LU factorization for feature transformation

Linear feature space transformations are often used for speaker or environment adaptation. Usually, numerical methods are sought to obtain solutions. In this paper, we derive a closed-form solution to ML estimation of full feature transformations. Closed-form solutions are desirable because the problem is quadratic and thus blind numerical analysis may converge to poor local optima. We decompose the transformation into upper and lower triangular matrices, which are estimated alternatively using the EM algorithm. Furthermore, we extend the theory to Bayesian adaptation. On the Switchboard task, we obtain 1.6% WER improvement by combining the method with MLLR, or 4% absolute using adaptation.