An Approximation Method of the Quadratic Discriminant Function and Its Application to Estimation of High-Dimensional Distribution

Shinichiro OMACHI  Masako OMACHI  Hirotomo ASO  

IEICE TRANSACTIONS on Information and Systems   Vol.E90-D    No.8    pp.1160-1167
Publication Date: 2007/08/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e90-d.8.1160
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Image Recognition and Understanding)
pattern recognition,  quadratic discriminant function,  small sample size problem,  simplified quadratic discriminant function,  normal mixture,  

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In statistical pattern recognition, it is important to estimate the distribution of patterns precisely to achieve high recognition accuracy. In general, precise estimation of the parameters of the distribution requires a great number of sample patterns, especially when the feature vector obtained from the pattern is high-dimensional. For some pattern recognition problems, such as face recognition or character recognition, very high-dimensional feature vectors are necessary and there are always not enough sample patterns for estimating the parameters. In this paper, we focus on estimating the distribution of high-dimensional feature vectors with small number of sample patterns. First, we define a function, called simplified quadratic discriminant function (SQDF). SQDF can be estimated with small number of sample patterns and approximates the quadratic discriminant function (QDF). SQDF has fewer parameters and requires less computational time than QDF. The effectiveness of SQDF is confirmed by three types of experiments. Next, as an application of SQDF, we propose an algorithm for estimating the parameters of the normal mixture. The proposed algorithm is applied to face recognition and character recognition problems which require high-dimensional feature vectors.