Gopinath, “Extended mllt for gaussian mixture models.pdfVIP

Extended MLLT for Gaussian Mixture Models Peder A. Olsen and Ramesh A. Gopinath IBM, T. J. Watson Research Center 134 and Taconic Parkway Yorktown Heights, NY 10598 (914) 945 {3772,2794}, (fax) (914) 945 4490 {pederao,rameshg}@ EDICS Category SA 1.6.4 Prior to publication, please maintain the enclosed paper in confidence and use it only for purposes of evaluating the merit of the proposed paper, and other activities reasonably related to the review process, and please do not make it available, in whole or in part, to the public. The authors thanks IEEE Trans- actions in Speech and Audio Processing for their courtesy and professionalism in this matter. Abstract In MLLT the inverse covariance matrix (precision matrix) of Gaus- sian mixture component j, j = 1, . . . , m is modeled by AT ΛjA, where Λj ∈ Rd×d+ are diagonal matrices and A ∈ Rd×d is a global data trans- formation matrix. This framework is extended to consider Λj ∈ RD×D and A ∈ RD×d for D ≥ d. The model uses a naturally approximating basis expansion for positive definite matrices and yields greater control of the number of parameters used in modeling covariances than methods considered by previous authors. Moreover, the method yields a practical solution to the design of the matrix considered in the recently proposed MLT model. The extended MLLT (EMLLT) model can be viewed as a generalization of several other covariance modeling techniques such as Fac- tor Analysis [26]. Experimental results in a speech recognition task shows a relative gain of 35% over a baseline diagonal covariance model and 28% over the MLLT model corresponding to the baseline when D = 14d. The EMLLT model yields a surprising 16% relative gain over a full covariance model. Also EMLLT is invariant to linear transformations of the data. 1 Introduction The Gaussian mixture model can be written f(x|Θ) = m∑ j=1 πjN (x;μj , Σj) (1) 1 where x = (x1, . . . , xd)T ∈ Rd×1, Θ = (π?, μ?, Σ?), π? = (π1, . . . , πm) ∈ R+1×m, 1 = ∑m j=1 πj μ? = (μ1, .