Optimization of the smoothing parameter of variable kernel estimator

Classification methods based on unsupervised statistical estimation of the probability density function have a large scope, but many problems affect performance of these methods to find the optimal choice of window width of estimator. In this article, we looked at a variable kernel estimator of the probability density function which is a hybrid method of the k-nearest neighbor´s estimator (k-NN) and the Parzen kernel estimator. This estimator combines the properties of both techniques in order to have a method that works well on a wide variety of situations and exploits the advantages of both. The optimization algorithm is founded on the principle of maximum entropy that provides an optimal choice of the discretization step of combining nonparametric estimator of Parzen kernel and k-NN with a minimum classification error rate. Experimental results are finally announced to highlight the robustness of the approach used.