Frequency analysis of subsequence time series clustering and evaluation of phase alignment preprocessing

Abstract

Although Subsequence Time Series (STS) clustering has been one of the most popular techniques to extract typical subsequence patterns from time-series data, previous studies have gave surprising reports that cluster centers obtained using STS clustering closely resemble sine waves with little relation to input time-series data. This means that STS clustering cannot be used for its original purpose, extraction of typical subsequences. Despite this serious fact, its mathematical structure has seldom been studied. The main contribution of this paper is that we give a theoretical analysis of STS clustering from a frequency-analysis viewpoint and identify that sine waves are generated due to the superposition of time series subsequences, which have the same spectra but different phases. Another contribution is that we propose a clustering algorithm, which uses a phase alignment preprocessing, to avoid sine-wave patterns.