A Study of Statistical Pattern Verification

Abstract

A decision theoretic approach to the problem of verifying that a given observation "belongs" to a claimed pattern is examined. The problem presupposes a nonzero probability of impersonations, and verifier actions are ternary in general: a claimed identity is either 1) accepted or 2) rejected, or it is 3) "blanked" when the verifier refuses to take either of the actions 1) and 2). Corresponding costs-of-wrong decision will be typically different in applications like speaker verification. We characterize sample observations by normal distributions and provide explicit results for the analytically simple situation of "efficient" measurements whose interpattern variances are much greater than their intrapattern variances. In our specific model this will imply that the pdf of a measurement under the "impersonator" hypothesis is "diffuse" in relation to the pdf of the same measurement under any of several "true-pattern" hypotheses. We demonstrate that the likelihood ratio function, in a typical verification task, possesses a finite upper bound and that this is related to a certain threshold effect for verifier decisions. We further mention the suitability of a minimax strategy for verification and compare its performance with those of optimal (minimum-cost) and maximum-likelihood procedures for the binary decision (accept-or-reject) problem. We provide numerical examples that illustrate the minimax performance as a function of 1) a parameter which reflects the peculiarity of the claimed pattern, and of 2) the measurement dimensionality.