Supervised dimensionality reduction technology of generalized discriminant component analysis and its kernelization forms. (April 2022) - Zhou, Ruixu; Gao, Wensheng; Ding, Dengwei; Liu, Weidong
Highlights: Supervised subspace projection is a major method conducive to pattern recognition. Generalized discriminant component analysis is aimed at dimensionality reduction. Kernelization forms are proposed for nonlinear subspace projection. Multi-dimensional Fisher discriminant analysis are improved. The theoretical validity and technical advantages are comprehensively verified. Abstract: Supervised subspace projection technology is a major method for dimensionality reduction in pattern recognition. At present, most supervised subspace projection algorithms are derived from the multi-dimensional extended version of Fisher linear discriminant analysis (FDA), also known as Multi-dimensional Fisher discriminant analysis (MD-FDA). However, MD-FDA needs to be improved further because the projection vectors in the noise-subspace cannot be sorted and the ill-condition of the within-class scatter matrix may cause severe numerical instabilities. Generalized discriminant component analysis (GDCA), the generalization of MD-FDA, together with its kernelization forms are proposed and correspondingly rigorous mathematical proofs are detailed in this paper. By virtue of 5 validation data sets derived from UCI Machine Learning Repository and our laboratory, the theoretical validity and technical advantages of GDCA as well as its kernelization forms are verified, and the effectiveness of the newly proposed method is demonstrated in comparison with 36 kinds of state-of-the-art dimensionality reduction algorithms.