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Discriminant Analysis Based On hyperellipsoid

Distribution

**Jun S. Huang and Mark C. K. Yang ^{*}**

Academia Sinica

Taipei, Taiwan, R.O.C.

Unviersity of Florida

Gainesville, Florida 32611,USA.

In classical pattern recognition methods, discriminant analysis has been widely used. Much commercial software for this anaalysis is available. However, little has been done on discriminant analysis with a multivariate distribution of finite range. This is improtant to optical character recognition where the size of an input character is always normalized to a fixed value, and thus, all extracted feature values have finite ranges. In this paper, the hyperell psoid probability density function, which is zero outside of a hyperellipsoid, is used to model the data and to con struct the discriminant function using the Bayes rule. Two data sets, onefrom handwritten English capital letters and another from remote sensing of five crops, are used for illustration. Three classification rules, one based on multinormal distribution, one on gyperellipsoid distribution, and one on the k-nearest neighbor rule, are compared. It is found that the rule with hyperellipsoid dis tribution performs almost as well as the rule with multinormal distribution on the first data set but does much better on the second. The k-nearest neighbor rule is the worst on both data sets. This study demonstrates that the discriminant rule with hyperellipsoid sidtribution should be considered as a viable candidate when all features have finite ranges.

Keywords: discriminant analysis, hyperellipsoid distribution, multinormal distribution, k-nearest neighbor rule, character recognition

Received April 7, 1993; revised October 23, 1993.

Communicated by Soo-Chang Pei.