Eigenvector-Based Feature Extraction for Classification

This paper shows the importance of the use of class information in feature extraction for classification and inappropriateness of conventional PCA to feature extraction for classification. We consider two eigenvector-based approaches that take into account the class information. The first approach is parametric and optimizes the ratio of between-class variance to within-class variance of the transformed data. The second approach is a nonparametric modification of the first one based on local calculation of the between-class covariance matrix. We compare the two approaches with each other, with conventional PCA, and with plain nearest neighbor classification without feature extraction.