Analysis of Embedding Space of Speech Synthesis System as High-Dimension, Low-Sample-Size Data

Principal component analysis (PCA) is often used to visualize and cluster embedding vectors of deep-learning models; however large noise can degrade the results of PCA when the dimension of the embedding vectors is much larger than the data size. These types of data are referred to as high-dimension, low-sample-size (HDSS) data, where the number of data dimension is much larger than the sample size, and they must be treated differently than typical data, because the eigenvalues of a HDSS data covariance matrix are impacted by large noise. Previous studies on HDSS data proposed the noise reduction methodology (NRM) and cross-data matrix methodology (CDM) to reduce such effects. In this study, we apply NRM and CDM to visualize the embedding vectors of an end-to-end speech synthesis system. Experimental results show that the NRM can estimate reduced eigenvalues by eliminating the large noise and that the CDM can provide a more reasonable visualization, although the results are dependent on the initial CDM clusters. In addition, we propose a method for estimating the power exponent of a general spiked model to assess whether the estimated eigenvalues are consistent.