On restricting modalities in likelihood-ratio based biometric score fusion

Likelihood-ratio based biometric score fusion (LR fusion) has attracted attention since it maximizes accuracy if a log-likelihood ratio (LLR) is accurately estimated. It can also allow a user to select a subset of modalities at the authentication phase by setting LLRs corresponding to missing query samples to 0 (we refer to LR fusion with/without this mode as selective/non-selective LR fusion). However, a recent study proposed a modality selection attack, in which an impostor inputs only query samples whose LLRs are larger than 0 (i.e. takes an optimal strategy), against selective LR fusion, and showed that it degrades overall accuracy even if a genuine user also takes this optimal strategy. In this paper, we investigate the impact of the modality selection attack in more details. Specifically, we study whether the overall accuracy is improved by eliminating “goat” templates, whose LLRs tend to be less than or equal to 0 for genuine users. We investigate, both theoretically and experimentally, whether this restriction of modalities (i.e. elimination of goat templates) increases the KL (Kullback-Leibler) divergence between a genuine score distribution and an impostor's one, which can be compared with password entropy. We first show a negative result that the restriction of modalities hardly increases the KL divergence in selective LR fusion. We then show that it can increase the KL divergence in non-selective LR fusion.