Fast and Exact Warping of Time Series Using Adaptive Segmental Approximations

Similarity search is a core module of many data analysis tasks, including search by example, classification, and clustering. For time series data, Dynamic Time Warping (DTW) has been proven a very effective similarity measure, since it minimizes the effects of shifting and distortion in time. However, the quadratic cost of DTW computation to the length of the matched sequences makes its direct application on databases of long time series very expensive. We propose a technique that decomposes the sequences into a number of segments and uses cheap approximations thereof to compute fast lower bounds for their warping distances. We present several, progressively tighter bounds, relying on the existence or not of warping constraints. Finally, we develop an index and a multi-step technique that uses the proposed bounds and performs two levels of filtering to efficiently process similarity queries. A thorough experimental study suggests that our method consistently outperforms state-of-the-art methods for DTW similarity search.