关键词: 降维, 判别分析, 核诱导的距离, 鲁棒性

Abstract: This paper proposes a robust discriminant analysis based on kernel-induced distance measure (KI-RDA). KI-RDA not only extends the linear discriminant analysis (LDA), but also extends the newest and powerful algorithm called robust discriminant analysis based on nonparametric maximum entropy (MaxEnt-RDA). By using robust radial basis function (RBF) kernels, KI-RDA can effectively deal with the data mixed with noise as well as the non-Gaussian distributed nonlinear data. Its robustness is accredited to that KI-RDA makes use of the kernel-induced non-Euclidean distance instead of the Euclidean distance in LDA to characterize the within-class and between-class divergence respectively. With the aid of these divergences, the paper defines a discriminant criterion which is similar to LDA for feature extraction, but this leads to a corresponding nonlinear optimization problem. With the further help of approximation strategy, the problem is converted into a generalized eigenvalue problem which can be solved directly so as to get a closed-form solution of the dimensionality reduction matrix. At last, experiments on multifold datasets verify the effectiveness of KI-RDA.?Because of the diversity of kernel functions, KI-RDA is actually a general discriminant analysis framework.

Key words: dimensionality reduction, discriminant analysis, kernel-induced distance, robustness