288
## 19 0.00 2.5 0.5007608 0.06359573
## 20 0.01 2.5 0.1420114 0.05169829
## 21 0.02 2.5 0.1216924 0.03737395
## 22 0.03 2.5 0.1256515 0.03480375
## 23 0.04 2.5 0.1372200 0.03343265
## 24 0.05 2.5 0.1484109 0.03130288
## 25 0.00 3.0 0.5007608 0.06359573
## 26 0.01 3.0 0.1399669 0.04958882
## 27 0.02 3.0 0.1191985 0.03629600
## 28 0.03 3.0 0.1256522 0.03480335
## 29 0.04 3.0 0.1372200 0.03343265
## 30 0.05 3.0 0.1484109 0.03130288
## 31 0.00 3.5 0.5007608 0.06359573
## 32 0.01 3.5 0.1371179 0.04736768
## 33 0.02 3.5 0.1175965 0.03528741
## 34 0.03 3.5 0.1256522 0.03480335
## 35 0.04 3.5 0.1372200 0.03343265
## 36 0.05 3.5 0.1484109 0.03130288
## 37 0.00 4.0 0.5007608 0.06359573
## 38 0.01 4.0 0.1340051 0.04544560
## 39 0.02 4.0 0.1170109 0.03499190
## 40 0.03 4.0 0.1256522 0.03480335
## 41 0.04 4.0 0.1372200 0.03343265
## 42 0.05 4.0 0.1484109 0.03130288plot(sonar_svm_tuned)
sonar_svm_tuned$best.parameters## gamma cost
## 39 0.02 4# gamma = 0.02, cost = 4
sonar_svm <- svm(V61 ~ ., data = sonarTrain, gamma = 0.02, cost = 4)
sonar_predict <- predict(sonar_svm, x);
sqrt(sum((y-sonar_predict)^2))/length(y)## [1] 0.03728963#[1] 0.03728963
#2a) Next tune an SVM employing a linear kernel. Compare the results.
sonar_svm <- svm(V61 ~ ., data = sonarTrain, kernel="linear")
summary(sonar_svm)##
## Call:
## svm(formula = V61 ~ ., data = sonarTrain, kernel = "linear")
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: linear
## cost: 1
## gamma: 0.01666667
## epsilon: 0.1
##
##
## Number of Support Vectors: 120#gamma = 0.01666667, cost = 1
## tune `svm' for classification with kernel = "linear",
## using one split for training/validation set
# gamma = 0.0 0.01 0.02 0.03 0.04 0.05; cost = 1.0 1.5 2.0 2.5 3.0 3.5
sonar_svm_tuned <- tune(svm, V61~., data = sonarTrain, kernel="linear",
ranges = list(gamma = seq(0,.05,.01), cost = seq(1,4,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
summary(sonar_svm_tuned)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## gamma cost
## 0 1
##
## - best performance: 0.3313263
##
## - Detailed performance results:
## gamma cost error dispersion
## 1 0.00 1.0 0.3313263 0.1460075
## 2 0.01 1.0 0.3313263 0.1460075
## 3 0.02 1.0 0.3313263 0.1460075
## 4 0.03 1.0 0.3313263 0.1460075
## 5 0.04 1.0 0.3313263 0.1460075
## 6 0.05 1.0 0.3313263 0.1460075
## 7 0.00 1.5 0.3454587 0.1468720
## 8 0.01 1.5 0.3454587 0.1468720
## 9 0.02 1.5 0.3454587 