Geometric Discriminant Analysis for I-vector Based Speaker Verification

Many i-vector based speaker verification use linear discriminant analysis (LDA) as a post-processing stage. LDA maximizes the arithmetic mean of the Kullback-Leibler (KL) divergences between different pairs of speakers. However, for speaker verification, speakers with small divergence are easily misjudged. LDA is not optimal because it does not emphasize on enlarging small divergences. In addition, LDA makes an assumption that the i-vectors of different speakers are well modeled by Gaussian distributions with identical class covariance. Actually, the distributions of different speakers can have different covariances. Motivated by these observations, we explore speaker verification with geometric discriminant analysis (GDA), which uses geometric mean instead of arithmetic mean when maximizing the KL divergences. It puts more emphasis on enlarging small divergences. Furthermore, we study the heteroscedastic extension of GDA (HGDA), taking different covariances into consideration. Experiments on i-vector machine learning challenge indicate that, when the number of training speakers becomes smaller, the relative performance improvement of GDA and HGDA compared with LDA becomes larger. GDA and HGDA are better choices especially when training data is limited.