Time Series Motif Discovery and Anomaly Detection Based on Subseries Join

Time series are composed of sequences of data items measured at typically uniform intervals. Time series arise frequently in many scientific and engineering applications, including finance, medicine, digital audio, and motion capture. Time series motifs are repeated similar subseries in one or multiple time series data. Time series anomalies are unusual subseries in one or multiple time series data. Finding motifs and anomalies in time series data are closely related problems and are useful in many domains, including medicine, motion capture, meteorology, and finance. This paper presents a novel approach for both the motif discovery problem and the anomaly detection problem. First, we use a subseries join operation to match similar subseries and to obtain similarity relationships among subseries of the time series data. The subseries join algorithm we use can efficiently and effectively tolerate noise, time-scaling, and phase shifts. Based on the similarity relationships found among subseries of the time series data, the motif discovery and anomaly detection problems can be converted to graph-theoretic problems solvable by known graphtheoretic algorithms. Experiments demonstrate the effectiveness of the proposed approach to discover motifs and anomalies in real-world time series data. Experiments also demonstrate that the proposed approach is efficient when applied to large time series datasets.