Nonparametric feature selection

Abstract

Two groups ofL-dimensional observations of sizeN_{1}andN_{2}are known to be random vector variables from two unknown probability distribution functions [1]. A method is discussed for obtaining anl-dimensional linear subspace of the observation space in which thel-variate marginal distributions are most separated, based on a nonparametric estimate of probability density functions and a distance criterion. The distance used essentially is theL_{2}norm of the difference between Parzen estimates of the two densities. An algorithm is developed that determines the subspace for which the distance between the two densities is maximized. Computer simulations are performed.