Orthogonal discriminant analysis revisited

Orthogonal discriminant analysis (ODA) methods extend traditional discriminant analysis (DA) methods under the condition of orthonormality of features. Despite many practical successes of the ODA methods in the literature of face recognition, some basic properties and crucial problems with respect to the ODA methods have not been explored or solved yet. For this sake, we revisit ODA in this paper. First, we introduce a new technique quite different from traditional one to answer one open problem raised by Cai et al. (IEEE Transactions on Image Processing, 2006), i.e., a unified theoretical justification for understanding and explaining the experimental phenomenon that the eigenvalues of the ODA methods are consistently larger than their DA counterparts. Comprehensive comparisons and extensive experiments on twenty real data sets verify our theoretical conclusion. Second, we reveal a fundamental problem concerning the usability of the ODA methods through our experiments, i.e., they are not consistently better than those of the corresponding DA methods in terms of the performance of recognition, especially when they were used onto low-dimensional problems.