# svm {e1071}

### Description

`svm`

is used to train a support vector machine. It can be used to carry out general regression and classification (of nu and epsilon-type), as well as density-estimation. A formula interface is provided.

### Usage

## S3 method for class 'formula': svm((formula, data = NULL, ..., subset, na.action = na.omit, scale = TRUE)) ## S3 method for class 'default': svm((x, y = NULL, scale = TRUE, type = NULL, kernel = "radial", degree = 3, gamma = if (is.vector(x)) 1 else 1 / ncol(x), coef0 = 0, cost = 1, nu = 0.5, class.weights = NULL, cachesize = 40, tolerance = 0.001, epsilon = 0.1, shrinking = TRUE, cross = 0, probability = FALSE, fitted = TRUE, ..., subset, na.action = na.omit))

### Arguments

- formula
- a symbolic description of the model to be fit.
- data
- an optional data frame containing the variables in the model. By default the variables are taken from the environment which ‘svm’ is called from.
- x
- a data matrix, a vector, or a sparse matrix (object of class
`Matrix`

provided by the Matrix package, or of class`matrix.csr`

provided by the SparseM package, or of class`simple_triplet_matrix`

provided by the slam package). - y
- a response vector with one label for each row/component of
`x`

. Can be either a factor (for classification tasks) or a numeric vector (for regression). - scale
- A logical vector indicating the variables to be scaled. If
`scale`

is of length 1, the value is recycled as many times as needed. Per default, data are 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. - type
`svm`

can be used as a classification machine, as a regression machine, or for novelty detection. Depending of whether`y`

is a factor or not, the default setting for`type`

is`C-classification`

or`eps-regression`

, respectively, but may be overwritten by setting an explicit value.

Valid options are:`C-classification`

`nu-classification`

`one-classification`

(for novelty detection)`eps-regression`

`nu-regression`

- kernel
- the kernel used in training and predicting. You might consider changing some of the following parameters, depending on the kernel type.

- linear:
- u'*v
- polynomial:
- (gamma*u'*v + coef0)^degree
- radial basis:
- exp(-gamma*|u-v|^2)
- sigmoid:
- tanh(gamma*u'*v + coef0)

- degree
- parameter needed for kernel of type
`polynomial`

(default: 3) - gamma
- parameter needed for all kernels except
`linear`

(default: 1/(data dimension)) - coef0
- parameter needed for kernels of type
`polynomial`

and`sigmoid`

(default: 0) - cost
- cost of constraints violation (default: 1)---it is the ‘C’-constant of the regularization term in the Lagrange formulation.
- nu
- parameter needed for
`nu-classification`

,`nu-regression`

, and`one-classification`

- class.weights
- a named vector of weights for the different classes, used for asymmetric class sizes. Not all factor levels have to be supplied (default weight: 1). All components have to be named.
- cachesize
- cache memory in MB (default 40)
- tolerance
- tolerance of termination criterion (default: 0.001)
- epsilon
- epsilon in the insensitive-loss function (default: 0.1)
- shrinking
- option whether to use the shrinking-heuristics (default:
`TRUE`

) - cross
- if a integer value k>0 is specified, a k-fold cross validation on the training data is performed to assess the quality of the model: the accuracy rate for classification and the Mean Squared Error for regression
- fitted
- logical indicating whether the fitted values should be computed and included in the model or not (default:
`TRUE`

) - probability
- logical indicating whether the model should allow for probability predictions.
- ...
- additional parameters for the low level fitting function
`svm.default`

- subset
- An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)
- na.action
- A function to specify the action to be taken if
`NA`

s are found. The default action is`na.omit`

, which leads to rejection of cases with missing values on any required variable. An alternative is`na.fail`

, which causes an error if`NA`

cases are found. (NOTE: If given, this argument must be named.)

### Details

For multiclass-classification with k levels, k>2, `libsvm`

uses the ‘one-against-one’-approach, in which k(k-1)/2 binary classifiers are trained; the appropriate class is found by a voting scheme. `libsvm`

internally uses a sparse data representation, which is also high-level supported by the package SparseM. If the predictor variables include factors, the formula interface must be used to get a correct model matrix.

`plot.svm`

allows a simple graphical visualization of classification models.

The probability model for classification fits a logistic distribution using maximum likelihood to the decision values of all binary classifiers, and computes the a-posteriori class probabilities for the multi-class problem using quadratic optimization. The probabilistic regression model assumes (zero-mean) laplace-distributed errors for the predictions, and estimates the scale parameter using maximum likelihood.

### Values

An object of class `"svm"`

containing the fitted model, including:

- 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`

) - coefs
- The corresponding coefficients times the training labels.
- rho
- The negative intercept.
- sigma
- In case of a probabilistic regression model, the scale parameter of the hypothesized (zero-mean) laplace distribution estimated by maximum likelihood.
- 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))).

### References

- Chang, Chih-Chung and Lin, Chih-Jen:

*LIBSVM: a library for Support Vector Machines*

http://www.csie.ntu.edu.tw/~cjlin/libsvm - Exact formulations of models, algorithms, etc. can be found in the document:

Chang, Chih-Chung and Lin, Chih-Jen:

*LIBSVM: a library for Support Vector Machines*

http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.ps.gz - More implementation details and speed benchmarks can be found on: Rong-En Fan and Pai-Hsune Chen and Chih-Jen Lin:

*Working Set Selection Using the Second Order Information for Training SVM*

http://www.csie.ntu.edu.tw/~cjlin/papers/quadworkset.pdf

### Note

Data are scaled internally, usually yielding better results.

Parameters of SVM-models usually *must* be tuned to yield sensible results!

### See Also

`predict.svm`

`plot.svm`

`tune.svm`

`matrix.csr`

(in package SparseM)

### Examples

data(iris) attach(iris) ## classification mode # default with factor response: model <- svm(Species ~ ., data = iris) # alternatively the traditional interface: x <- subset(iris, select = -Species) y <- Species model <- svm(x, y) print(model) summary(model) # test with train data pred <- predict(model, x) # (same as:) pred <- fitted(model) # Check accuracy: table(pred, y) # compute decision values and probabilities: pred <- predict(model, x, decision.values = TRUE) attr(pred, "decision.values")[1:4,] # visualize (classes by color, SV by crosses): plot(cmdscale(dist(iris[,-5])), col = as.integer(iris[,5]), pch = c("o","+")[1:150 %in% model$index + 1]) ## try regression mode on two dimensions # create data x <- seq(0.1, 5, by = 0.05) y <- log(x) + rnorm(x, sd = 0.2) # estimate model and predict input values m <- svm(x, y) new <- predict(m, x) # visualize plot(x, y) points(x, log(x), col = 2) points(x, new, col = 4) ## density-estimation # create 2-dim. normal with rho=0: X <- data.frame(a = rnorm(1000), b = rnorm(1000)) attach(X) # traditional way: m <- svm(X, gamma = 0.1) # formula interface: m <- svm(~., data = X, gamma = 0.1) # or: m <- svm(~ a + b, gamma = 0.1) # test: newdata <- data.frame(a = c(0, 4), b = c(0, 4)) predict (m, newdata) # visualize: plot(X, col = 1:1000 %in% m$index + 1, xlim = c(-5,5), ylim=c(-5,5)) points(newdata, pch = "+", col = 2, cex = 5) # weights: (example not particularly sensible) i2 <- iris levels(i2$Species)[3] <- "versicolor" summary(i2$Species) wts <- 100 / table(i2$Species) wts m <- svm(Species ~ ., data = i2, class.weights = wts)

Documentation reproduced from package e1071, version 1.6-7. License: GPL-2