Similarity normalization for speaker verification by fuzzy fusion

Abstract

Similarity or likelihood normalization techniques are important for speaker verification systems as they help to alleviate the variations in the speech signals. In the conventional normalization, the a priori probabilities of the cohort speakers are assumed to be equal. From this standpoint, we apply the theory of fuzzy measure and fuzzy integral to combine the likelihood values of the cohort speakers in which the assumption of equal a priori probabilities is relaxed. This approach replaces the conventional normalization term by the fuzzy integral which acts as a non-linear fusion of the similarity measures of an utterance assigned to the cohort speakers. We illustrate the performance of the proposed approach by testing the speaker verification system with both the conventional and the fuzzy algorithms using the commercial speech corpus TI46. The results in terms of the equal error rates show that the speaker verification system using the fuzzy integral is more flexible and more favorable than the conventional normalization method.

Introduction

Speaker verification is one of the challenging areas of speech research and has many applications including telecommunications, security systems, banking transactions, database management, forensic tasks, command and control, and others. Technically, it is one of the two tasks in speaker recognition. In other words, a speaker recognition system can be divided into two categories: speaker identification and speaker verification. A speaker identification recognizer tries to assign an unknown speaker to one of the reference speakers based on the closet measure of similarity, whereas a speaker verification recognizer is aimed to either accept or reject an unknown speaker by verifying the identity claim. Thus, the main point to distinguish between these two tasks is the number of decision alternatives. For speaker identification, the decision alternatives are equal to the number of the speakers. For speaker verification, there are only two alternatives, i.e. either accept or reject the claimed speaker. Different tasks of recognition can be used to serve different purposes. The verification systems are more appropriate for most commercial applications; whereas the identification systems are useful for the study of parametric and speech material modeling. For more details in recent developments on speaker recognition, the readers are referred to Refs. [1], [2], [3].

In speaker verification systems, the normalization techniques are important as they help to alleviate the variations in the speech signals, which are due to noise, different recording and transmission conditions [1]. There are two types of normalization techniques for speaker recognition: parameter and similarity. Some typical works in the parameter type were proposed by Atal [4], Furui [5], and in the similarity type were by Higgin et al. [6], Matsui and Furui [7]. It has also been reported that most of speaker verification systems are based on the similarity-domain normalization [8]. We therefore, in this paper, will focus our attention to the verification mode with respect to the similarity normalization.

Generally in most similarity normalization techniques, the likelihood values of the utterance coming from the cohort speakers, whose models are closest to the claimant model, are assumed to be equal likely. In reality, however, this assumption is not often true as the similarity measures between each cohort speaker and the client speaker may be different. Basing our motivation on this drawback, we introduce a new normalized log-likelihood method using the concept of fuzzy fusion. We relax the assumption of equal likelihood by imposing the fuzzy measures of the similarities between the cohort speaker models and the client model. Then the scoring of the cohort models can be obtained by the fuzzy integral which acts as a fusion operator with respect to the fuzzy measures. The rest of this paper is organized as follows. In Section 2, we present the basic formulations of the normalization techniques according to the similarity domain. In Section 3, the concepts of fuzzy measure and fuzzy integral are introduced. The fuzzy fusion for scoring the normalized log likelihood is implemented in Section 4. We compare the performance between the conventional and the proposed techniques using a commercial speech database in Section 5. Finally, Section 6 concludes the new application for speaker recognition and suggests possible development.