An Acoustic-Phonetic and a Model-Theoretic Analysis of Subspace Distribution Clustering Hidden Markov Models

Abstract. Recently, we proposed a new derivative to conventional continuous density hidden Markov modeling (CDHMM) that we call “subspace distribution clustering hidden Markov modeling” (SDCHMM). SDCHMMs can be created by tying low-dimensional subspace Gaussians in CDHMMs. In tasks we tried, usually only 32–256 subspace Gaussian prototypes were needed in SDCHMM-based system to maintain recognition performance of its original CDHMM-based system — a reduction of Gaussian parameters by one to three orders of magnitude. Consequently, both recognition time and memory were greatly reduced. We also have showed that if the underlying subspace distribution tying structure is known, it may be used to train an SDCHMM-based system with as little as eight minutes of speech from scratch. All the results suggest that there is substantial redundancy in conventional CDHMM and that SDCHMM is a more compact model. In this paper, we analyze the tying structure from two perspectives: from the acoustic-phonetic perspective showing that the tying structure seems to capture prominent relationship among phones; and, from the model-theoretic perspective showing that SDCHMMs, if properly created from CDHMMs, may be preferred over the latter as they are less complex and have the potential of greater generalization power.