Semi-Markov Clustering

Clustering of subsequences of time series is a widely studied and applied class of techniques [3, 4, 2, 6, 1, 5, 7] which aims at interpreting a time series as a shorter sequence of symbols, each of which represent a segment of the series with a pattern that is similar to other segments that has been assigned the same symbol. The research field of subsequence clustering, which was already a widely applied and studied technique, took a dramatic turn after Keogh, Lin and Truppel [4] published a paper which claimed that clustering subsequences using sliding window approaches is meaningless. They had discovered that techniques such as the standard k-means clustering of the segments of a time series created by a sliding window of a fixed size are often looking the same regardless of the input data. When using a fixed size sliding window one will often create segments that are in different phases with respect to the pattern in the data which makes it difficult to learn meaningful patterns. Here we extend the objective function of k-means clustering from fixed window segments to segmentations of varying length. In this new clustering framework there is no need for using overlapping windows. Semi-markov clustering does not cluster a fixed set of segments, but works with all possible segmentations to find one way of segmenting the sequence into consistent patterns. Unlike in the fixed window setting, the result is a segmentation into consistent patterns and centroids that look exactly like those patterns. We report results on several dataset including the artificial Cylinder-Bell-Funnel set, ECG and accelerometer traces from body worn sensors.