An algorithm for nonmetric discriminant analysis
Raveh, Pattern Recognition 16(2) (1983) 253259; J. Amer. Statist. Assoc. 84 (1989) 176183, proposed a nonmetric discriminant procedure for two groups based on maximization of an index of separation. He used Zangwill's modified Powell's conjugate directions method, which is a maximization procedure without derivatives, to estimate the parameters. The index of separation was generalized by Guttman, Psychometrika 53 (1988) 393405 for multiple groups, and was named disco (discriminant coefficient). In this paper, we compare nonmetric discriminant analysis with canonical discriminant analysis. We propose a simple gradient-based algorithm that calculates the parameters in nonmetric discriminant analysis for multiple groups by maximizing the disco. We provide a proof of the convergence of the algorithm.
canonical discriminant analysis linear discriminant analysis contraction mapping