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[Help-glpk] formulating svm

From: Kaustubh Raosaheb Patil
Subject: [Help-glpk] formulating svm
Date: Tue, 16 Mar 2010 13:51:06 +0100
User-agent: Mozilla-Thunderbird (X11/20090105)


I am trying to formulated a linear programming svm (support vector machine) using glpk. The problem is described as follows, given a set of observations X (a matrix with n rows and m columns) and a vector y with class labels {+1,-1} for each of the observations (n entries); find the following optimized solutions;


minimize 0.5 * SUM{from j=1 to m} |wj| - ( SUM{from i=1 to n} alphai * (yi*(w^T*xi - 1)) )

i and j indicate the vector/matrix elements
here vector w is the weight vector of length m
alpha is a vector of length n (Lagrange multipliers)


maximize SUM{for i=1 to n} alphai - 0.5 * SUM{from i,j=1 to n} alphai*alphaj*yi*yj*(xi^T*xj)

subject to alphai >= 0 for i=1 to n

specifically I would like to use the R interface to glpk. I am not sure how these objective functions can be converted into a vector of coefficients.

Any suggestions are welcome.


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