Efficient processing of similarity search under time warping in sequence databases: an index-based approach

This paper discusses an effective processing of similarity search that supports time warping in large sequence databases. Time warping enables finding sequences with similar patterns even when they are of different lengths. Previous methods for processing similarity search that supports time warping fail to employ multi-dimensional indexes without false dismissal since the time warping distance does not satisfy the triangular inequality. They have to scan all the database, thus suffer from serious performance degradation in large databases. Another method that hires the suffix tree, which does not assume any distance function, also shows poor performance due to the large tree size. In this paper, we propose a novel method for similarity search that supports time warping. Our primary goal is to enhance the search performance in large databases without permitting any false dismissal. To attain this goal, we devise a new distance function Dtw−lb that consistently underestimates the time warping distance and also satisfies the triangular inequality. Dtw−lb uses a 4-tuple feature vector that is extracted from each sequence and is invariant to time warping. For efficient processing of similarity search, we employ a multi-dimensional index that uses the 4-tuple feature vector as indexing attributes and Dtw−lb as a distance function. We prove that our method does not incur false dismissal. To verify the superiority of our method, we perform extensive experiments. The results reveal that our method achieves significant speedup up to 43 times with a data set containing real-world S&P 500 stock data sequences and up to 720 times with data sets containing a very large volume of synthetic data sequences. The performance gain becomes larger: (1) as the number of data sequences gets larger, (2) the average length of data sequences gets longer, and (3) as the tolerance in a query gets smaller. Considering the characteristics of real databases, these tendencies imply that our approach is suitable for practical applications.