0.1468720
## 10 0.03 1.5 0.3454587 0.1468720
## 11 0.04 1.5 0.3454587 0.1468720
## 12 0.05 1.5 0.3454587 0.1468720
## 13 0.00 2.0 0.3516189 0.1494875
## 14 0.01 2.0 0.3516189 0.1494875
## 15 0.02 2.0 0.3516189 0.1494875
## 16 0.03 2.0 0.3516189 0.1494875
## 17 0.04 2.0 0.3516189 0.1494875
## 18 0.05 2.0 0.3516189 0.1494875
## 19 0.00 2.5 0.3605445 0.1509295
## 20 0.01 2.5 0.3605445 0.1509295
## 21 0.02 2.5 0.3605445 0.1509295
## 22 0.03 2.5 0.3605445 0.1509295
## 23 0.04 2.5 0.3605445 0.1509295
## 24 0.05 2.5 0.3605445 0.1509295
## 25 0.00 3.0 0.3644351 0.1505470
## 26 0.01 3.0 0.3644351 0.1505470
## 27 0.02 3.0 0.3644351 0.1505470
## 28 0.03 3.0 0.3644351 0.1505470
## 29 0.04 3.0 0.3644351 0.1505470
## 30 0.05 3.0 0.3644351 0.1505470
## 31 0.00 3.5 0.3680924 0.1524489
## 32 0.01 3.5 0.3680924 0.1524489
## 33 0.02 3.5 0.3680924 0.1524489
## 34 0.03 3.5 0.3680924 0.1524489
## 35 0.04 3.5 0.3680924 0.1524489
## 36 0.05 3.5 0.3680924 0.1524489
## 37 0.00 4.0 0.3726178 0.1532045
## 38 0.01 4.0 0.3726178 0.1532045
## 39 0.02 4.0 0.3726178 0.1532045
## 40 0.03 4.0 0.3726178 0.1532045
## 41 0.04 4.0 0.3726178 0.1532045
## 42 0.05 4.0 0.3726178 0.1532045plot(sonar_svm_tuned)
sonar_svm_tuned$best.parameters## gamma cost
## 1 0 1# gamma = 0, cost = 1
sonar_svm <- svm(V61 ~ ., data = sonarTrain, gamma = 0, cost = 1, kernel="linear")
sonar_predict <- predict(sonar_svm, x);
error <- sqrt(sum((y-sonar_predict)^2))/length(y)
#[1] 0.058146812b) In past homework, trees were used to classify the sonar data. Compare the best result using trees with the best result using SVM.
print("In Homework 2 Problem 4 Sonar Test Error using trees was 0.2564103")## [1] "In Homework 2 Problem 4 Sonar Test Error using trees was 0.2564103"paste("Smaller Sonar Test Error using SVM was",error)## [1] "Smaller Sonar Test Error using SVM was 0.0581468133184799"Question 3. The in class example (svm1.r) used the glass data set. Use the Random Forest technique on the glass data. Compare the Random Forest results with the results obtained in class with SVM.
library(randomForest)## Warning: package 'randomForest' was built under R version 3.1.3## randomForest 4.6-10
## Type rfNews() to see new features/changes/bug fixes.library(mlbench)## Warning: package 'mlbench' was built under R version 3.1.3#install.packages("mlbench")
data(Glass, package = "mlbench")
str(Glass)## 'data.frame': 214 obs. of 10 variables:
