## DIMACS TR: 2004-08

## Simultaneous Feature Selection And Margin Maximization Using Saddle Point Approach

### Authors: Yuri Goncharov, Ilya Muchnik and Leonid Shvartser

**
ABSTRACT
**

A new SVM wrapper method, which simultaneously maximizes margin and
minimizes feature space is introduced. For these purposes we modify the
standard criterion by adding to the basic objective function a third term,
which directly penalizes a chosen set of variables. The new criterion
divided the set of all variables into three subsets: deleted, selected and
weighted features. We are showing that the question can be formulated as a
particular min-max problem for convex-concave functions, which in turn can
be solved by saddle point polynomial algorithms. We analyzed a set of such
algorithms and realized one, which is taking to account specificity of our
problem. The algorithm is examined on a classification Benchmark and its
ability to improve the recognition results is shown. We also show that the
developed method can be easily transfered to the Support Vector Regression
case.

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2004/2004-08.ps.gz

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