SpADe: On Shape-based Pattern Detection in Streaming Time Series

Monitoring predefined patterns in streaming time series is useful to applications such as trend-related analysis, sensor networks and video surveillance. Most current studies on such monitoring employ Euclidean distance to calculate the similarities between given query patterns and subsequences of streaming time series. Euclidean distance has been shown to be ineffective in measuring distances of time series in which shifting and scaling usually exist. Consequently, warping distances such as dynamic time warping (DTW), longest common subsequence (LCSS), have been proposed to handle warps in temporal dimension. However, they are inadequate in handling shifting and scaling in amplitude dimension. Moreover, they have been designed mainly for full sequence matching, whereas in online monitoring applications, we typically have no knowledge on the positions and lengths of possible matching subsequences. In this paper, we first discuss the weaknesses of existing warping distances on detecting patterns from streaming time series. We then propose a novel warping distance, which we name Spatial Assembling Distance (SpADe), that is able to handle shifting and scaling in both temporal and amplitude dimensions. We further propose an efficient approach for continuous pattern detection using SpADe, that is fundamental for subsequence matching on streaming data. Finally, our experimental results show that SpADe is effective and efficient for continuous pattern detection in streaming time series.