Norm Discriminant Eigenspace Transform for Pattern Classification.

Most of the supervised dimensionality reduction (DR) methods design interclass scatter as the separability between the class means, which may force to assume unimodal Gaussian likelihoods and their projection space trends toward the class means. This paper presents a novel DR approach, norm discriminant eigenspace transform (NDET), in which average norms ( l ) of classes have been utilized to characterize the interclass separability and the within-class distance characterizes the intraclass compactness. NDET is intended to accommodate data distributions that may be multimodal and non-Gaussian. We derive an upper bound for NDET, and a specific solution space to attain this bound. Existence of the specific solution is very unwonted, thereby we have considered the solution space of upper bound to achieve better reduction of dimensionality and discrimination of classes. Also, a nonlinear version of NDET (kernel NDET) is developed to model nonlinear relationships between the features. We show, experimentally (on synthetic data) that NDET effectively overcomes the limitations, which arise due to unimodal and data distribution assumptions of the traditional algorithms. Extensive empirical studies are made; and the proposed method is compared with closely related state-of-the-art schemes on UCI machine learning repository and face recognition data sets, to establish its novelty.