%A P. S. Bradley
%A O. L. Mangasarian
%A W. N. Street
%T Feature Selection via Mathematical Programming
%D December 1995
%R 95-21
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X 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. One feature selection algorithm via
concave minimization (FSV) improved cross-validation on
a cancer prognosis database by 23.7\% while reducing problem
features from 32 to 4.