Gaussian mixture models (GMMs) are commonly used to model the spectral distribution of speech signals for text-independent speaker verification. Mean vectors of the GMM, used in conjunction with support vector machine (SVM), have shown to be effective in characterizing speaker information. In addition to the mean vectors, covariance matrices capture the correlation between spectral features, which also represent some salient information about speaker identity. This paper investigates the use of local correlation between different dimensions of acoustic vector by using factor analysis and linear Gaussian model. Log-Euclidean inner product kernel is used to measure the similarity between two speech utterances in the form of covariance matrices. Experiments carried on NIST 2006 speaker verification tasks shows promising results.