On a modified form of Parzen estimator for nonparametric pattern recognition

Abstract

The use of Bayesian Strategy in pattern recognition problems involves the estimation of probability density function of each of the categories of patterns. If the functional forms of the density functions are not known, the estimation has to be done nonparametrically. A commonly used nonparametric density estimator makes use of the weighting function technique, developed for the one dimensional case by Parzen and later extended to the multi-dimensional case by Murthy. Several authors (Shanmugam, Koontz and Fukunaga, and Duin) have suggested modified forms of Parzen estimator for a variety of applications. In this paper, we derive a form of Parzen estimator which uses a data dependent smoothing matrix and a Gaussian weighting function. We show that this form of Parzen estimator has some desirable parametric properties. We also establish that the estimator is asymptotically consistent.