## $ RI : num 1.52 1.52 1.52 1.52 1.52 ...
## $ Na : num 13.6 13.9 13.5 13.2 13.3 ...
## $ Mg : num 4.49 3.6 3.55 3.69 3.62 3.61 3.6 3.61 3.58 3.6 ...
## $ Al : num 1.1 1.36 1.54 1.29 1.24 1.62 1.14 1.05 1.37 1.36 ...
## $ Si : num 71.8 72.7 73 72.6 73.1 ...
## $ K : num 0.06 0.48 0.39 0.57 0.55 0.64 0.58 0.57 0.56 0.57 ...
## $ Ca : num 8.75 7.83 7.78 8.22 8.07 8.07 8.17 8.24 8.3 8.4 ...
## $ Ba : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Fe : num 0 0 0 0 0 0.26 0 0 0 0.11 ...
## $ Type: Factor w/ 6 levels "1","2","3","5",..: 1 1 1 1 1 1 1 1 1 1 ...Glass$Type## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [36] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [71] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [106] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [141] 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5
## [176] 5 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
## [211] 7 7 7 7
## Levels: 1 2 3 5 6 7index <- 1:nrow(Glass)
set.seed(pi)
testindex <- sample(index, trunc(length(index)/3))
testset <- Glass[testindex, ]
trainset <- Glass[-testindex, ]
x <- subset(trainset, select=-Type)
y <- trainset$Type
rf_Glass_Model <- randomForest(x,y)
xTest <- subset(testset, select=-Type)
yTest <- testset$Type
predictGlass <- predict(rf_Glass_Model, xTest)
error <- 1-sum(predictGlass == yTest)/length(yTest)
#[1] 0
paste("Random Forest, with seed = pi, error =",error)## [1] "Random Forest, with seed = pi, error = 0.183098591549296"print("From class example, with seed = pi, error = 0.3239437")## [1] "From class example, with seed = pi, error = 0.3239437"Question 4. Choose a new data set which we haven’t used in class yet (suggestion: choose one from http://archive.ics.uci.edu/ml/.) Use SVM to classify the data set. Try different kernels. Does changing the kernel make a difference? Which kernel resulted in the smallest error? Use another technique to classify the data set. Which resulted in the better model? (Make sure you describe the data set)
setwd("c:/Users/Andrew/SkyDrive/AGZ_Home/workspace_R/UCSC/MachinLearning/All_data")
abalone <- read.csv(file="abalone.data",header=FALSE)
head(abalone)## V1 V2 V3 V4 V5 V6 V7 V8 V9
## 1 M 0.455 0.365 0.095 0.5140 0.2245 0.1010 0.150 15
## 2 M 0.350 0.265 0.090 0.2255 0.0995 0.0485 0.070 7
## 3 F 0.530 0.420 0.135 0.6770 0.2565 0.1415 0.210 9
## 4 M 0.440 0.365 0.125 0.5160 0.2155 0.1140 0.155 10
## 5 I 0.330 0.255 0.080 0.2050 0.0895 0.0395 0.055 7
## 6 I 0.425 0.300 0.095 0.3515 0.1410 0.0775 0.120 8colnames(abalone)<- c("Sex","Length","Diameter","Height","Whole weight", "Shucked weight", "Viscera weight", "Shell weight", "Rings")
str(abalone)## 'data.frame': 4177 obs. of 9 variables:
