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141
Exact Indexing of Dynamic Time Warping
, 2002
"... The problem of indexing time series has attracted much research interest in the database community. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However is has been forcefully shown that the Euclidean distance is a very brittle distance me ..."
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Cited by 235 (31 self)
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The problem of indexing time series has attracted much research interest in the database community. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However is has been forcefully shown that the Euclidean distance is a very brittle distance measure. Dynamic Time Warping (DTW) is a much more robust distance measure for time series, allowing similar shapes to match even if they are out of phase in the time axis.
Fast Similarity Search in the Presence of Noise, Scaling, and Translation in TimeSeries Databases
 In VLDB
, 1995
"... We introduce a new model of similarity of time sequences that captures the intuitive notion that two sequences should be considered similar if they have enough nonoverlapping timeordered pairs of subsequences thar are similar. The model allows the amplitude of one of the two sequences to be scaled ..."
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Cited by 198 (6 self)
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We introduce a new model of similarity of time sequences that captures the intuitive notion that two sequences should be considered similar if they have enough nonoverlapping timeordered pairs of subsequences thar are similar. The model allows the amplitude of one of the two sequences to be scaled by any suitable amount and its offset adjusted appropriately. Two subsequences are considered similar if one can be enclosed within an envelope of a specified width drawn around the other. The model also allows nonmatching gaps in the matching subsequences. The matching subsequences need not be aligned along the time axis. Given this model of similarity,we present fast search techniques for discovering all similar sequences in a set of sequences. These techniques can also be used to find all (sub)sequences similar to a given sequence. We applied this matching system to the U.S. mutual funds data and discovered interesting matches.
Discovering similar multidimensional trajectories
 In ICDE
, 2002
"... We investigate techniques for analysis and retrieval of object trajectories in a two or three dimensional space. Such kind of data usually contain a great amount of noise, that makes all previously used metrics fail. Therefore, here we formalize nonmetric similarity functions based on the Longest C ..."
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Cited by 173 (6 self)
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We investigate techniques for analysis and retrieval of object trajectories in a two or three dimensional space. Such kind of data usually contain a great amount of noise, that makes all previously used metrics fail. Therefore, here we formalize nonmetric similarity functions based on the Longest Common Subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to the similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translating of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and Time Warping distance functions (for real and synthetic data) and show the superiority of our approach, especially under the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach. 1
Rule discovery from time series
 In Proceedings of the 1997 ACM SIGKDD International Conference, ACM SIGKDD
, 1997
"... We consider the problem of finding rules relating patterns in a time series to other patterns in that series, or patterns in one series to patterns in another series. A simple example is a rule such as "a period of low telephone call activity is usually followed by a sharp rise ill call vohune". Exa ..."
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Cited by 143 (0 self)
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We consider the problem of finding rules relating patterns in a time series to other patterns in that series, or patterns in one series to patterns in another series. A simple example is a rule such as "a period of low telephone call activity is usually followed by a sharp rise ill call vohune". Examples of rules relating two or more time series are "if the Microsoft stock price goes up and lntel falls, then IBM goes up the next. day, " and "if Microsoft goes up strongly fro " one day, then declines strongly on the next day, and on the same days Intel stays about, level, then IBM stays about level. " Our emphasis is in the discovery of local patterns in multivariate time series, in contrast to traditional time series analysis which largely focuses on global models. Thus, we search for rules whose conditions refer to patterns in time series. However, we do not want to define beforehand which patterns are to be used; rather, we want the patterns to be formed fl’om the data in the context of rule discovery. We describe adaptive methods for finding rules of the above type fi’om timeseries data. The methods are based on discretizing the sequence hy methods resembling vector quantization. \,Ve first form subsequences by sliding window through the time series, and then cluster these subsequences by using a suitable measure of timeseries similarity. The discretized version of the time series is obtained by taldng the cluster identifiers corresponding to the subsequence. Once tl,e timeseries is discretized, we use simple rule finding methods to obtain rifles from the sequence. "vVe present empMcal resuh.s on the behavior of the method.
Querying Shapes of Histories
, 1995
"... We present a shape de nition language, called SDL, for retrieving objects based on shapes contained in the histories associated with these objects. It is a small, yet powerful, language that allows a rich variety of queries about the shapes found in historical time sequences. An interesting feature ..."
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Cited by 107 (4 self)
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We present a shape de nition language, called SDL, for retrieving objects based on shapes contained in the histories associated with these objects. It is a small, yet powerful, language that allows a rich variety of queries about the shapes found in historical time sequences. An interesting feature of SDL is its ability to perform blurry matching. A "blurry" match is one where the user cares about the overall shape but does not care about specific details. Another important feature of SDL is its efficient implementability. The SDL operators are designed to be greedy to reduce nondeterminism, which in turn substantially reduces the amount of backtracking in the implementation. We give transformation rules for rewriting an SDL expression into a more efficient form as well as an index structure for speeding up the execution of SDL queries.
