Factor Analyzed Subspace Modeling and Selection

We present a novel subspace modeling and selection approach for noisy speech recognition. In subspace modeling, we develop a factor analysis (FA) representation of noisy speech, which is a generalization of a signal subspace (SS) representation. Using FA, noisy speech is represented by the extracted common factors, factor loading matrix, and specific factors. The observation space of noisy speech is accordingly partitioned into a principal subspace, containing speech and noise, and a minor subspace, containing residual speech and residual noise. We minimize the energies of speech distortion in the principal subspace as well as in the minor subspace so as to estimate clean speech with residual information. Importantly, we explore the optimal subspace selection via solving the hypothesis test problems. We test the equivalence of eigenvalues in the minor subspace to select the subspace dimension. To fulfill the FA spirit, we also examine the hypothesis of uncorrelated specific factors/residual speech. The subspace can be partitioned according to a consistent confidence towards rejecting the null hypothesis. Optimal solutions are realized through the likelihood ratio tests, which arrive at the approximated chi-square distributions as test statistics. In the experiments on the Aurora2 database, the FA model significantly outperforms the SS model for speech enhancement and recognition. Subspace selection via testing the correlation of residual speech achieves higher recognition accuracies than that of testing the equivalent eigenvalues in the minor subspace.