Nonparametric measures of dependence for biometric data studies

This paper explores the possibility of using nonparametric dependence characteristics to evaluate biometric systems or algorithms. The extensions of classical rank correlation coefficients to the case when only a given number of top matches is used, are investigated. Difficulties with these coefficients in capturing the total correlation are noted. A version of a scan statistic, which measures co-occurrence of rankings for two arbitrary algorithms, is studied. The exact covariance structure of this statistic is found for a pair of independent algorithms. In the general case, its asymptotic normality is derived by using classical results on linear rank statistics. The concept of copula is shown to be useful for the study of nonparametric dependence characteristics. The results are applied to an example from the FERET (Face Recognition Technology) program. It is demonstrated that the random scores of considered recognition methods can be modeled by a two-parameter family of copulas exhibiting strong tail dependence.