Approaches for Multi-Class Discriminant Analysis for Ranking Principal Components

The problem of ranking features computed by principal component analysis (PCA) in N-class problems have been addressed by the multi-class discriminant principal component analysis (MDPCA) and the Fisher discriminability criterion (FDC). These methods are motivated by the fact that PCA components do not necessarily represent important discriminant directions to separate sample groups. Given a database, the MDPCA builds a linear support vector machine (SVM) ensemble to get the separating hyperplanes that are combined through an AdaBoost technique to determine the discriminant contribution of each PCA feature. The FDC technique sorts PCA components according to the ratio of the between-class scatter over the within-class scatter. In this paper, we review these techniques and compare their performance in facial expression experiments. The classification results have shown the benefits of sorting principal components using FDC and the MDPCA though both methodologies are not so efficient when compared with PCA for reconstruction tasks.