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84
Locally Adaptive Dimensionality Reduction for Indexing Large Time Series Databases
 In proceedings of ACM SIGMOD Conference on Management of Data
, 2002
"... Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced d ..."
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Cited by 252 (28 self)
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Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced data with a multidimensional index structure. Many dimensionality reduction techniques have been proposed, including Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Adaptive Piecewise Constant Approximation (APCA). While previous techniques (e.g., SVD, DFT and DWT) choose a common representation for all the items in the database that minimizes the global reconstruction error, APCA approximates each time series by a set of constant value segments' of varying lengths' such that their individual reconstruction errors' are minimal. We show how APCA can be indexed using a multidimensional index structure. We propose two distance measures in the indexed space that exploit the high fidelity of APCA for fast searching: a lower bounding Euclidean distance approximation, and a nonlower bounding, but very tight Euclidean distance approximation and show how they can support fast exact searchin& and even faster approximate searching on the same index structure. We theoretically and empirically compare APCA to all the other techniques and demonstrate its' superiority.
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 188 (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
Finding Motifs in Time Series
, 2002
"... The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously ..."
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Cited by 83 (15 self)
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The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs," because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition, it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification. In this work we carefully motivate, then introduce, a nontrivial definition of time series motifs. We propose an efficient algorithm to discover them, and we demonstrate the utility and efficiency of our approach on several real world datasets.
Segmenting Time Series: A Survey and Novel Approach
 In an Edited Volume, Data mining in Time Series Databases. Published by World Scientific
, 1993
"... In recent years, there has been an explosion of interest in mining time series databases. As with most computer science problems, representation of the data is the key to efficient and effective solutions. One of the most commonly used representations is piecewise linear approximation. This represen ..."
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Cited by 55 (0 self)
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In recent years, there has been an explosion of interest in mining time series databases. As with most computer science problems, representation of the data is the key to efficient and effective solutions. One of the most commonly used representations is piecewise linear approximation. This representation has been used by various researchers to support clustering, classification, indexing and association rule mining of time series data. A variety of algorithms have been proposed to obtain this representation, with several algorithms having been independently rediscovered several times. In this paper, we undertake the first extensive review and empirical comparison of all proposed techniques. We show that all these algorithms have fatal flaws from a data mining perspective. We introduce a novel algorithm that we empirically show to be superior to all others in the literature.
Indexing SpatioTemporal Trajectories with Chebyshev Polynomials
 Proc. 2004 SIGMOD, toappear
"... In this thesis, we investigate the subject of indexing large collections of spatiotemporal trajectories for similarity matching. Our proposed technique is to first mitigate the dimensionality curse problem by approximating each trajectory with a low order polynomiallike curve, and then incorporate ..."
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Cited by 54 (0 self)
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In this thesis, we investigate the subject of indexing large collections of spatiotemporal trajectories for similarity matching. Our proposed technique is to first mitigate the dimensionality curse problem by approximating each trajectory with a low order polynomiallike curve, and then incorporate a multidimensional index into the reduced space of polynomial coefficients. There are many possible ways to choose the polynomial, including Fourier transforms, splines, nonlinear regressions, etc. Some of these possibilities have indeed been studied before. We hypothesize that one of the best approaches is the polynomial that minimizes the maximum deviation from the true value, which is called the minimax polynomial. Minimax approximation is particularly meaningful for indexing because in a branchandbound search (i.e., for finding nearest neighbours), the smaller the maximum deviation, the more pruning opportunities there exist. In general, among all the polynomials of the same degree, the optimal minimax polynomial is very hard to compute. However, it has been shown that the Chebyshev approximation is almost identical to the optimal minimax polynomial, and is easy to compute [32]. Thus, we shall explore how to use
Variable Length Queries for Time Series Data
 IN ICDE
, 2000
"... Finding similar patterns in a time sequence is a wellknown problem that has been addressed by many authors. Most of the current techniques work well for queries of a prespecified length, but fail for variable length queries. We propose a new indexing technique that works well for variable length ..."
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Cited by 51 (8 self)
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Finding similar patterns in a time sequence is a wellknown problem that has been addressed by many authors. Most of the current techniques work well for queries of a prespecified length, but fail for variable length queries. We propose a new indexing technique that works well for variable length queries. Our idea is to store index structures at different resolutions for a given dataset. The resolutions are based on wavelets. A number of subqueries at different resolutions are generated for each variable length query. The ranges of the subqueries are progressively refined based on results from previous subqueries. Our experiments show that the total cost for our method is 4 to 20 times less than the current techniques including Linear Scan. Because of the need to store information at multiple resolution levels, the storage requirement of our method could potentially be large. In the second part of the paper, we show how the index information can be compressed with minimal information loss. According to our experimental results, even after compressing the size of the index to one fifth, the total cost of our method is 3 to 15 times less than the current techniques.
Indexing large humanmotion databases
 In Proc. 30th VLDB Conf
, 2004
"... Datadriven animation has become the industry standard for computer games and many animated movies and special effects. In particular, motion capture data recorded from live actors, is the most promising approach offered thus far for animating realistic human characters. However, the manipulation of ..."
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Cited by 46 (5 self)
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Datadriven animation has become the industry standard for computer games and many animated movies and special effects. In particular, motion capture data recorded from live actors, is the most promising approach offered thus far for animating realistic human characters. However, the manipulation of such data for general use and reuse is not yet a solved problem. Many of the existing techniques dealing with editing motion rely on indexing for annotation, segmentation, and reordering of the data. Euclidean distance is inappropriate for solving these indexing problems because of the inherent variability found in human motion. The limitations of Euclidean distance stems from the fact that it is very sensitive to distortions in the time axis. A partial solution to this problem, Dynamic Time Warping (DTW), aligns the time axis
Iterative deepening dynamic time warping for time series
 In Proc 2 nd SIAM International Conference on Data Mining
, 2002
"... Time series are a ubiquitous form of data occurring in virtually every scientific discipline and business application. There has been much recent work on adapting data mining algorithms to time series databases. For example, Das et al. attempt to show how association rules can be learned from time s ..."
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Cited by 34 (8 self)
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Time series are a ubiquitous form of data occurring in virtually every scientific discipline and business application. There has been much recent work on adapting data mining algorithms to time series databases. For example, Das et al. attempt to show how association rules can be learned from time series [7]. Debregeas and Hebrail [8]
Mining Motifs in Massive Time Series Databases
 In Proceedings of IEEE International Conference on Data Mining (ICDM’02
, 2002
"... The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously ..."
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Cited by 33 (0 self)
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The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs", because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification.
Robust Similarity Measures for Mobile Object Trajectories
 Proc. of DEXA Workshops
, 2002
"... We investigate techniques for similarity analysis of spatiotemporal trajectories for mobile objects. Such kind of data may contain a great amount of outliers, which degrades the performance of Euclidean and Time Warping Distance. Therefore, here we propose the use of nonmetric distance functions b ..."
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Cited by 24 (1 self)
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We investigate techniques for similarity analysis of spatiotemporal trajectories for mobile objects. Such kind of data may contain a great amount of outliers, which degrades the performance of Euclidean and Time Warping Distance. Therefore, here we propose the use of nonmetric distance functions based on the Longest Common Subsequence (LCSS), in conjunction with a sigmoidal matching function. Finally, we compare these new methods to various L p Norms and also to Time Warping distance (for real and synthetic data) and we present experimental results that validate the accuracy and efficiency of our approach, especially under the strong presence of noise.