8Assignment

Irving Cedillo

5

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#a
x1<- runif(500)-.5
x2<- runif(500)-.5

y<- 1*(x1^2 -x2^2 >0)

fake_data<-data.frame(x1,x2,y)|>
  mutate( y = factor(y, levels = c(0, 1), labels = c("Class_0", "Class_1"))  )

#b
ggplot(data = fake_data,
       mapping = aes(x=x1, y=x2, color = factor(y))) +
  geom_point()

#c,d
data_split = initial_split(fake_data, prop = 0.80, strata = y)

training = training(data_split)
testing = testing(data_split)

ctrl<- trainControl(
  method  = 'cv',
  number = 5,
  classProbs = TRUE,
  summaryFunction = twoClassSummary
)

set.seed(12345)

log_reg<-train(
  y~x1+x2,
  data=training, 
  method='glm',
  family='binomial',
  preProcess = c("BoxCox", "center", "scale"),
  metric='ROC',
  trControl = ctrl
)


training$predicted_class <- predict(log_reg, training)

ggplot(data = training,
       mapping = aes(x=x1, y=x2, color = factor(predicted_class))) +
  geom_point()

log_reg_2<-train(
  y~tan(x2)+sin(x1*x1)+cos(x2*x2),
  data=training, 
  method='glm',
  family='binomial',
  preProcess = c("BoxCox", "center", "scale"),
  metric='ROC',
  trControl = ctrl
)


training$predicted_class_2 <- predict(log_reg_2, training)

ggplot(data = training,
       mapping = aes(x=x1, y=x2, color = factor(predicted_class_2))) +
  geom_point()

#g
svm<-train(
  y~x1+x2,
  data=training, 
  method='svmLinear',
  preProcess = c("BoxCox", "center", "scale"),
  metric='ROC',
  trControl = ctrl
)


training$predicted_class_svm <- predict(svm, training)

ggplot(data = training,
       mapping = aes(x=x1, y=x2, color = factor(predicted_class_svm))) +
  geom_point()

#h
svm<-train(
  y~x1+x2,
  data=training, 
  method='svmRadial',
  preProcess = c("BoxCox", "center", "scale"),
  metric='ROC',
  trControl = ctrl
)


training$predicted_class_nlsvm <- predict(svm, training)

ggplot(data = training,
       mapping = aes(x=x1, y=x2, color = factor(predicted_class_nlsvm))) +
  geom_point()

The SVM radial was able to identify the linear separation between the generated classes the best from the output plot. Interestingly enoguht the linear SVM was not able to correctly classify or differentiate between the two classes.

7

attach(Auto)

The following object is masked from package:ggplot2:

    mpg

data_auto <- Auto |>
  mutate(
    Class_MPG = as.factor(ifelse(mpg > median(mpg), "Above_Med", "Below_Med"))
  )|>
  select(-mpg)

svm_grid_linear <- expand.grid(
   C =c(0.1,1,10,100)
)


svm_grid <- expand.grid(
  sigma= c(0.01,0.05,0.1),
  C =c(0.1,1,10,100)
)

ctrl<- trainControl(
  method  = 'cv',
  number = 5,
  classProbs = TRUE,
  summaryFunction = twoClassSummary
)


svm_model_linear <- suppressWarnings(train(
  Class_MPG ~ .,
  data = data_auto,
  method='svmLinear',
  preProcess = c("BoxCox", "center", "scale"),
  metric='ROC',
  trControl = ctrl,
  tuneGrid = svm_grid_linear
))

print(svm_model_linear)

Support Vector Machines with Linear Kernel 

392 samples
  8 predictor
  2 classes: 'Above_Med', 'Below_Med' 

Pre-processing: Box-Cox transformation (7), centered (310), scaled (310) 
Resampling: Cross-Validated (5 fold) 
Summary of sample sizes: 313, 314, 314, 313, 314 
Resampling results across tuning parameters:

  C      ROC        Sens       Spec     
    0.1  0.9499671  0.9079487  0.8670513
    1.0  0.9585076  0.9335897  0.8669231
   10.0  0.9606213  0.8979487  0.8771795
  100.0  0.9682512  0.8980769  0.9078205

ROC was used to select the optimal model using the largest value.
The final value used for the model was C = 100.

svm_model_Radial<- suppressWarnings(train(
  Class_MPG ~ .,
  data = data_auto,
  method='svmRadial',
  preProcess = c("BoxCox", "center", "scale"),
  metric='ROC',
  trControl = ctrl,
  tuneGrid = svm_grid
))

print(svm_model_Radial)

