Smoothing Parameters Selection for Dimensionality Reduction Method based on Probabilistic Distance - Application to Handwritten Recognition

Abstract

Here, we intend to give a rule for the choice of the smoothing parameter of the orthogonal estimate of Patrick-Fisher distance in the sense of the Mean Integrate Square Error. The orthogonal series density estimate precision depends strongly on the choice of such parameter which corresponds to the number of terms in the series expansion used. By using series of random simulations, we illustrate the better performance of its dimensionality reduction in the mean of the misclassification rate. We show also its better behavior for real data. Different invariant shape descriptors describing handwritten digits are extracted from a large database. It serves to compare the proposed adjusted Patrick-Fisher distance estimator with a conventional feature selection method in the mean of the probability error of classification.In the following, we just recall the orthogonal series density estimation method by presenting its essen-325