Generalized nonlinear discriminant analysis and its small sample size problems

Authors:
Li Zhang;Wei Da Zhou;Pei-Chann Chang
Affiliations:
Research Center of Machine Learning and Data Analysis, School of Computer Science and Technology, Soochow University, Suzhou 215006, Jiangsu, China and Institute of Intelligent Information Process ...;Institute of Intelligent Information Processing, Xidian University, Xi'an 710071, Shaanxi, China;Department of Information Management, Yuan Ze University, Taoyuan 32026, Taiwan, China
Venue:
Neurocomputing
Year:
2011

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Abstract

This paper develops a generalized nonlinear discriminant analysis (GNDA) method and deals with its small sample size (SSS) problems. GNDA is a nonlinear extension of linear discriminant analysis (LDA), while kernel Fisher discriminant analysis (KFDA) can be regarded as a special case of GNDA. In LDA, an under sample problem or a small sample size problem occurs when the sample size is less than the sample dimensionality, which will result in the singularity of the within-class scatter matrix. Due to a high-dimensional nonlinear mapping in GNDA, small sample size problems arise rather frequently. To tackle this issue, this research presents five different schemes for GNDA to solve the SSS problems. Experimental results on real-world data sets show that these schemes for GNDA are very effective in tackling small sample size problems.