svmr {rchemo}

SVM Regression and Discrimination

Description

SVM models with Gaussian (RBF) kernel

svmr: SVM regression (SVMR).

svmda: SVM discrimination (SVMC).

The functions uses function svm of package e1071 (Meyer et al. 2021) available on CRAN (e1071 uses the tool box LIVSIM; Chang & Lin, http://www.csie.ntu.edu.tw/~cjlin/libsvm).

The SVM models are fitted with parameterization 'C', not the 'nu' parameterization.

The RBF kernel is defined by: exp(-gamma * |x - y|^2).

For tuning the model, usual preliminary ranges are for instance:

- cost = 10^(-5:15)

- epsilon = seq(.1, .3, by = .1)

- gamma = 10^(-6:3)

Usage

svmr(X, y, cost = 1, epsilon = .1, gamma = 1, scale = FALSE)

svmda(X, y, cost = 1, epsilon = .1, gamma = 1, scale = FALSE)

## S3 method for class 'Svm'
predict(object, X, ...)  

## S3 method for class 'Svm'
summary(object, ...)  

Arguments

X

For the main functions: Training X-data (n, p). — For the auxiliary functions: New X-data (m, p) to consider.

y

Training Y-data (n).

cost

The cost of constraints violation cost parameter. See svm.

epsilon

The epsilon parameter in the insensitive-loss function. See svm.

gamma

The gamma parameter in the RBF kernel.

scale

Logical. If TRUE, X and Y are scaled internally.

object

For the auxiliary functions: A fitted model, output of a call to the main function.

...

For the auxiliary functions: Optional arguments.

Value

For svmr and svmda:

fm

list of outputs such as: call; type; kernel; cost; degree; gamma; coef0; nu; epsilon; sparse; scaled; x.scale; y.scale; nclasses; levels; tot.nSV; nSV; labels; SV: The resulting support vectors (possibly scaled); index: The index of the resulting support vectors in the data matrix. Note that this index refers to the preprocessed data (after the possible effect of na.omit and subset); rho: The negative intercept; compprob; probA, probB: numeric vectors of length k(k-1)/2, k number of classes, containing the parameters of the logistic distributions fitted to the decision values of the binary classifiers (1 / (1 + exp(a x + b))); sigma: In case of a probabilistic regression model, the scale parameter of the hypothesized (zero-mean) laplace distribution estimated by maximum likelihood; coefs: The corresponding coefficients times the training labels; na.action; fitted; decision.values; residuals; isnum.

For predict.Svm:

pred

predictions for each observation.

For summary.Svm:display of call, parameters, and number of support vectors

Note

The first example illustrates SVMR. The second one is the example of fitting the function sinc(x) described in Rosipal & Trejo 2001 p. 105-106. The third one illustrates SVMC.

References

Meyer, M. 2021 Support Vector Machines - The Interface to libsvm in package e1071. FH Technikum Wien, Austria, [e-mail]. https://cran.r-project.org/web/packages/e1071/vignettes/svmdoc.pdf

Chang, cost.-cost. & Lin, cost.-J. (2001). LIBSVM: a library for support vector machines. Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm. Detailed documentation (algorithms, formulae, . . . ) can be found in http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.ps.gz

Examples

## EXAMPLE 1 (SVMR)

n <- 50 ; p <- 4
Xtrain <- matrix(rnorm(n * p), ncol = p)
ytrain <- rnorm(n)
m <- 3
Xtest <- Xtrain[1:m, , drop = FALSE] 
ytest <- ytrain[1:m]

fm <- svmr(Xtrain, ytrain)
predict(fm, Xtest)

pred <- predict(fm, Xtest)$pred
msep(pred, ytest)

summary(fm)

## EXAMPLE 2 

x <- seq(-10, 10, by = .2)
x[x == 0] <- 1e-5
n <- length(x)
zy <- sin(abs(x)) / abs(x)
y <- zy + rnorm(n, 0, .2)
plot(x, y, type = "p")
lines(x, zy, lty = 2)
X <- matrix(x, ncol = 1)

fm <- svmr(X, y, gamma = .5)
pred <- predict(fm, X)$pred
plot(X, y, type = "p")
lines(X, zy, lty = 2)
lines(X, pred, col = "red")

## EXAMPLE 3 (SVMC)

n <- 50 ; p <- 8
Xtrain <- matrix(rnorm(n * p), ncol = p)
ytrain <- sample(c("a", "10", "d"), size = n, replace = TRUE)
m <- 5
Xtest <- Xtrain[1:m, ] ; ytest <- ytrain[1:m]

cost <- 100 ; epsilon <- .1 ; gamma <- 1 
fm <- svmda(Xtrain, ytrain,
    cost = cost, epsilon = epsilon, gamma = gamma)
predict(fm, Xtest)

pred <- predict(fm, Xtest)$pred
err(pred, ytest)

summary(fm)