Exploiting Low-Dimensional Structures to Enhance DNN Based Acoustic Modeling in Speech Recognition
Table 1: Comparison of “Rank” of DNN posterior matrix, projected posterior matrix and RPCA senone posterior matrix.
['[EMPTY]', 'DNN', 'Projected', 'Robust PCA']
To provide an insight into the dimension of the senone subspaces, we construct matrices of 1000 class-specific senone posteriors and compute the number of singular values required to preserve 95% variability of the data. Due to skewed distribution of the posteriors, we take their log prior to singular value decomposition. We refer to the number of required singular values as roughly the “Rank” of senone matrices. An ideal posterior feature should have its maximum component at the support indicating its associated class. Hence, we group the posteriors as “correct” if the maximum component corresponds to the correct class and “incorrect” if the maximum component corresponds to the incorrect class. Another approach referred to as robust PCA based posteriors will be discussed in the subsequent section. We collect posterior features for each senone from training data using ground truth based GMM-HMM forced alignment. RPCA decomposition is applied to data of each senone-class to reveal the true underlying dimension of the class-specific senone subspaces. We can see that the true dimension (7.6) of the class-specific subspaces of senone posteriors is indeed far lower than the DNN posteriors (36.6) and yet lower than the projected posteriors (11.9). Exploiting this multi low-rank structure of speech can lead to posterior enhancement via low-rank representation at utterance level