Accelerating time series searching with large uniform scaling

Abstract

Similarity search is arguably the most important primitive in time series data mining. It is useful in its own right as an exploratory tool, and a subroutine in almost all higher level algorithms, such as motif discovery, anomaly detection, classification, clustering and summarization. Because of this, and the prevalence of time series data, the last decade has seen fast algorithms for time series similarity search under Dynamic Time Warping (DTW) and Uniform Scaling (US) distance measures. However, current state-of-the-art algorithms for US have only been demonstrated for the modest amounts of rescaling in datasets produced by human behaviors such as gestures, speech, music performance and physiological measurements such as heartbeats and respiration. As we shall show, in many industrial and commercial contexts we may encounter much greater amounts of rescaling, rendering current solutions little better than brute force search. To mitigate this problem we introduce novel lower bounds, LBnew, which, for the first time allows efficient search even in domains that exhibit more than a factor-of-two variability in scale. We demonstrate the utility of our ideas with both theoretical guarantees and comprehensive experiments on real data from commercial important domains, including power consumption monitoring and ECG monitoring. The results show the application of our lower bounds significantly outperforms state-of-the-art approaches for accelerating similarity searching of time series with more than a factor-of-two variability in scale as well as highlevel time series mining tasks.