Thesis - Instituto de Telecomunicações

96 CHAPTER 5. FEATURE SELECTION AND CLASSIFICATIONwith n f representing the number of dimensions.Several other windows can be used with the method, the restriction being that thewindow should have unitary area (volume). Examples are the rectangular window, thetriangular or the normal function windows. A free parameter that needs to be tuned isthe window width. In some works this parameter is also estimated with the criteria ofminimizing the Mean Square Error (MSE) of the difference between the estimated and thereal density function [129, 76]. In figure 5.1 we present two examples of the KDE modelingfor two window widths of the normal function.Figure 5.1: Kernel density estimation. A solid line represents the PDF of the model thatgenerated the data. The samples are marked with an x and two examples of KDE estimationsare presented for two different window widths of the normal function.Reduced Set Density EstimationA recent method called Reduced Set Density Estimation for modeling a non-parametricdensity function was introduced on [88]. It is assumed that the data is a good representativeof the source, and that it can be modeled by a KDE method. The idea is to select an optimalset of points from the original set to represent the data. The optimality criteria is theminimization of the MSE of a distance between the KDE density function and the ReducedSet Density Estimation (RSDE) estimated density function. The points will be selectedwith an associated weight. Using a reduced set, the time complexity of the estimator is