Nonlinear Discriminant Principal Component Analysis for Image Classification and Reconstruction

In this paper we present a nonlinear version of the discriminant principal component analysis, named NDPCA, that is based on kernel support vector machines (KSVM) and the AdaBoost technique. Specifically, the problem of ranking principal components, computed from two-class databases, is addressed by applying the AdaBoost procedure in a nested loop: each iteration of the inner loop boosts weak classifiers to a moderate one while the outer loop combines the moderate classifiers to build the global discriminant vector. In the proposed NDPCA, each weak learner is a linear classifier computed through a separating hyperplane defined by a KSVM decision boundary in the PCA space. We compare the proposed methodology with counterpart ones using facial expressions of the Radboud and Jaffe image databases. Our experimental results have shown that NDPCA outperforms the PCA in classification tasks. Also, it is competitive if compared with counterpart techniques given also suitable results for reconstruction.