A method of extracting latent semantic components from noisy categorical time-series data applied to human sleep stage data

Abstract

A method to extract latent semantic components from noisy categorical time-series data based on the Takens’ time-delay-embedding method and singular value decomposition is presented. A demonstration of this method to analyze a sleep stage time-series is demonstrated. The first component extracted by this method, i.e., the component with the largest singular value can be considered the circadian rhythm. The second component, which exhibits damping oscillation, can be interpreted as the ultradian rhythm, and matched with the moving-averaged $c_{2}$; which is an estimation of the cortico-thalamo-cortical loop strength calculated from the corresponding electroencephalogram data using the method previously reported. The sleep stage is treated as a nominal variable instead of an ordinal variable in this method; however, the quantitative variation of sleep state is extracted from the sleep stage time-series. We believe that this result suggests the validity and usefulness of both the methods, i.e., the method reported in the present study and the method reported in a previous study.