# SVM Regression and Discrimination SVM models with Gaussian (RBF) kernel. `svmr`: SVM regression (SVMR). `svmda`: SVM discrimination (SVMC). 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) 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). latin1 ```r 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. ## Returns 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. ## References Meyer, M. 2021 Support Vector Machines - The Interface to libsvm in package e1071. FH Technikum Wien, Austria, David.Meyer@R-Project.org. 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 ## 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. ## Examples ```r ## 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) ```

svm function