Support Vector Machines with Radial Basis Function Kernel 

392 samples
  8 predictor
  2 classes: 'Above_Med', 'Below_Med' 

Pre-processing: Box-Cox transformation (7), centered (310), scaled (310) 
Resampling: Cross-Validated (5 fold) 
Summary of sample sizes: 313, 314, 314, 314, 313 
Resampling results across tuning parameters:

  sigma  C      ROC        Sens       Spec     
  0.01     0.1  0.9172650  0.7819231  0.8632051
  0.01     1.0  0.9368080  0.9130769  0.8670513
  0.01    10.0  0.9383925  0.9182051  0.8619231
  0.01   100.0  0.9343031  0.9435897  0.8210256
  0.05     0.1  0.9190007  0.5229487  0.7587179
  0.05     1.0  0.9158514  0.4443590  0.9384615
  0.05    10.0  0.9118376  0.4443590  0.9333333
  0.05   100.0  0.9077449  0.4750000  0.9180769
  0.10     0.1  0.9127120  0.4562821  0.7332051
  0.10     1.0  0.9128008  0.4597436  0.8153846
  0.10    10.0  0.9046220  0.3310256  0.9538462
  0.10   100.0  0.9024195  0.4542308  0.8102564

ROC was used to select the optimal model using the largest value.
The final values used for the model were sigma = 0.01 and C = 10.

plot(svm_model_Radial)

8

attach(OJ)
set.seed(12345)
train_index <- createDataPartition(
  OJ$Purchase, 
  p = 800 / nrow(OJ), 
  list = FALSE
) 

training = OJ[train_index, ]
testing = OJ[-train_index, ]

svm_grid <- expand.grid(
  sigma= c(0.01,0.05,0.1),
  C =c(0.01,.1,1,2,4,6,8,10)
)

svm_model<-suppressWarnings(train(
  Purchase ~.,
  data = training, 
  method='svmRadial',
  preProcess = c("BoxCox", "center", "scale"),
  metric='ROC',
  trControl = ctrl,
  tuneGrid = svm_grid
)
)

print(svm_model)

Support Vector Machines with Radial Basis Function Kernel 

801 samples
 17 predictor
  2 classes: 'CH', 'MM' 

Pre-processing: Box-Cox transformation (7), centered (17), scaled (17) 
Resampling: Cross-Validated (5 fold) 
Summary of sample sizes: 641, 640, 642, 640, 641 
Resampling results across tuning parameters:

  sigma  C      ROC        Sens       Spec     
  0.01    0.01  0.8717847  0.7566590  0.8366615
  0.01    0.10  0.8725668  0.7608037  0.8398361
  0.01    1.00  0.8916834  0.8854829  0.7501792
  0.01    2.00  0.8924311  0.8916053  0.7404506
  0.01    4.00  0.8919574  0.8875237  0.7403994
  0.01    6.00  0.8915870  0.8915843  0.7371224
  0.01    8.00  0.8912611  0.8895434  0.7306196
  0.01   10.00  0.8918123  0.8875026  0.7242704
  0.05    0.01  0.8714394  0.7751315  0.8269329
  0.05    0.10  0.8787731  0.8690722  0.7341014
  0.05    1.00  0.8860286  0.8957080  0.7179724
  0.05    2.00  0.8829385  0.8977488  0.6921659
  0.05    4.00  0.8809011  0.8895434  0.6952893
  0.05    6.00  0.8801076  0.8875026  0.6888377
  0.05    8.00  0.8792789  0.8874816  0.6887865
  0.05   10.00  0.8780326  0.8854408  0.6952381
  0.10    0.01  0.8698243  0.7935199  0.7949309
  0.10    0.10  0.8711035  0.8527667  0.7276498
  0.10    1.00  0.8790906  0.9018304  0.6825397
  0.10    2.00  0.8775910  0.8936251  0.6857143
  0.10    4.00  0.8721282  0.8874816  0.6823861
  0.10    6.00  0.8668637  0.8834000  0.6663594
  0.10    8.00  0.8605169  0.8772775  0.6599590
  0.10   10.00  0.8544256  0.8792973  0.6534562

ROC was used to select the optimal model using the largest value.
The final values used for the model were sigma = 0.01 and C = 2.

train_predictions <-predict(svm_model, newdata=training)
train_error<- mean(train_predictions != training$Purchase)
cat("\nTraining Error:", round(train_error, 1), "\n")

Training Error: 0.2 

test_predictions <-predict(svm_model, newdata=testing)
test_error<- mean(test_predictions != testing$Purchase)
cat("\nTest Error:", round(train_error, 1), "\n")

Test Error: 0.2