A heteroscedastic extension of LDA based on multi-class matusita affinity

Linear discriminant analysis (LDA), a conventional feature extraction technique, is a homoscedastic solution and ignores the second order information of the data. A heteroscedastic extension of LDA has been previously proposed which relies on the average pairwise Chernoff distances of the classes. However, in a multi-class scenario with number of classesC >; 2, the average of pairwise distances is not directly related to the classification error rate. Furthermore, the corresponding method imposes a high computational complexity of order O(C(C - 1)). This paper proposes an inherently multi-class heteroscedastic extension of LDA based on Matusita´s separability measure, a multi-class generalization of the Chernoff distance which is related to multi-class error bounds. The proposed feature extractor can be trained non-iteratively with computational complexity of O(C). Experimental comparisons with the Chernoffmethod demonstrate both a performance improvement when estimated parameters are used, and a reduction of factor C - 1 in the computational load as predicted.