Multi-class pairwise linear dimensionality reduction using heteroscedastic schemes

Linear dimensionality reduction (LDR) techniques have been increasingly important in pattern recognition (PR) due to the fact that they permit a relatively simple mapping of the problem onto a lower-dimensional subspace, leading to simple and computationally efficient classification strategies. Although the field has been well developed for the two-class problem, the corresponding issues encountered when dealing with multiple classes are far from trivial. In this paper, we argue that, as opposed to the traditional LDR multi-class schemes, if we are dealing with multiple classes, it is not expedient to treat it as a multi-class problem per se. Rather, we shall show that it is better to treat it as an ensemble of Chernoff-based two-class reductions onto different subspaces, whence the overall solution is achieved by resorting to either Voting, Weighting, or to a Decision Tree strategy. The experimental results obtained on benchmark datasets demonstrate that the proposed methods are not only efficient, but that they also yield accuracies comparable to that obtained by the optimal Bayes classifier.