A Novel Nonparametric Linear Discriminant Analysis for High-Dimensional Data Classification

Linear discriminant analysis (LDA) has played an important role for dimension reduction in patter recognition field. Basically, LDA has three deficiencies in dealing with classification problems. First, LDA is well-suited only for normally distributed data. Second, the number of features can be extracted are limited by the rank of between-class scatter matrix. Third, the singularity problem arises when dealing with high-dimensional data with small training samples. Nonparametric dimension reduction method, such as nonparametric discriminant analysis (NDA), is able to overcome the first two limitations of LDA, and the last problem is often resolved by regularization or eigendecomposition techniques. In this study, we propose a novel nonparametric dimension reduction method with regularization to overcome all of the previously mentioned problems. The experimental results on real datasets demonstrate that the proposing method obtains satisfactory results, even in badly posed classification conditions. Keywords—Linear discriminant analysis (LDA), dimension reduction, feature extraction, small sample size problem, regularization.