## $ Sex : Factor w/ 3 levels "F","I","M": 3 3 1 3 2 2 1 1 3 1 ...
## $ Length : num 0.455 0.35 0.53 0.44 0.33 0.425 0.53 0.545 0.475 0.55 ...
## $ Diameter : num 0.365 0.265 0.42 0.365 0.255 0.3 0.415 0.425 0.37 0.44 ...
## $ Height : num 0.095 0.09 0.135 0.125 0.08 0.095 0.15 0.125 0.125 0.15 ...
## $ Whole weight : num 0.514 0.226 0.677 0.516 0.205 ...
## $ Shucked weight: num 0.2245 0.0995 0.2565 0.2155 0.0895 ...
## $ Viscera weight: num 0.101 0.0485 0.1415 0.114 0.0395 ...
## $ Shell weight : num 0.15 0.07 0.21 0.155 0.055 0.12 0.33 0.26 0.165 0.32 ...
## $ Rings : int 15 7 9 10 7 8 20 16 9 19 ...# Use SVM to classify the data set. Try different kernels.
abaloneTrain<-abalone[1:2500,]
abaloneTest<-abalone[2501:4177,]
x <- subset(abaloneTest, select = -Rings)
y <- abaloneTest$Rings
abalone_svm <- svm(Rings ~ ., data = abaloneTrain)
summary(abalone_svm)##
## Call:
## svm(formula = Rings ~ ., data = abaloneTrain)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 1
## gamma: 0.1
## epsilon: 0.1
##
##
## Number of Support Vectors: 2045# cost: 1 gamma: 0.1
abalone_predict <- predict(abalone_svm, x);
sqrt(sum((y-abalone_predict)^2))/length(y)## [1] 0.04347119#[1] 0.04347144
## tune `svm' for classification with kernel = "radial basis" (default),
## using one split for training/validation set
# gamma = 0.0 0.1 0.2 0.3 0.4; cost = 1.0 1.5 2.0 2.5 3.0 3.5
abalone_svm_tuned <- tune(svm, Rings ~., data = abaloneTrain,
ranges = list(gamma = seq(0,.4,.1), cost = seq(1,3,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
summary(abalone_svm_tuned)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## gamma cost
## 0.1 3
##
## - best performance: 5.281191
##
## - Detailed performance results:
## gamma cost error dispersion
## 1 0.0 1.0 12.414036 1.3636946
## 2 0.1 1.0 5.329160 0.5056530
## 3 0.2 1.0 5.323441 0.5037028
## 4 0.3 1.0 5.347942 0.5134076
## 5 0.4 1.0 5.408453 0.5359393
## 6 0.0 1.5 12.414036 1.3636946
## 7 0.1 1.5 5.308079 0.4842634
## 8 0.2 1.5 5.305380 0.4857427
## 9 0.3 1.5 5.345411 0.5042479
## 10 0.4 1.5 5.400286 0.5293523
## 11 0.0 2.0 12.414036 1.3636946
## 12 0.1 2.0 5.293217 0.4800094
## 13 0.2 2.0 5.308880 0.4833429
## 14 0.3 2.0 5.361479 0.5074635
## 15 0.4 2.0 5.403508 0.5277766
## 16 0.0 2.5 12.414036 1.3636946
## 17 0.1 2.5 5.284263 0.4767232
## 18 0.2 2.5 5.312076 0.4807368
## 19 0.3 2.5 5.368984 0.5045782
## 20 0.4 2.5 5.420778 0.5335321
## 21 0.0 3.0 12.414036 1.3636946
## 22 0.1 3.0 5.281191 0.4707592
## 23 0.2 3.0 5.319004 0.4801740
## 24 0.3 3.0 5.374947 0.5039710
## 25 0.4 3.0 5.440579 0.5386105abalone_svm_tuned$best.parameters## gamma cost
## 22 0.1 3# gamma = 0.1, cost = 2
abalone_svm <- svm(Rings ~ ., data = abaloneTrain, gamma = 0.1, cost = 2)
abalone_predict <- predict(abalone_svm, x);
rb_error <- sqrt(sum((y-abalone_predict)^2))/length(y)
rb_error #[1] 0.04342107## [1] 0.04341996# Change kernel to "linear"
abalone_svm <- svm(Rings ~ ., data = abaloneTrain, kernel="linear")
summary(abalone_svm)##
## Call:
## svm(formula = Rings ~ ., data = abaloneTrain, kernel = "linear")
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: linear
## cost: 1
## gamma: 0.1
## epsilon: 0.1
##
##
## Number of Support Vectors: 2082# cost: 1 gamma: 0.1
abalone_predict <- predict(abalone_svm, x);
sqrt(sum((y-abalone_predict)^2))/length(y)## [1] 0.0471688#[1]0.0471688
# Change kernel to "polynomial"
abalone_svm <- svm(Rings ~ ., data = abaloneTrain, kernel="polynomial")
summary(abalone_svm)##
## Call:
## svm(formula = Rings ~ ., data = abaloneTrain, kernel = "polynomial")
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: polynomial
## cost: 1
## degree: 3
## gamma: 0.1
## coef.0: 0
## epsilon: 0.1
##
##
## Number of Support Vectors: 2083# cost: 1 gamma: 0.1
abalone_predict <- predict(abalone_svm, x);
sqrt(sum((y-abalone_predict)^2))/length(y)## [1] 0.04901388#[1] 0.04901388
# Does changing the kernel make a difference?
print("Changing kernel has not made much difference")## [1] "Changing kernel has not made much difference"# Which kernel resulted in the smallest error?
print("Radial basis kernel has the smallest error")## [1] "Radial basis kernel has the smallest error"# Use another technique to classify the data set.
