Discriminant analysis and similarity measure

The cosine similarity measure is often applied after discriminant analysis in pattern recognition. This paper first analyzes why the cosine similarity is preferred by establishing the connection between the cosine similarity based decision rule in the discriminant analysis framework and the Bayes decision rule for minimum error. The paper then investigates the challenges inherent of the cosine similarity and presents a new similarity that overcomes these challenges. The contributions of the paper are thus threefold. First, the application of the cosine similarity after discriminant analysis is discovered to have its theoretical roots in the Bayes decision rule. Second, some inherent problems of the cosine similarity such as its inadequacy in addressing distance and angular measures are discussed. Finally, a new similarity measure, which overcomes the problems by integrating the absolute value of the angular measure and the l(p) norm (the distance measure), is presented to enhance pattern recognition performance. The effectiveness of the proposed new similarity measure in the discriminant analysis framework is evaluated using a large scale, grand challenge problem, namely, the Face Recognition Grand Challenge (FRGC) problem. Experimental results using 36,818 FRGC images on the most challenging FRGC experiment, the FRGC Experiment 4, show that the new similarity measure improves face recognition performance upon other popular similarity measures, such as the cosine similarity measure, the normalized correlation, and the Euclidean distance measure. (C) 2013 Elsevier Ltd. All rights reserved.