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<TITLE>Feature Selection via Mathematical Programming </TITLE>
<H2>Feature Selection via Mathematical Programming </H2>
 P. S. Bradley,  O. L. Mangasarian and  W. N. Street<BR>
MP-TR-95-21<BR>
December 1995
<p>
 The problem of discriminating between two finite point sets in $n$-dimensional feature space by a separating plane that utilizes as few of the features as possible, is formulated as a mathematical program with a parametric objective function and linear constraints. The step function that appears in the objective function can be approximated by a sigmoid or by a concave exponential on the nonnegative real line, or it can be treated exactly by considering the equivalent linear program with equilibrium constraints (LPEC). Computational tests of these three approaches on publicly available real-world databases have been carried out and compared with an adaptation of the optimal brain damage (OBD) method for reducing neural network complexity.<P>
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