A Probabilistic Approach to Fast Pattern Matching in Time Series Databases
 Proceedings of the 3 rd International Conference of Knowledge Discovery and Data Mining
, 1997
"... The problem of efficiently and accurately locating patterns of interest in massive time series data sets is an important and nontrivial problem in a wide variety of applications, including diagnosis and monitoring of complex systems, biomedical data analysis, and exploratory data analysis in scient ..."
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Cited by 100 (15 self)
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The problem of efficiently and accurately locating patterns of interest in massive time series data sets is an important and nontrivial problem in a wide variety of applications, including diagnosis and monitoring of complex systems, biomedical data analysis, and exploratory data analysis in scientific and business time series. In this paper a probabilistic approach is taken to this problem. Using piecewise linear segmentations as the underlying representation, local features (such as peaks, troughs, and plateaus) are defined using a prior distribution on expected deformations from a basic template. Global shape information is represented using another prior on the relative locations of the individual features. An appropriately defined probabilistic model integrates the local and global information and directly leads to an overall distance measure between sequence patterns based on prior knowledge. A search algorithm using this distance measure is shown to efficiently and accurately f...
Querying and Mining of Time Series Data: Experimental Comparison of Representations and Distance Measures
"... The last decade has witnessed a tremendous growths of interests in applications that deal with querying and mining of time series data. Numerous representation methods for dimensionality reduction and similarity measures geared towards time series have been introduced. Each individual work introduci ..."
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Cited by 65 (20 self)
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The last decade has witnessed a tremendous growths of interests in applications that deal with querying and mining of time series data. Numerous representation methods for dimensionality reduction and similarity measures geared towards time series have been introduced. Each individual work introducing a particular method has made specific claims and, aside from the occasional theoretical justifications, provided quantitative experimental observations. However, for the most part, the comparative aspects of these experiments were too narrowly focused on demonstrating the benefits of the proposed methods over some of the previously introduced ones. In order to provide a comprehensive validation, we conducted an extensive set of time series experiments reimplementing 8 different representation methods and 9 similarity measures and their variants, and testing their effectiveness on 38 time series data sets from a wide variety of application domains. In this paper, we give an overview of these different techniques and present our comparative experimental findings regarding their effectiveness. Our experiments have provided both a unified validation of some of the existing achievements, and in some cases, suggested that certain claims in the literature may be unduly optimistic. 1.
Derivative dynamic time warping
 In SIAM International Conference on Data Mining
, 2001
"... Time series are a ubiquitous form of data occurring in virtually every scientific discipline. A common task with time series data is comparing one sequence with another. In some domains a very simple distance measure, such as Euclidean distance will suffice. However, it is often the case that two se ..."
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Cited by 62 (1 self)
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Time series are a ubiquitous form of data occurring in virtually every scientific discipline. A common task with time series data is comparing one sequence with another. In some domains a very simple distance measure, such as Euclidean distance will suffice. However, it is often the case that two sequences have the approximately the same overall
Making Timeseries Classification More Accurate Using Learned Constraints
 In proc. of SDM Int’l Conf
, 2004
"... It has long been known that Dynamic Time Warping (DTW) is superior to Euclidean distance for classification and clustering of time series. However, until lately, most research has utilized Euclidean distance because it is more efficiently calculated. A recently introduced technique that greatly miti ..."
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Cited by 60 (18 self)
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It has long been known that Dynamic Time Warping (DTW) is superior to Euclidean distance for classification and clustering of time series. However, until lately, most research has utilized Euclidean distance because it is more efficiently calculated. A recently introduced technique that greatly mitigates DTWs demanding CPU time has sparked a flurry of research activity. However, the technique and its many extensions still only allow DTW to be applied to moderately large datasets. In addition, almost all of the research on DTW has focused exclusively on speeding up its calculation; there has been little work done on improving its accuracy. In this work, we target the accuracy aspect of DTW performance and introduce a new framework that learns arbitrary constraints on the warping path of the DTW calculation. Apart from improving the accuracy of classification, our technique as a side effect speeds up DTW by a wide margin as well. We show the utility of our approach on datasets from diverse domains and demonstrate significant gains in accuracy and efficiency.
Scaling up Dynamic Time Warping for Datamining Applications
 In Proc. 6th Int. Conf. on Knowledge Discovery and Data Mining
, 2000
"... There has been much recent interest in adapting data mining algorithms to time series databases. Most of these algorithms need to compare time series. Typically some variation of Euclidean distance is used. However, as we demonstrate in this paper, Euclidean distance can be an extremely brittle dist ..."
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Cited by 51 (3 self)
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There has been much recent interest in adapting data mining algorithms to time series databases. Most of these algorithms need to compare time series. Typically some variation of Euclidean distance is used. However, as we demonstrate in this paper, Euclidean distance can be an extremely brittle distance measure. Dynamic time warping (DTW) has been suggested as a technique to allow more robust distance calculations, however it is computationally expensive. In this paper we introduce a modification of DTW which operates on a higher level abstraction of the data, in particular, a Piecewise Aggregate Approximation (PAA). Our approach allows us to outperform DTW by one to two orders of magnitude, with no loss of accuracy.