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 be lured into the recess of numerically valid, albeit poor, attractors. We decompose the transforma-tion into upper and lower triangular matrices, which are esti-mated 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.