Linear dimensionality reduction by maximizing the Chernoff distance in the transformed space

Linear dimensionality reduction (LDR) techniques are quite important in pattern recognition due to their linear time complexity and simplicity. In this paper, we present a novel LDR technique which, though linear, aims to maximize the Chernoff distance in the transformed space; thus, augmenting the class separability in such a space. We present the corresponding criterion, which is maximized via a gradient-based algorithm, and provide convergence and initialization proofs. We have performed a comprehensive performance analysis of our method combined with two well-known classifiers, linear and quadratic, on synthetic and real-life data, and compared it with other LDR techniques. The results on synthetic and standard real-life datasets show that the proposed criterion outperforms the latter when combined with both linear and quadratic classifiers. ∗Member of the IEEE. Department of Computer Science, University of Concepción, Edmundo Larenas 215, Concepción, 4030000, Chile. Phone: +56 41 220-4305, Fax: +56 41 222-1770. E-mail: [email protected]. Partially supported by the Chilean National Fund for Scientific and Technological Development, FONDECYT grant No. 1060904. †Institute of Informatics, National University of San Juan, Cereceto y Meglioli, San Juan, 5400, Argentina. E-mail: [email protected]