library(randomForest)
xTrain <- subset(abaloneTrain, select = -Rings)
yTrain <- abaloneTrain$Rings
rf_Abalone_Model <- randomForest(xTrain,yTrain)
predictAbalone <- predict(rf_Abalone_Model, x)
sqrt(sum((y-predictAbalone)^2))/length(y)## [1] 0.04631641#[1] 0.04631641
# Which resulted in the better model?
print("SVM with Radial basis kernel is better model")## [1] "SVM with Radial basis kernel is better model"Quesiton 5. Use SVM with kernel = “linear” to create regression predictions on the data set created using these lines of code:
x <- seq(0.1, 5, by = 0.05) # the observed feature
y <- log(x) + rnorm(x, sd = 0.2) # the target for the observed feature
Next try various kernels and added features with SVM. Can you improve the model by adding an extra feature which might be a function of the first feature? Compare both lm.ridge and svm. Which method produced a better model? (don’t forget to tune your models)
x <- seq(0.1, 5, by = 0.05) # the observed feature
y <- log(x) + rnorm(x, sd = 0.2) # the target for the observed feature
dataset <- as.data.frame(cbind(x,y))
str(dataset)## 'data.frame': 99 obs. of 2 variables:
## $ x: num 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 ...
## $ y: num -2.3 -2.29 -1.81 -1.44 -1.11 ...dataset_svm <- svm(y ~ ., data = dataset, kernel = "linear")
summary(dataset_svm)##
## Call:
## svm(formula = y ~ ., data = dataset, kernel = "linear")
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: linear
## cost: 1
## gamma: 1
## epsilon: 0.1
##
##
## Number of Support Vectors: 80#gamma = 1 cost = 1
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.04381142#[1] 0.04381142
## tune `svm' for classification with kernel = "linear",
## using one split for training/validation set
# gamma = 0.0 0.5 1.0 1.5 2.0; cost = 1.0 1.5 2.0 2.5 3.0 3.5
dataset_svm_tuned <- tune(svm, y~., data = dataset, kernel="linear",
ranges = list(gamma = seq(0,2,.5), cost = seq(1,3.5,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
summary(dataset_svm_tuned)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## gamma cost
## 0 3
##
## - best performance: 0.1908039
##
## - Detailed performance results:
## gamma cost error dispersion
## 1 0.0 1.0 0.1912521 0.1463126
## 2 0.5 1.0 0.1912521 0.1463126
## 3 1.0 1.0 0.1912521 0.1463126
## 4 1.5 1.0 0.1912521 0.1463126
## 5 2.0 1.0 0.1912521 0.1463126
## 6 0.0 1.5 0.1908978 0.1460247
## 7 0.5 1.5 0.1908978 0.1460247
## 8 1.0 1.5 0.1908978 0.1460247
## 9 1.5 1.5 0.1908978 0.1460247
## 10 2.0 1.5 0.1908978 0.1460247
## 11 0.0 2.0 0.1913567 0.1456044
## 12 0.5 2.0 0.1913567 0.1456044
## 13 1.0 2.0 0.1913567 0.1456044
## 14 1.5 2.0 0.1913567 0.1456044
## 15 2.0 2.0 0.1913567 0.1456044
## 16 0.0 2.5 0.1912236 0.1456750
## 17 0.5 2.5 0.1912236 0.1456750
## 18 1.0 2.5 0.1912236 0.1456750
## 19 1.5 2.5 0.1912236 0.1456750
## 20 2.0 2.5 0.1912236 0.1456750
## 21 0.0 3.0 0.1908039 0.1450031
## 22 0.5 3.0 0.1908039 0.1450031
## 23 1.0 3.0 0.1908039 0.1450031
## 24 1.5 3.0 0.1908039 0.1450031
## 25 2.0 3.0 0.1908039 0.1450031
## 26 0.0 3.5 0.1908219 0.1450436
## 27 0.5 3.5 0.1908219 0.1450436
## 28 1.0 3.5 0.1908219 0.1450436
## 29 1.5 3.5 0.1908219 0.1450436
## 30 2.0 3.5 0.1908219 0.1450436plot(dataset_svm_tuned)
dataset_svm_tuned$best.parameters## gamma cost
## 21 0 3#gamma = 0, cost = 2.5
dataset_svm <- svm(y ~ ., data = dataset, kernel = "linear", gamma=0, cost=2.5)
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.04361607#[1] 0.04361607
#5) Next try various kernels and added features with SVM.
