Optimal Reduced-Rank Quadratic Classifiers Using the Fukunaga-Koontz Transform, with Applications to Automated Target Recognition

XIAOMING HUO; MICHAEL ELAD,; ANA GEORGINA FLESIA; BOB MUISE; ROBERT STANFILL; JEROME FRIEDMAN; BOGDAN POPESCU; JIHONG CHEN; ABHIJIT MAHALANOBIS; DAVID L. DONOHO

Orlando, Florida

Simposio; SPIE's 7th Annual International Symposium on Aerospace/Defense Sensing, Simulation, and Controls (AeroSense),; 2003

SPIE

In target recognition applications of discriminant or 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: Σ1 and Σ2. The following matrix is considered: Λ = (Σ1 +Σ2)−1/2Σ1(Σ1 +Σ2)−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 Gaussian 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.