Objective function of an SVM - r

Question

I have used the svm function in the e1071 package of R software to model my data using variables selected by my feature selection method. I have obtained predictions from this model using the predict.svm function in the same package. I want to compute the value of the objective function of the svm model using the R software. How can I do this?
Below is my code for my first feature selection technique-Information Gain
P1<-Fold1T$Class_NASQ
InfGainF1 <- information.gain(P1~., Fold1T[,-20])
subset <- cutoff.k(InfGainF1, 8)
f <- as.simple.formula(subset, "P1")
ModelInGF1<-svm(as.factor(P1)~ NSDQ.COMP+S.P.100+S.P.500+NYSE.COMP+NYSE.A.M.MKT +
RSEL.2000+ALL.ORD+HG.SENG ,data=Fold1T[,-20], kernel="radial",gamma=0.5,cost=16)
PredictInGF1<-predict(ModelInGF1,NewData=Fold1V[,-20])
######### Accuracy ########
confusionMatrix(PredictInGF1, P1)
Thanks

Answer 1

While learning about SVR back in 2010 I explored how predicted values are computed. To do this, I went over the file "svminternals.pdf" located in the e1071/doc subfolder and play my custom code (shown after the toy data) using the following data set
ToyData <- data.frame(X1=c(12.4,14.6,13.4,12.9,15.2,13.6,9.2), X2=c(2.1,9.2,1.9,0.8,1.1,8.6,1.1),Y=c(14.2,16.9,15.5,14.7,17.3,16,10.9))
You may explore the following code to see if is somehow helpful to you.
#LINEAR KERNEL
ToyData <- read.csv("ToyData.csv", header=T)
X <- as.matrix(ToyData[,1:2])
Y <- as.vector(ToyData[,3])
SVRLinear <- svm (X, Y, kernel="linear", epsilon=0.1, cost=1, scale=FALSE)
V <- as.matrix(SVRLinear$SV)
Vt <- t(V)
A <- as.matrix(SVRLinear$coefs)
(r <- SVRLinear$rho)
write.csv(V, file="SVLinear.csv")
write.csv(A, file="CoefsLinear.csv")
F <- (X %*% Vt) %*% A - r
write.csv(F, file="FittedLinear.csv")
#RBF KERNEL: Exp[(-gamma||x-z||^2)/2]
ToyData <- read.csv("ToyData.csv", header=T)
X <- as.matrix(ToyData[,1:2])
Y <- as.vector(ToyData[,3])
SVRRadial <- svm (X, Y, kernel="radial", epsilon=0.1, gamma=0.1, cost=5, scale=FALSE)
V <- as.matrix(SVRRadial$SV)
A <- as.matrix(SVRRadial$coefs)
(g <- SVRRadial$gamma)
(r <- SVRRadial$rho)
write.csv(V, file="SVRadial.csv")
write.csv(A, file="CoefsRadial.csv")
Kernel <- matrix(0, nrow(X), nrow(V))
for (i in 1:nrow(X)) {
for (j in 1:nrow(V)) {
Xi <- X[i,]
Vj <- V[j,]
XiMinusVj <- Xi - Vj
SumSqXiMinusVj <- XiMinusVj %*% XiMinusVj
Kernel[i,j] <- exp(-g*SumSqXiMinusVj)
}
}
F <- Kernel %*% A - r
write.csv(F, file="FittedRadial.csv")

Answer 2

I want to add the answer how to reproduce the predict value with the model parameter when scale option is open.In e1071,data are default scaled internally (both x and y variables) to zero mean and unit variance. The center and scale values are returned and used for later predictions.(http://www.inside-r.org/node/57517). According to the above code,I write the following code which may help to you.
ToyData <- data.frame(X1=c(12.4,14.6,13.4,12.9,15.2,13.6,9.2), X2=c(2.1,9.2,1.9,0.8,1.1,8.6,1.1),Y=c(14.2,16.9,15.5,14.7,17.3,16,10.9))
X <- as.matrix(ToyData[,1:2])
Y <- as.vector(ToyData[,3])
SVRRadial <- svm (X, Y, kernel="radial", epsilon=0.1, gamma=0.1, cost=5)
pred<-predict(SVRRadial,X)
toys<-ToyData
#scale the feature
sc_x<-data.frame(SVRRadial$x.scale)
for(col in row.names(sc_x)){
toys[[col]]<-(ToyData[[col]]-sc_x[[col,1]])/sc_x[[col,2]]
}
#compute the predict value, the method is same to the above code
X<-as.matrix(toys[,1:2])
V <- as.matrix(SVRRadial$SV)
A <- as.matrix(SVRRadial$coefs)
g <- SVRRadial$gamma
r <- SVRRadial$rho
Kernel <- matrix(0, nrow(X), nrow(V))
for (i in 1:nrow(X)) {
for (j in 1:nrow(V)) {
Xi <- X[i,]
Vj <- V[j,]
XiMinusVj <- Xi - Vj
SumSqXiMinusVj <- XiMinusVj %*% XiMinusVj
Kernel[i,j] <- exp(-g*SumSqXiMinusVj)
}
}
F <- Kernel %*% A - r
#restore the predict value from standard format to original format
my_pred<-F
sc_y<-data.frame(SVRRadial$y.scale)
my_pred<-my_pred*sc_y[[2]]+sc_y[[1]]
summary(my_pred-pred)
reference link:How to reproduce predict.svm in R?