Parzen Discriminant Analysis

In this paper, we propose a non-parametric discriminant analysis method (no assumption on the distributions of classes), called Parzen discriminant analysis (PDA). Through a deep investigation on the non-parametric density estimation, we find that minimizing/maximizing the distances between each data sample and its nearby similar/dissimilar samples is equivalent to minimizing an upper bound of the Bayesian error rate. Based on this theoretical analysis, we define our criterion as maximizing the average local dissimilarity scatter with respect to a fixed average local similarity scatter. All local scatters are calculated in fixed size local regions, resembling the idea of Parzen estimation. Experiments in UCI machine learning database show that our method impressively outperforms other related neighbor based non-parametric methods.