Unsupervised Phoneme Segmentation Using Mahalanobis Distance

Abstract One of the fundamental problems in speech engineering is phoneme segmentation. Approaches to phoneme segmentation can be divided into two categories: supervised and unsupervised segmentation. The approach of this paper belongs to the 2nd category, which tries to perform phonetic segmentation without using any prior knowledge on linguistic contents and acoustic models. In an earlier work, we formulated the segmentation problem into an optimization problem through statistics and information analysis. An objective function, summation of squared error (SSE), is developed by using Euclidean distance of cepstral features. However, it is not known whether or not Euclidean distance yields the best distance metric to estimate the goodness of segmentations. A popular generalization of Euclidean distance is Mahalanobis distance (MD). In this paper, we study whether and how MD can be used to improve the performance of segmentation. The essential problem here is how to determine the parameters (covariance matrix) for MD calculation. We deal with this problem in a learning framework and propose two criteria for determining the optimal parameters: Minimum of Summation Variance (MSV) and Maximum of Discrimination Variance (MDV). MSV minimizes the summation of variance within phonemes, while MDV maximizes the variance between phonemes and minimizes the variance within phonemes at the same time. Both of them can lead to close form solutions by using matrix calculation. We also propose an algorithm to learn the parameters without using labeled data. We carried out experiments on the TIMIT database to eveluate the proposed methods. The results indicate that the use of learning MD can increase the correct recall rates. We also found the use of power can further improve the results.