svmpath {svmpath}

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 validation 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, eps = 1e-10, Nmoves = 3 * n, digits = 6, lambda.min = 1e-04,ridge=0, ...)

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

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

ridge

Sometimes the algorithm encounters singularities; in this case a small value of ridge, around 1e-12, can help. Default is ridge=0

...

additional arguments to some of the functions called by svmpath. One such argument that can be passed is ridge (default is 1e-10). This is used to produce "stable" solutions to linear equations.

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)