A Fast Method of Computing Persistent Homology of Time Series Data

Abstract

This study proposes a method that speeds up computing persistent homology of time series data. Persistent homology is recently used for clutering time series data and detecting periodicity of them. The proposed method uses line segments to approximate a trajectory in delay-coordinate space. Cubic Bézier curves are fitted to given data and divided into line segments. The distance between line segments is defined and calculated to construct the Vietoris-Rips complex of segments. Exploiting the Vietoris-Rips complex enables us to use fast software like Ripser. In experiments, the performance of the proposed method is compared with that of the ordinary method. The proposed method was 30 times or more faster than the ordinary method. It also smooths noisy data and produces more precise persistent homology.