A Fixed-Point Algorithm for Finding the Optimal Covariance Matrix in Kernel Density Modeling

In this paper, we apply the methodology of cross-validation maximum likelihood estimation to the problem of multivariate kernel density modeling. We provide a fixed point algorithm to find the covariance matrix for a Gaussian kernel according to this criterion. We show that the algorithm leads to accurate models in terms of entropy estimation and Parzen classification. By means of a set of experiments, we show that the method considerably improves the performance traditionally expected from Parzen classifiers. The accuracy obtained in entropy estimation suggests its usefulness in ICA and other information-theoretic signal processing techniques