Closed motifs for streaming time series classification

A streaming time series is a continuous and unbounded group of chronological observations that are found in many scientific and business applications. Motifs that are frequent subsequences are highly representative for the time series and play an important role in time series mining. Discovering motifs in time series has received much attention during recent years, and several algorithms have been proposed to solve this problem. However, these algorithms can only find motifs with a predefined length, which greatly affects their performance and practicality. Recent algorithms can discover motifs with different lengths, but require multiple scanning of the time series and are thus not applicable to streaming time series. In addition, it is difficult to determine the optimal length of interesting motifs; a suboptimal choice results in missing the key motifs or having too many redundant motifs. To overcome this challenge, we introduce the notion of a \(closed\) motif; a motif is \(closed\) if there is no motif with a longer length having the same number of occurrences. We propose a novel algorithm \(closedMotif\) to discover closed motifs in a single scan for streaming time series. We also use the nearest neighbor classifier with the most distinctive closed motifs to validate their potential in time series classification. Extensive experiments show that our approach can efficiently discover motifs with different lengths. In addition, our closed-motif-based classifier is shown to be more accurate than \(Logical\text{- }Shapelet\) , a state-of-the-art time series classifier. Finally, we demonstrate the scalability of \(closedMotif\) on several large datasets in diverse domains like video surveillance, sensor networks, and biometrics.