In this paper, we describe a novel speaker adaptation algorithm based on Gaussian mixture weight adaptation. A small number of latent speaker vectors are estimated with non-negative matrix factorization (NMF). These base vectors encode the correlations between Gaussian activations as learned from the train data. Expressing the speaker dependent Gaussian mixture weights as a linear combination of a small number of base vectors, reduces the number of parameters that must be estimated from the enrollment data. In order to learn meaningful correlations between Gaussian activations from the train data, the NMF-based weight adaptation was combined with vocal tract length normalization (VTLN) and feature-space maximum likelihood linear regression (fMLLR) based speaker adaptive training based. Evaluation on the 5k closed and 20k open vocabulary Wall Street Journal tasks shows a 4% relative word error rate reduction over the speaker independent recognition system which already incorporates VTL...