1. Importer les données

library(kernlab)
data(spam)
summary(spam[,56:58])

  capitalLong       capitalTotal          type     
 Min.   :   1.00   Min.   :    1.0   nonspam:2788  
 1st Qu.:   6.00   1st Qu.:   35.0   spam   :1813  
 Median :  15.00   Median :   95.0                 
 Mean   :  52.17   Mean   :  283.3                 
 3rd Qu.:  43.00   3rd Qu.:  266.0                 
 Max.   :9989.00   Max.   :15841.0                 

set.seed(5678)
perm <- sample(4601,3000)
app <- spam[perm,]
valid <- spam[-perm,]

2. Construire et analyser un algorithme de SVM

mod.svm <- ksvm(type~.,data=app,kernel="vanilladot",C=1)

 Setting default kernel parameters  

mod.svm

Support Vector Machine object of class "ksvm" 

SV type: C-svc  (classification) 
 parameter : cost C = 1 

Linear (vanilla) kernel function. 

Number of Support Vectors : 599 

Objective Function Value : -546.7826 
Training error : 0.067 

3. Sélectionner les paramètres d’un SVM

C <- c(0.1,1,10,100)
degree <- c(1,2,3)
scale <- 1
sigma <- c(0.0001,0.001,0.01,0.1,1)

library(caret)
gr.poly <- expand.grid(C=C,degree=degree,scale=scale)
ctrl <- trainControl(method="cv",number=3)
set.seed(123)
sel.poly <- train(type~.,data=app,method="svmPoly",trControl=ctrl,tuneGrid=gr.poly)
sel.poly

Support Vector Machines with Polynomial Kernel 

3000 samples
  57 predictor
   2 classes: 'nonspam', 'spam' 

No pre-processing
Resampling: Cross-Validated (3 fold) 
Summary of sample sizes: 2000, 2000, 2000 
Resampling results across tuning parameters:

  C      degree  Accuracy   Kappa    
    0.1  1       0.9270000  0.8461040
    0.1  2       0.9100000  0.8105364
    0.1  3       0.9083333  0.8077676
    1.0  1       0.9280000  0.8479742
    1.0  2       0.8936667  0.7774023
    1.0  3       0.8920000  0.7745405
   10.0  1       0.9270000  0.8460247
   10.0  2       0.8853333  0.7608912
   10.0  3       0.8830000  0.7553775
  100.0  1       0.9240000  0.8395595
  100.0  2       0.8806667  0.7518021
  100.0  3       0.8763333  0.7413648

Tuning parameter 'scale' was held constant at a value of 1
Accuracy was used to select the optimal model using the largest value.
The final values used for the model were degree = 1, scale = 1 and C = 1.

gr.radial <- expand.grid(C=C,sigma=sigma)
set.seed(345)
sel.radial <- train(type~.,data=app,method="svmRadial",trControl=ctrl,tuneGrid=gr.radial)
sel.radial

Support Vector Machines with Radial Basis Function Kernel 

3000 samples
  57 predictor
   2 classes: 'nonspam', 'spam' 

No pre-processing
Resampling: Cross-Validated (3 fold) 
Summary of sample sizes: 2000, 2000, 2000 
Resampling results across tuning parameters:

  C      sigma  Accuracy   Kappa    
    0.1  1e-04  0.6060000  0.0000000
    0.1  1e-03  0.7663333  0.4578780
    0.1  1e-02  0.8990000  0.7825103
    0.1  1e-01  0.7610000  0.4447726
    0.1  1e+00  0.6060000  0.0000000
    1.0  1e-04  0.7723333  0.4734765
    1.0  1e-03  0.9000000  0.7855698
    1.0  1e-02  0.9276667  0.8470048
    1.0  1e-01  0.9050000  0.7958078
    1.0  1e+00  0.7576667  0.4321881
   10.0  1e-04  0.8970000  0.7790195
   10.0  1e-03  0.9280000  0.8477454
   10.0  1e-02  0.9353333  0.8636455
   10.0  1e-01  0.9040000  0.7948708
   10.0  1e+00  0.7626667  0.4475051
  100.0  1e-04  0.9203333  0.8315819
  100.0  1e-03  0.9333333  0.8594359
  100.0  1e-02  0.9283333  0.8486409
  100.0  1e-01  0.8966667  0.7797074
  100.0  1e+00  0.7603333  0.4430619

Accuracy 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.

mod.poly <- ksvm(type~.,data=app,kernel="polydot",kpar=list(degree=1,scale=1,offset=1),C=1,prob.model = TRUE)
mod.radial <- ksvm(type~.,data=app,kernel="rbfdot",kpar=list(sigma=0.01),C=10,prob.model = TRUE)

4. Faire de la prévision

prev.class.poly <- predict(mod.poly,newdata=valid)
prev.class.radial <- predict(mod.radial,newdata=valid)
prev.class.poly[1:10]

 [1] spam    spam    spam    spam    spam    spam    spam    spam    nonspam spam   
Levels: nonspam spam

prev.class.radial[1:10]

 [1] spam    spam    spam    spam    spam    spam    spam    spam    nonspam spam   
Levels: nonspam spam

prev.prob.poly <- predict(mod.poly,newdata=valid,type="probabilities")
prev.prob.radial <- predict(mod.radial,newdata=valid,type="probabilities")
round(head(prev.prob.poly),3)

     nonspam  spam
[1,]   0.056 0.944
[2,]   0.412 0.588
[3,]   0.000 1.000
[4,]   0.172 0.828
[5,]   0.005 0.995
[6,]   0.066 0.934

5. Estimer les performances de l’algorithme

library(tidyverse)
prev.class <- data.frame(poly=prev.class.poly,radial=prev.class.radial,obs=valid$type)
prev.class %>% summarise_all(funs(err=mean(obs!=.))) %>% select(-obs_err) %>% round(3)

  poly_err radial_err
1    0.082      0.077

library(plotROC)
prev.prob <- data.frame(poly=prev.prob.poly[,2],radial=prev.prob.radial[,2],obs=valid$type)
df.roc <- prev.prob %>% gather(key=Methode,value=score,poly,radial)
ggplot(df.roc)+aes(d=obs,m=score,color=Methode)+geom_roc()+theme_classic()

library(pROC)
df.roc %>% group_by(Methode) %>% summarize(AUC=pROC::auc(obs,score))

# A tibble: 2 x 2
  Methode   AUC
  <chr>   <dbl>
1 poly    0.966
2 radial  0.973