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Proceedings Paper

Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition
Author(s): Xiaoming Huo; Michael Elad; Ana Georgina Flesia; Robert R. Muise; S. Robert Stanfill; Jerome Friedman; Bogdan Popescu; Jihong Chen; Abhijit Mahalanobis; David L. Donoho
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Paper Abstract

In target recognition applications of discriminant of classification analysis, each 'feature' is a result of a convolution of an imagery with a filter, which may be derived from a feature vector. It is important to use relatively few features. We analyze an optimal reduced-rank classifier under the two-class situation. Assuming each population is Gaussian and has zero mean, and the classes differ through the covariance matrices: ∑1 and ∑2. The following matrix is considered: Λ=(∑1+∑2)-1/21(∑1+∑2)-1/2. We show that the k eigenvectors of this matrix whose eigenvalues are most different from 1/2 offer the best rank k approximation to the maximum likelihood classifier. The matrix Λ and its eigenvectors have been introduced by Fukunaga and Koontz; hence this analysis gives a new interpretation of the well known Fukunaga-Koontz transform. The optimality that is promised in this method hold if the two populations are exactly Guassian with the same means. To check the applicability of this approach to real data, an experiment is performed, in which several 'modern' classifiers were used on an Infrared ATR data. In these experiments, a reduced-rank classifier-Tuned Basis Functions-outperforms others. The competitive performance of the optimal reduced-rank quadratic classifier suggests that, at least for classification purposes, the imagery data behaves in a nearly-Gaussian fashion.

Paper Details

Date Published: 16 September 2003
PDF: 14 pages
Proc. SPIE 5094, Automatic Target Recognition XIII, (16 September 2003); doi: 10.1117/12.499594
Show Author Affiliations
Xiaoming Huo, Georgia Institute of Technology (United States)
Michael Elad, Stanford Univ. (United States)
Ana Georgina Flesia, Stanford Univ. (United States)
Robert R. Muise, Lockheed Martin Missiles and Fire Control (United States)
S. Robert Stanfill, Lockheed Martin (United States)
Jerome Friedman, Stanford Univ. (United States)
Bogdan Popescu, Stanford Univ. (United States)
Jihong Chen, Georgia Institute of Technology (United States)
Abhijit Mahalanobis, Lockheed Martin Missiles and Fire Control (United States)
David L. Donoho, Stanford Univ. (United States)


Published in SPIE Proceedings Vol. 5094:
Automatic Target Recognition XIII
Firooz A. Sadjadi, Editor(s)

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