svmpath {svmpath}R Documentation

Fit the entire regularization path for a 2-class SVM

Description

The SVM has a regularization or cost parameter C, which controls the amount by which points overlap their soft margins. Typically either a default large value for C is chosen (allowing minimal overlap), or else a few values are compared using a valication set. This algorithm computes the entire regularization path (i.e. for all possible values of C for which the solution changes), with a cost a small (~3) multiple of the cost of fitting a single model.

Usage

svmpath(x, y, K, kernel.function = poly.kernel, param.kernel = 1, trace, plot.it, linear.plot, eps = 1e-10, Nmoves = 3 * n, digits = 6, lambda.min = 1e-04, ...)

Arguments

x the data matrix (n x p) with n rows (observations) on p variables (columns)
y The {-1,+1} valued response variable.
K a n x n kernel matrix, with default value K= kernel.function(x, x)
kernel.function This is a user-defined function. Provided are poly.kernel (the default, with parameter set to default to a linear kernel) and radial.kernel
param.kernel parameter(s) of the kernels
trace if TRUE, a progress report is printed as the algorithm runs; default is FALSE
plot.it a flag indicating whether a plot should be produced (default FALSE; only usable with p=2
linear.plot if TRUE, the plotting routine exploits the knowledge that the solution is linear; otherwise a contour algorithm is used. The default is missing(kernel) (i.e. TRUE if a default linear kernel is used
eps a small machine number which is used to identify minimal step sizes
Nmoves the maximum number of moves
digits the number of digits in the printout
lambda.min The smallest value of lambda = 1/C; default is lambda=10e-4, or C=10000
... additional arguments to some of the functions called by svmpath

Details

The algorithm used in svmpath() is described in detail in "The Entire Regularization Path for the Support Vector Machine" by Hastie, Rosset, Tibshirani and Zhu (2004). It exploits the fact that the "hinge" loss-function is piecewise linear, and the penalty term is quadratic. This means that in the dual space, the lagrange multipliers will be pieceise linear (c.f. lars).

Value

a "svmpath" object is returned, for which there are print, summary, coef and predict methods.

Warning

Currently the algorithm can get into machine errors if epsilon is too small, or if lambda.min is too small. Increasing either from their defaults should make the problems go away, by terminating the algorithm slightly early.

Note

This implementation of the algorithm does not use updating to solve the "elbow" linear equations. This is possible, since the elbow changes by a small number of points at a time. Future version of the software will do this. The author has encountered numerical problems with early attempts at this.

Author(s)

Trevor Hastie

References

The paper http://www-stat.stanford.edu/~hastie/Papers/svmpath.pdf, as well as the talk http://www-stat.stanford.edu/~hastie/TALKS/svmpathtalk.pdf.

See Also

print, coef, summary, predict, and FilmPath

Examples

data(svmpath)
attach(unbalanced.separated)
svmpath(x,y,trace=TRUE,plot=TRUE)
detach(2)
## Not run: svmpath(x,y,kernel=radial.kernel,param.kernel=.8)

[Package svmpath version 0.92 Index]