Subsequence Join in Streaming Time Series under Dynamic Time Warping

Subsequence join in time series is to search for couples of similar subsequences from multiple time series. The task is useful in data mining on time series; nevertheless, it is extremely difficult because of its enormous computational cost. The task should use normalized time series during the search execution and be performed under an efficient distance measure to obtain accurate resulting couples. The task is more challenging when it works in a streaming environment in which time-series data might be collected very quickly. To address this problem, we propose an efficient method of subsequence join in streaming time series under Dynamic Time Warping (DTW), supporting z-score normalization. The proposed method utilizes a technique of subsequence extraction based on major extrema of streaming time series to search for couples of similar subsequences from coevolving time series. This method can identify couples of similar subsequences of the same length or different lengths. The experimental results show that the proposed method has high performance and can bring out interesting couples of similar subsequences. In addition, this method acts as an approximation algorithm suitable for a streaming scenario where users often expect fast responses from the task of subsequence join over time-series streams of high rates.