Kernel SODA: A Feature Reduction Technique Using Kernel Based Analysis

A feature extraction technique called Successively Orthogonal Discriminant Analysis (SODA) has been recently proposed to overcome the limitation of Linear Discriminant Analysis (LDA), whose objective is to find a projection vector such that the projected values of data from both classes have maximum class separability. However, in LDA, only one such vector can be found due to the rank deficiency for binary classification problems. On the other hand, as a feature extraction technique, the proposed algorithm SODA attempts to obtain a transformation matrix instead of a vector. In this paper, the kernel version of SODA is presented in both intrinsic space and empirical space. To obtain the solution without sacrificing numerical efficiency, we propose a relaxed formulation and data selection for large scale computations. Simulations are conducted on 5 data sets from UCI database to verify and evaluated the new approach.