An estimator of the L-2-probabilistic dependence measure for vectorial reduction dimension. Multiclass case
We introduce an estimate of the L-2-probabilistic dependence measure constructed with the generalized Fourier series which is able to realize a linear vector feature dimensional reduction in the discriminate multi-class problem. It generalizes the Patrick-Fischer distance estimate generally used for dimensionality reduction of the feature space in the case of binary classification. It has a direct relationship with the probability classification error. We compare the proposed algorithm with the well known linear discriminate analysis (LDA) and with a generalized version of a multi class recursive linear extractor based on the L-2-probabilistic dependence measure (RID L-2-PMD). For vector Gaussian mixtures such comparison is done in the mean of the probability error of classification which is estimated by a multivariate Kernel probability density function. The corresponding smoothing parameters are optimized analytically in the sense of the Mean Integrated Square Error (MISE). The non Gaussian case is evaluated with the error of the k nearest neighborhood classifier. Finally we will illustrate the importance of the proposed method by testing it in the context of the face recognition.
l-2-probabilistic dependence measure reduction dimension smoothing parameter