TEXT-INDEPENDENT SPEAKER RECOGNITION USING PROBABILISTIC ABSTRACT SVM WITH GMM ADJUSTMENT

1. INTRODUCTION There are two major models for speaker recognition: discriminative model and generative model. Discriminative model consists of Artificial Neural Networks (ANN) and Support Vector Machines (SVM), etc. Generative model consists of Hidden Markov Model (HMM) and Gaussian Mixture Model (GMM), etc. Each one of them can construct speaker models for speaker recognition tasks, and previous studies show good performances. Discriminative models have good property of making full use of discriminative information of
TEXT-INDEPENDENT SPEAKER RECOGNITION USING PROBABILISTIC SVM WITH GMM ADJUSTMENT
Fenglei Hou and Bingxi Wang Department of Information Science, Institute of Information Engineering, Information Engineering University, Zhengzhou 450002, P.R. China Email: houfl@ bingxiwang@
For SVM there are two outputs corresponding to two classes C+ and C− . So the posterior probability outputs of the SVM are P (C+ | x) = 1 1 + exp(− f (x)) 1 1 + exp( f (x)) (4)
different classes, while generative models use statistical information. In a word, discriminative models use intra-class information and generative models uses intra-class information. Since discriminative model and generative model has both advantages of themselves, they also have disadvantages of lack using the other kind of information. Experiments show the two kinds of models have different kind of errors in performance [1]. Combining the discriminative model and the generative model can improve the performance of a speaker recognition system. There are several methods to combine the two kinds of models, model A and model B: (1). A and B are parallel (2). A embeds into B (3). B embeds into A This paper presents a new method to combine both discriminative model and the generative model to make use of the two kinds of models. Support vector machine is recently proved to be a good discriminative classifier for many kinds of pattern recognition applications, which also shows advantages in training and performance compare to artificial neural networks. Gaussian mixture models have become the dominant approach fro modeling in text-independent speaker recognition applications over the past several years because GMMs can present speaker’s statistical characters properly. A classifier that can produce a posterior probability is very useful in practical
P (C− | x) =
(5)
Here f (x) can be viewed as the distance from x to the support vectors [5]. That is to say that the posterior probability outputs of SVMs are based on the distance of testing vectors and support vectors. So the outputs reflect the inter-class information. The outputs of Gaussian mixture model are used to adjust the output of SVM to make more accurate reflection to the real data cases, since GMMs model the intra-class information properly. The outputs of GMM are [6]:
f (x) = ∑ yiα i k (xi , x) + b
i
(2)
One method of producing probabilistic outputs was proposed by Wahba [4], which used a logisபைடு நூலகம்ic link function, P (C | x) = p (x) = 1 1 + exp(− f (x)) (3)
ABSTRACT There are two most popular techniques in pattern recognition, discriminative classifiers and generative model classifiers. Combining them together could improve the performance of the recognition system. This paper presents a novel method for text-independent speaker recognition. This system uses the output of the Gaussian mixture model to adjust the probabilistic output of the support vector machine. The new probabilistic SVM/GMM model based speaker recognition system is tested on the NIST 2003 speaker recognition evaluation database. Results on text-independent speaker identification and verification are provided to demonstrate the effectiveness of such systems. Keywords: Speaker recognition, probabilistic Support vector machine, Gaussian Mixture model
recognition situations. Many decision methods are based on Bayes rule. Probabilistic output of the classifier makes it possible to use existing results of these theories. Especially in cases when a classifier is making a small part of an overall decision, and the classification outputs must be combined for the overall decision. Standard SVMs do not provide probabilistic output. Several methods were presented recently to deal with this problem. Vapnik [2] proposes a method to fit the posterior probability with a sum of cosine terms which shows promising results. But this method requires a solution of a linear system for every evaluation of the SVM. Platt [3] uses a parametric form of a sigmoid to fit the posterior probability. This method is quite simple in the form but the parameters need to be determined by training. This paper combines the SVM and GMM to utilize the abilities of both models. This method use GMM’s output to adjust the probabilistic output of SVM. In training phase, both SVMs and GMMs are trained independently. While in testing phase, the probability outputs of the GMMs are used to adjust the posterior probability output of SVMs. Likelihood scoring is performed using the new hybrid model. In Section 2 the algorithm of this method is described in detail. In Section 3 experiments on the NIST 2003 speaker recognition evaluation data are presented and the results are discussed in Section 4. Section 5 contains the concluding remarks. 2. PROBABILISTIC SVM/GMM MODEL Let xi , xi = 1,..., N be a set of data points and yi , yi = 1,..., N be corresponding target classes. The output of the standard SVM is