Many studies have proven the effectiveness of discriminative training for speaker verification based on probabilistic linear discriminative analysis (PLDA) with i-vectors as features. Most of them directly optimize the log-likelihood ratio score function of the PLDA model instead of explicitly train the PLDA model. But this optimization process removes some of the constraints that normally are imposed on the PLDA log likelihood ratio score function. This may deteriorate the verification performance when the amount of training data is limited. In this paper, we first show two constraints which the score function should follow, and then we propose a new constrained discriminative training algorithm which keeps these constraints. Our experiments show that our method obtained significant improvements in the verification performance in the male trials of the telephone speaker verification tasks of NIST SRE08 and SRE10.
