A method for approximate subsequence matching is introduced, that significantly improves the efficiency of subsequence matching in large time series data sets under the dynamic time warping (DTW) distance measure. Our method is called EBSM, shorthand for Embedding-Based Subsequence Matching. The key idea is to convert subsequence matching to vector matching using an embedding. This embedding maps each database time series into a sequence of vectors, so that every step of every time series in the database is mapped to a vector. The embedding is computed by applying full dynamic time warping between reference objects and each database time series. At runtime, given a query object, an embedding of that object is computed in the same manner, by running dynamic time warping between the reference objects and the query. Comparing the embedding of the query with the database vectors is used to efficiently identify relatively few areas of interest in the database sequences. Those areas of interest are then fully explored using the exact DTW-based subsequence matching algorithm. Experiments on a large, public time series data set produce speedups of over one order of magnitude compared to brute-force search, with very small losses (< 1%) in retrieval accuracy.

This paper proposes a general framework for matching similar subsequences in both time series and string databases. The matching results are pairs of query subsequences and database subsequences. The framework finds all possible pairs of similar subsequences if the distance measure satisfies the “consistency ” property, which is a property introduced in this paper. We show that most popular distance functions, such as the Euclidean distance, DTW, ERP, the Frechét distance for time series, and the Hamming distance and Levenshtein distance for strings, are all “consistent”. We also propose a generic index structure for metric spaces named “reference net”. The reference net occupies O(n) space, where n is the size of the dataset and is optimized to work well with our framework. The experiments demonstrate the ability of our method to improve retrieval performance when combined with diverse distance measures. The experiments also illustrate that the reference net scales well in terms of space overhead and query time. 1.