Download ISLR Chapter 9 Support Vector Machines Lab Manual and more Exercises Statistics in PDF only on Docsity!
Chapter 9 - Support Vector Machines
Lab Solution
1 Problem 8
(a). Create a training set containing a random sample of 800 observations, and a test set containing the remaining observations.
library (ISLR) set.seed (1) train = sample ( dim (OJ)[1], 800) OJ.train = OJ[train, ] OJ.test = OJ[-train, ]
(b). Fit a support vector classifier to the training data using cost=0.01, with Purchase as the re- sponse and the other variables as predictors. Use the summary() function to produce summary statistics, and describe the results obtained.
library (e1071,quietly = T) svm.linear = svm (Purchase ~ ., kernel = "linear", data = OJ.train, cost = 0.01) summary (svm.linear)
Call:
svm(formula = Purchase ~ ., data = OJ.train, kernel = "linear", cost = 0.01)
Parameters:
SVM-Type: C-classification
SVM-Kernel: linear
cost: 0.
gamma: 0.
Number of Support Vectors: 432
( 215 217 )
Number of Classes: 2
Levels:
CH MM
(c). What are the training and test error rates?
train.pred = predict (svm.linear, OJ.train) table (OJ.train$Purchase, train.pred)
train.pred
CH MM
CH 439 55
MM 78 228
test.pred = predict (svm.linear, OJ.test) table (OJ.test$Purchase, test.pred)
test.pred
CH MM
CH 141 18
MM 31 80
(d). Use the tune() function to select an optimal cost. Consider values in the range 0.01 to 10.
tune.out = tune (svm, Purchase ~ ., data = OJ.train, kernel = "linear", ranges = list (cost = 10^ seq (-2, 1, by = 0.25))) summary (tune.out)
Parameter tuning of 'svm':
- sampling method: 10-fold cross validation
- best parameters:
cost
0.
- best performance: 0.
- Detailed performance results:
cost error dispersion
1 0.01000000 0.16625 0.
2 0.01778279 0.16625 0.
3 0.03162278 0.16375 0.
4 0.05623413 0.16000 0.
5 0.10000000 0.16250 0.
6 0.17782794 0.16250 0.
7 0.31622777 0.16125 0.
8 0.56234133 0.16625 0.
9 1.00000000 0.16875 0.
10 1.77827941 0.16750 0.
11 3.16227766 0.16375 0.
12 5.62341325 0.16750 0.
13 10.00000000 0.16500 0.
(e). Compute the training and test error rates using this new value for cost.
test.pred = predict (svm.radial, OJ.test) table (OJ.test$Purchase, test.pred)
test.pred
CH MM
CH 141 18
MM 28 83
tune.out = tune (svm, Purchase ~ ., data = OJ.train, kernel = "radial", ranges = list (cost = 10^ seq (-2, 1, by = 0.25))) summary (tune.out)
Parameter tuning of 'svm':
- sampling method: 10-fold cross validation
- best parameters:
cost
0.
- best performance: 0.
- Detailed performance results:
cost error dispersion
1 0.01000000 0.38250 0.
2 0.01778279 0.38250 0.
3 0.03162278 0.38000 0.
4 0.05623413 0.20750 0.
5 0.10000000 0.18250 0.
6 0.17782794 0.17875 0.
7 0.31622777 0.16875 0.
8 0.56234133 0.17000 0.
9 1.00000000 0.17625 0.
10 1.77827941 0.17250 0.
11 3.16227766 0.17500 0.
12 5.62341325 0.17250 0.
13 10.00000000 0.18250 0.
svm.radial = svm (Purchase ~ ., data = OJ.train, kernel = "radial", cost = tune.out$best.parameters$cost) train.pred = predict (svm.radial, OJ.train) table (OJ.train$Purchase, train.pred)
train.pred
CH MM
CH 448 46
MM 78 228
test.pred = predict (svm.radial, OJ.test) table (OJ.test$Purchase, test.pred)
test.pred
CH MM
CH 144 15
MM 29 82
(g). Repeat parts (b) through (e) using a support vector machine with a polynomial kernel. Set degree=2.
svm.poly = svm (Purchase ~ ., data = OJ.train, kernel = "poly", degree = 2) summary (svm.poly)
Call:
svm(formula = Purchase ~ ., data = OJ.train, kernel = "poly", degree = 2)
Parameters:
SVM-Type: C-classification
SVM-Kernel: polynomial
cost: 1
degree: 2
gamma: 0.
coef.0: 0
Number of Support Vectors: 454
( 224 230 )
Number of Classes: 2
Levels:
CH MM
train.pred = predict (svm.poly, OJ.train) table (OJ.train$Purchase, train.pred)
train.pred
CH MM
CH 461 33
MM 105 201
test.pred = predict (svm.poly, OJ.test) table (OJ.test$Purchase, test.pred)
test.pred
CH MM
CH 149 10
MM 41 70
tune.out = tune (svm, Purchase ~ ., data = OJ.train, kernel = "poly", degree = 2, ranges = list (cost = 10^ seq (-2, 1, by = 0.25))) summary (tune.out)
Parameter tuning of 'svm':
- sampling method: 10-fold cross validation
