Feature Extraction Based on Decision Boundaries

This material is posted here with permission of the IEEE. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by sending a blank email message to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. < Abstract > In this paper, a novel approach to feature extraction for classification is proposed based directly on the decision boundaries. We note that feature extraction is equivalent to retaining informative features or eliminating redundant features, thus first the terms "discriminantly informative feature" and "discriminantly redundant feature" are defined relative to feature extraction for classification. Next it is shown how discriminantly redundant features and discriminantly informative features are related to decision boundaries. A novel characteristic of the proposed method arises by noting that usually only a portion of the decision boundary is effective in discriminating between classes, and the concept of the effective decision boundary is therefore introduced. Next a procedure to extract discriminantly informative features based on a decision boundary is proposed. The proposed feature extraction algorithm has several desirable properties: (1) it predicts the minimum number of features necessary to achieve the same classification accuracy as in the original space for a given pattern recognition problem, and (2) it finds the necessary feature vectors. The proposed algorithm does not deteriorate under the circumstances of equal class means or equal class covariances as some previous algorithms do. Experiments show that the performance of the proposed algorithm compares favorably with those of previous algorithms.