Accelerating Similarity Search for Elastic Measures: A Study and New Generalization of Lower Bounding Distances

Similarity search is a core analytical task, and its performance critically depends on the choice of distance measure. For time-series querying, elastic measures achieve state-of-the-art accuracy but are computationally expensive. Thus, fast lower bounding (LB) measures prune unnecessary comparisons with elastic distances to accelerate similarity search. Despite decades of attention, there has never been a study to assess the progress in this area. In addition, the research has disproportionately focused on one popular elastic measure, while other accurate measures have received little or no attention. Therefore, there is merit in developing a framework to accumulate knowledge from previously developed LBs and eliminate the notoriously challenging task of designing separate LBs for each elastic measure. In this paper, we perform the first comprehensive study of 11 LBs spanning 5 elastic measures using 128 datasets. We identify four properties that constitute the effectiveness of LBs and propose the Generalized Lower Bounding (GLB) framework to satisfy all desirable properties. GLB creates cache-friendly summaries, adaptively exploits summaries of both query and target time series, and captures boundary distances in an unsupervised manner. GLB outperforms all LBs in speedup (e.g., up to 13.5× faster against the strongest LB in terms of pruning power), establishes new state-of-the-art results for the 5 elastic measures, and provides the first LBs for 2 elastic measures with no known LBs. Overall, GLB enables the effective development of LBs to facilitate fast similarity search.