# Kernel = Radial Basis (default)
dataset_svm <- svm(y ~ ., data = dataset)
summary(dataset_svm)##
## Call:
## svm(formula = y ~ ., data = dataset)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: radial
## cost: 1
## gamma: 1
## epsilon: 0.1
##
##
## Number of Support Vectors: 73#gamma = 1 cost = 1
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.0282729#[1] 0.0282729
## tune `svm' for classification with kernel = radial basis,
## using one split for training/validation set
# gamma = 0.0 0.5 1.0 1.5 2.0; cost = 1 1.5 2.0 2.5 3.0
dataset_svm_tuned <- tune(svm, y~., data = dataset,
ranges = list(gamma = seq(0,2,.5), cost = seq(1,3.5,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
dataset_svm_tuned$best.parameters## gamma cost
## 25 2 3dataset_svm <- svm(y ~ ., data = dataset, gamma=1.5, cost=3.5)
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.02374744#[1] 0.02374744
dataset_svm <- svm(y ~ ., data = dataset, kernel="polynomial")
summary(dataset_svm)##
## Call:
## svm(formula = y ~ ., data = dataset, kernel = "polynomial")
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: polynomial
## cost: 1
## degree: 3
## gamma: 1
## coef.0: 0
## epsilon: 0.1
##
##
## Number of Support Vectors: 84#gamma = 1 cost = 1
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.04557566#[1] 0.04557566
## tune `svm' for classification with kernel = "polynomial",
## using one split for training/validation set
# gamma = 0.0 0.5 1.0 1.5 2.0; cost = 1 1.5 2.0 2.5 3.0
dataset_svm_tuned <- tune(svm, y~., data = dataset, kernel="polynomial",
ranges = list(gamma = seq(0,2,.5), cost = seq(1,3.5,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
dataset_svm_tuned$best.parameters## gamma cost
## 2 0.5 1dataset_svm <- svm(y ~ ., data = dataset, kernel="polynomial", gamma=0.5, cost=1.5)
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.04518411#[1] 0.04518411
dataset_svm <- svm(y ~ ., data = dataset, kernel = "sigmoid")
summary(dataset_svm)##
## Call:
## svm(formula = y ~ ., data = dataset, kernel = "sigmoid")
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: sigmoid
## cost: 1
## gamma: 1
## coef.0: 0
## epsilon: 0.1
##
##
## Number of Support Vectors: 99#gamma = 1 cost = 1
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.3460026#[1] 0.3460026
## tune `svm' for classification with kernel = "sigmoid",
## using one split for training/validation set
# gamma = 0.0 0.5 1.0 1.5 2.0; cost = 1 1.5 2.0 2.5 3.0
dataset_svm_tuned <- tune(svm, y~., data = dataset, kernel="sigmoid",
ranges = list(gamma = seq(0,2,.5), cost = seq(1,3.5,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
dataset_svm_tuned$best.parameters## gamma cost
## 1 0 1dataset_svm <- svm(y ~ ., data = dataset, kernel="sigmoid", gamma=0, cost=1)
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.0946527#[1] 0.0946527
#5) Can you improve the model by adding an extra feature which might be a
# function of the first feature? Compare both lm.ridge and svm.
xlog<-log(x)
dataset <- as.data.frame(cbind(x,xlog,y))
str(dataset)## 'data.frame': 99 obs. of 3 variables:
