Range Space Hyperspherical Discriminant Analysis

Fisher’s discriminant analysis (LDA) is one of the most widely used linear methods in pattern recognition. However, in practical case, the number of samples is relatively small respect to the dimention of sample vector space. Samples distribut sparsely in high dimensional space. LDA which is based on the Euclidean distance metric tends to the great inter-distance, which results to merge close classes. We adopt hypersphere model to denote high dimensional data structure information and present a range space hypersphere discriminant analysis (RHDA). RHDA maps data on a unit hypersphere of the range space and compute the discriminant space of each subclass. It computes the distance between test sample and the center of each class in the class discriminant sapce and classifies the test sample into class i only the distance from the test sample to the center of class i is the smallest. RHDA utilizes a normalized vector of the unit hypersphere to denote the structure information of a sample vector. It is designed for the deviation of problem of LDA. The kernel approach of range space hyperspherical discriminant analysis was also presented in this paper. This enables different maps for different kinds of data in high dimensional space. Experiment results on different databases verified the good performance beyond LDA and its relative developments.