Theorectical Analysis of Subsequence Time-Series Clustering from a Frequency-Analysis Viewpoint

Although Subsequence Time Series (STS) clustering is one of the most popular pattern discovery techniques from timeseries data, a mathematical methodology for analyzing STS clustering (or pattern discovery from time-series data) has attracted little attention. In the situation, it has had a surprising report [10] that cluster centers obtained using STS clustering closely resemble ”sine waves” with little relation to input time-series data. With this report as a start, establishment of the methodology has been recognized as a significant issue. The contributions of this paper are mainly two folds. 1) We give, for the first time, a theoretical analysis of Subsequence Time Series (STS) clustering from a frequency-analysis viewpoint and identify a mathematical background on which STS clustering generates sine wave patterns. This also gives a novel theoretical analysis methodology for pattern discovery from time-series data, and 2) we propose a clustering algorithm using a phase alignment preprocessing to avoid sine-wave patterns and refer to it as Phase Alignment STS (PA-STS) clustering. PA-STS clustering is the first algorithm, which is based on theoretical analysis, to obtain meaningful clustering results. We present experimental results that show the reliability of the theoretical results and the effectiveness of PA-STS clustering in application to UCR datasets.