Simple and effective connectionist nonparametric estimation of probability density functions

Abstract

Estimation of probability density functions (pdf) is one major topic in pattern recognition. Parametric techniques rely on an arbitrary assumption on the form of the underlying, unknown distribution. Nonparametric techniques remove this assumption In particular, the Parzen Window (PW) relies on a combination of local window functions centered in the patterns of a training sample. Although effective, PW suffers from several limitations. Artificial neural networks (ANN) are, in principle, an alternative family of nonparametric models. ANNs are intensively used to estimate probabilities (e.g., class-posterior probabilities), but they have not been exploited so far to estimate pdfs. This paper introduces a simple neural-based algorithm for unsupervised, non-parametric estimation of pdfs, relying on PW. The approach overcomes the limitations of PW, possibly leading to improved pdf models. An experimental demonstration of the behavior of the algorithm w.r.t. PW is presented, using random samples drawn from a standard exponential pdf. © Springer-Verlag Berlin Heidelberg 2006.