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Fast Time Series Classification Using Numerosity Reduction
 In ICML’06
, 2006
"... Many algorithms have been proposed for the problem of time series classification. However, it is clear that onenearestneighbor with Dynamic Time Warping (DTW) distance is exceptionally difficult to beat. This approach has one weakness, however; it is computationally too demanding for many realtime ..."
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Cited by 65 (12 self)
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Many algorithms have been proposed for the problem of time series classification. However, it is clear that onenearestneighbor with Dynamic Time Warping (DTW) distance is exceptionally difficult to beat. This approach has one weakness, however; it is computationally too demanding for many realtime applications. One way to mitigate this problem is to speed up the DTW calculations. Nonetheless, there is a limit to how much this can help. In this work, we propose an additional technique, numerosity reduction, to speed up onenearestneighbor DTW. While the idea of numerosity reduction for nearestneighbor classifiers has a long history, we show here that we can leverage off an original observation about the relationship between dataset size and DTW constraints to produce an extremely compact dataset with little or no loss in accuracy. We test our ideas with a comprehensive set of experiments, and show that it can efficiently produce extremely fast accurate classifiers. 1.
Approximate embeddingbased subsequence matching of time series
 In SIGMOD ’08: Proceedings of the 2008 ACM SIGMOD international conference on Management of data
, 2008
"... 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 EmbeddingBased Subsequence Matching. The key ..."
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Cited by 20 (6 self)
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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 EmbeddingBased 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 DTWbased subsequence matching algorithm. Experiments on a large, public time series data set produce speedups of over one order of magnitude compared to bruteforce search, with very small losses (< 1%) in retrieval accuracy.
Experimental comparison of representation methods and distance measures for time series data
 Data Mining and Knowledge Discovery
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Faster Retrieval with a TwoPass DynamicTimeWarping Lower Bound
, 2009
"... The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensi ..."
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Cited by 11 (0 self)
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The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensive lower bound (LB Keogh). We compare LB Keogh with a tighter lower bound (LB Improved). We find that LB Improvedbased search is faster. As an example, our approach is 2–3 times faster over randomwalk and shape time series.
Early Abandon to Accelerate Exact Dynamic Time Warping
, 2007
"... Abstract: Dynamic time warping is one of the important distance measures in similarity search of time series; however, the exact calculation of dynamic time warping has become a bottleneck. We propose an approach, named early abandon dynamic time warping, to accelerate the calculation. The method ch ..."
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Cited by 2 (0 self)
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Abstract: Dynamic time warping is one of the important distance measures in similarity search of time series; however, the exact calculation of dynamic time warping has become a bottleneck. We propose an approach, named early abandon dynamic time warping, to accelerate the calculation. The method checks if values of the neighbouring cells in the cumulative distance matrix exceed the tolerance, and if so, it will terminate the calculation of the related cell. We demonstrate the idea of early abandon on dynamic time warping by theoretical analysis, and show the utilities of early abandon dynamic time warping by thorough empirical experiments performed both on synthetic datasets and real datasets. The results show, early abandon dynamic time warping outperforms the dynamic time warping calculation in the light of processing time, and is much better when the tolerance is below the real dynamic time warping distance.
Towards Faster Activity Search Using Embeddingbased Subsequence Matching
"... Event search is the problem of identifying events or activity of interest in a large database storing long sequences of activity. In this paper, our topic is the problem of identifying activities of interest in databases where such activities are represented as time series. In the typical setup, the ..."
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Event search is the problem of identifying events or activity of interest in a large database storing long sequences of activity. In this paper, our topic is the problem of identifying activities of interest in databases where such activities are represented as time series. In the typical setup, the user presents a query that represents an activity of interest, and the system needs to retrieve the most similar activities stored in the database. We focus on the case where the best database matches are not segmented a priori: the database contains representations of long, continuous activity, that occurs throughout relatively extensive periods of time, and, given a query, there are no constraints as to when exactly a database match starts and ends within the longer activity pattern where it is contained. Using the popular DTW measure, the best database matches can be found using dynamic programming. However, retrieval time is linear to the size of the database and can become too long as the database size becomes larger. To achieve more efficient retrieval time, we apply to this problem a recently proposed technique called Embeddingbased Subsequence Matching (EBSM), and we demonstrate that using EBSM we can obtain significant speedups in retrieval time.
Faster Sequential Search with a TwoPass DynamicTimeWarping Lower Bound
, 2008
"... The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensi ..."
Abstract
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The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensive lower bound (LB Keogh). We compare LB Keogh with a tighter lower bound (LB Improved). We find that LB Improvedbased search is faster for sequential search. As an example, our approach is 3 times faster over randomwalk and shape time series. We also review some of the mathematical properties of the DTW. We derive a tight triangle inequality for the DTW. We show that the DTW becomes the l1 distance when time series are separated by a constant.