A Study on Performance Improvement Due to Linear Fusion in Biometric Authentication Tasks

In this paper, we initiate a theoretical study on ${N}$ -expert fusion ( ${N}~\boldsymbol {\geq }~2$ ) in the context of biometric authentication (BA). Optimal fusion weights, which depend on performances and variances of, and correlations among individual base-experts have been found, and we also give and prove some new theorems that serve as the basis for analyzing the performance of the overall system. Our conclusion is that provided that optimal weights are used as fusion coefficients, linear fusion will definitely lead to a better performance than the best individual expert. This contradicts many existing conclusions, which assert that fusion is not always beneficial and that performance improvement due to fusion is guaranteed only when some conditions as to base-experts’ performances, variances, and correlations are satisfied. Besides, for the first time the definition of correlation in the context of BA is clearly and explicitly given to avoid the long-standing ambiguity and vagueness concerning this term, and we make an initial attempt to propose and investigate three types of correlation coefficients. Furthermore, the connection between our proposed optimal fusion method and Fisher’s discriminant is discussed. Extensive experiments have been conducted to confirm our theoretical results and construct counter-examples for the existing conclusions.