## $ x : num 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 ...
## $ xlog: num -2.3 -1.9 -1.61 -1.39 -1.2 ...
## $ y : num -2.3 -2.29 -1.81 -1.44 -1.11 ...x <- dataset[,1:2]
dataset_svm <- svm(y ~ ., data = dataset, kernel = "linear")
summary(dataset_svm)##
## Call:
## svm(formula = y ~ ., data = dataset, kernel = "linear")
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: linear
## cost: 1
## gamma: 0.5
## epsilon: 0.1
##
##
## Number of Support Vectors: 70#gamma = 0.5 cost = 1
dataset_predict <- predict(dataset_svm, x);
sqrt(sum((y-dataset_predict)^2))/length(y)## [1] 0.02213159#[1] 0.02213159
## tune `svm' for classification with kernel = "linear",
## using one split for training/validation set
# gamma = 0.0 0.5 1.0 1.5 2.0; cost = 1.0 1.5 2.0 2.5 3.0 3.5
dataset_svm_tuned <- tune(svm, y~., data = dataset, kernel="linear",
ranges = list(gamma = seq(0,2,.5), cost = seq(1,3.5,0.5)),
tunecontrol = tune.control(sampling = "cross")
)
summary(dataset_svm_tuned)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## gamma cost
## 0 1.5
##
## - best performance: 0.05167865
##
## - Detailed performance results:
## gamma cost error dispersion
## 1 0.0 1.0 0.05197314 0.01480749
## 2 0.5 1.0 0.05197314 0.01480749
## 3 1.0 1.0 0.05197314 0.01480749
## 4 1.5 1.0 0.05197314 0.01480749
## 5 2.0 1.0 0.05197314 0.01480749
## 6 0.0 1.5 0.05167865 0.01508452
## 7 0.5 1.5 0.05167865 0.01508452
## 8 1.0 1.5 0.05167865 0.01508452
## 9 1.5 1.5 0.05167865 0.01508452
## 10 2.0 1.5 0.05167865 0.01508452
## 11 0.0 2.0 0.05170011 0.01509153
## 12 0.5 2.0 0.05170011 0.01509153
## 13 1.0 2.0 0.05170011 0.01509153
## 14 1.5 2.0 0.05170011 0.01509153
## 15 2.0 2.0 0.05170011 0.01509153
## 16 0.0 2.5 0.05194368 0.01518225
## 17 0.5 2.5 0.05194368 0.01518225
## 18 1.0 2.5 0.05194368 0.01518225
## 19 1.5 2.5 0.05194368 0.01518225
## 20 2.0 2.5 0.05194368 0.01518225
## 21 0.0 3.0 0.05195528 0.01515975
## 22 0.5 3.0 0.05195528 0.01515975
## 23 1.0 3.0 0.05195528 0.01515975
## 24 1.5 3.0 0.05195528 0.01515975
## 25 2.0 3.0 0.05195528 0.01515975
## 26 0.0 3.5 0.05198968 0.01517651
## 27 0.5 3.5 0.05198968 0.01517651
## 28 1.0 3.5 0.05198968 0.01517651
## 29 1.5 3.5 0.05198968 0.01517651
## 30 2.0 3.5 0.05198968 0.01517651dataset_svm_tuned$best.parameters## gamma cost
## 6 0 1.5#gamma = 0, cost = 2.5
dataset_svm <- svm(y ~ ., data = dataset, kernel = "linear", gamma=0, cost=2.5)
dataset_predict <- predict(dataset_svm, x);
svm_error<-sqrt(sum((y-dataset_predict)^2))/length(y)
#[1] 0.02130392
#install.packages("glmnet")
library(glmnet)## Warning: package 'glmnet' was built under R version 3.1.3## Loading required package: Matrix## Warning: package 'Matrix' was built under R version 3.1.2## Loaded glmnet 1.9-8
dataset <- cbind(x,xlog,y)
grid=10^seq(10,-2,length=100)
cv.out=cv.glmnet(as.matrix(dataset),y,alpha=0,lambda=grid)
cv.out$lambda.min## [1] 0.01#[1] 0.01
ridgeMod =glmnet(as.matrix(dataset),y,alpha=0,lambda=0.01)
ridgePredict <- predict(ridgeMod, newx = as.matrix(dataset))
error <-sqrt( sum((y-ridgePredict)^2))/length(y)
paste("Ridge Regression error",error)## [1] "Ridge Regression error 0.00319279474519351"paste("SVM error",svm_error)## [1] "SVM error 0.0221504098233445"print("lm.ridge produced a better model than SVM")## [1] "lm.ridge produced a better model than SVM"