ksvm: Support Vector Machines

Description

Support Vector Machines are an excellent tool for classification as well as regression. ksvm supports the classical C-classification, nu-classification, one-class-classification e-regression, nu-regression along with the Crammer-Singer method for multi-class classification spoc-classification. A probabilistic prediction function for classification is also included.

Usage

## S3 method for class 'formula':
ksvm(x, data = NULL, ..., subset, na.action = na.omit, scaled = TRUE)
## S3 method for class 'matrix':
\S4method{ksvm(x, y = NULL, scaled = TRUE, type = NULL, kernel ="rbfdot", kpar = list(sigma = 0.1)par = list(sigma = 0.1),
C = 1, nu = 0.2, epsilon = 0.1, class.weights = NULL, cachesize = 40, tol = 0.001,
shrinking = TRUE, cross = 0, fit = TRUE, ..., subset, na.action = na.omit)

Arguments

a symbolic description of the model to be fit. Note, that an intercept is always included, whether given in the formula or not. When not using a formula x is a matrix or vector containg the variables in the model

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which `ksvm' is called from.

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).

scaled

A logical vector indicating the variables to be scaled. If scaled is of length 1, the value is recycled as many times as needed and all non-binary variables are scaled. Per default, data are scaled internally (both x

type

ksvm can be used for classification , for regression, or for novelty detection. Depending on whether y is a factor or not, the default setting for type is C-classification or eps-regres

kernel

the kernel function used in training and predicting. This parameter can be set to any function, of class kernel, which computes a dot product between two vector arguments. kernlab provides the most popular kernel functions which can be used by

kpar

the list of hyper-parameters (kernel parameters). This is a list which contains the parameters to be used with the kernel function. For valid parameters for existing kernels are :

sigma(inverse kernel width for the Radial

cost of constraints violation (default: 1)---it is the `C'-constant of the regularization term in the Lagrange formulation.

parameter needed for nu-classification, one-classification, and nu-regression. The nu parameter sets the upper bound on the training error and the lower bound on the fraction of data points t

epsilon

epsilon in the insensitive-loss function used for eps-regression and nu-regression (default: 0.1)

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)

tol

tolerance of termination criterion (default: 0.001)

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

fit

indicates whether the fitted values should be computed and included in the model or not (default: TRUE)

...

additional parameters for the low level fitting function

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 NAs 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<

Value

An S4 object of class "ksvm" containing the fitted model, Accessor functions can be used to access the slots of the object (see examples) which include:
alphaThe resulting support vectors, (alpha vector) (possibly scaled).
alphaindexThe index of the resulting support vectors in the data matrix. Note that this index refers to the pre-processed data (after the possible effect of na.omit and subset)
coefsThe corresponding coefficients times the training labels.
bThe negative intercept.
nSVThe number of Support Vectors
errorTraining error
crossCross validation error, (when cross > 0)

Details

For multiclass-classification with k levels, k>2, ksvm 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. If the predictor variables include factors, the formula interface must be used to get a correct model matrix. The predict function can return probabilistic output (probability matrix) in the case of classification by setting the type parameter to "probabilities".

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
J. Platt Probabilistic outputs for support vector machines and comparison to regularized likelihood methods Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B. Schoelkopf and D. Schuurmans, Eds. Cambridge, MA: MIT Press, 2000. http://citeseer.nj.nec.com/platt99probabilistic.html
H.-T. Lin, C.-J. Lin and R. C. Weng A note on Platt's probabilistic outputs for support vector machines http://www.csie.ntu.edu.tw/~cjin/papers/plattprob.ps
C.-W. Hsu and C.-J. Lin A comparison on methods for multi-class support vector machines IEEE Transactions on Neural Networks, 13(2002) 415-425. http://www.csie.ntu.edu.tw/~cjlin/papers/multisvm.ps.gz
K. Crammer, Y. Singer On the learnability and design of output codes for multiclass prolems Computational Learning Theory, 35-46, 2000. http://www.cs.huji.ac.il/~kobics/publications/mlj01.ps.gz

Examples

Run this code

## simple example using the spam data set
data(spam)


## create test and training set
index <- sample(1:dim(spam)[1])
spamtrain <- spam[index[1:floor(2 * dim(spam)[1]/3)], ]
spamtest <- spam[index[((2 * ceiling(dim(spam)[1]/3)) + 1):dim(spam)[1]], ]

## train a support vector machine
filter <- ksvm(type~.,data=spamtrain,kernel="rbfdot",kpar=list(sigma=0.05),C=5,cross=3)
filter

## predict mail type on the test set
mailtype <- predict(filter,spamtest[,-58])

## Check results
table(mailtype,spamtest[,58])


## Another example with the famous iris data
data(iris)

## Create a kernel function using the build in rbfdot function
rbf <- rbfdot(sigma=0.1)
rbf

## train a support vector machine
irismodel <- ksvm(Species~.,data=iris,kernel=rbf,C=10)

irismodel

## get fitted values
fit(irismodel)

## Test on the training set with probabilities as output
predict(irismodel, iris[,-5], type="probabilities")


## regression
# create data
x <- seq(-20,20,0.1)
y <- sin(x)/x + rnorm(401,sd=0.03)

# train support vector machine
regm <- ksvm(x,y,epsilon=0.01,kpar=list(sigma=16),cross=3)
plot(x,y,type="l")
lines(x,predict(regm,x),col="red")

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