Results 1  10
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240
Survey of clustering data mining techniques
, 2002
"... Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in math ..."
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Cited by 408 (0 self)
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Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in mathematics, statistics, and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters is unsupervised learning, and the resulting system represents a data concept. From a practical perspective clustering plays an outstanding role in data mining applications such as scientific data exploration, information retrieval and text mining, spatial database applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition, and machine learning. This survey focuses on clustering in data mining. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique
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 316 (33 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.
Probabilistic discovery of time series motifs
, 2003
"... Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of thi ..."
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Cited by 185 (26 self)
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Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of this work were the poor scalability of the motif discovery algorithm, and the inability to discover motifs in the presence of noise. Here we address these limitations by introducing a novel algorithm inspired by recent advances in the problem of pattern discovery in biosequences. Our algorithm is probabilistic in nature, but as we show empirically and theoretically, it can find time series motifs with very high probability even in the presence of noise or “don’t care ” symbols. Not only is the algorithm fast, but it is an anytime algorithm, producing likely candidate motifs almost immediately, and gradually improving the quality of results over time.
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 141 (24 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.
Clustering of Time Series Subsequences is Meaningless: Implications for Past and Future Research
 In Proc. of the 3rd IEEE International Conference on Data Mining
, 2003
"... Time series data is perhaps the most frequently encountered type of data examined by the data mining community. Clustering is perhaps the most frequently used data mining algorithm, being useful in it’s own right as an exploratory technique, and also as a subroutine in more complex data mining algor ..."
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Cited by 117 (18 self)
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Time series data is perhaps the most frequently encountered type of data examined by the data mining community. Clustering is perhaps the most frequently used data mining algorithm, being useful in it’s own right as an exploratory technique, and also as a subroutine in more complex data mining algorithms such as rule discovery, indexing, summarization, anomaly detection, and classification. Given these two facts, it is hardly surprising that time series clustering has attracted much attention. The data to be clustered can be in one of two formats: many individual time series, or a single time series, from which individual time series are extracted with a sliding window. Given the recent explosion of interest in streaming data and online algorithms, the latter case has received much attention. In this work we make a surprising claim. Clustering of streaming time series is completely meaningless. More concretely, clusters extracted from streaming time series are forced to obey a certain constraint that is pathologically unlikely to be satisfied by any dataset, and because of this, the clusters extracted by any clustering algorithm are essentially random. While this constraint can be intuitively demonstrated with a simple illustration and is simple to prove, it has never appeared in the literature. We can justify calling our claim surprising, since it invalidates the contribution of dozens of previously published papers. We will justify our claim with a theorem, illustrative examples, and a comprehensive set of experiments on reimplementations of previous work. Although the primary contribution of our work is to draw attention to the fact that an apparent solution to an important problem is incorrect and should no longer be used, we also introduce a novel method which, based on the concept of time series motifs, is able to meaningfully cluster some streaming time series datasets.
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 111 (20 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.
On the Marriage of L_pnorms and Edit Distance
 IN VLDB
, 2004
"... Existing studies on time series are based on two categories of distance functions. The first category consists of the Lpnorms. They are metric distance functions but cannot support local time shifting. The second category consists of distance functions which are capable of handling local time shift ..."
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Cited by 101 (3 self)
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Existing studies on time series are based on two categories of distance functions. The first category consists of the Lpnorms. They are metric distance functions but cannot support local time shifting. The second category consists of distance functions which are capable of handling local time shifting but are nonmetric. The first
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 83 (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
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 82 (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.
Similarity search over time series data using wavelets
 In ICDE
, 2002
"... We consider the use of wavelet transformations as a dimensionality reduction technique to permit efficient similarity search over highdimensional timeseries data. While numerous transformations have been proposed and studied, the only wavelet that has been shown to be effective for this applicatio ..."
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Cited by 82 (0 self)
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We consider the use of wavelet transformations as a dimensionality reduction technique to permit efficient similarity search over highdimensional timeseries data. While numerous transformations have been proposed and studied, the only wavelet that has been shown to be effective for this application is the Haar wavelet. In this work, we observe that a large class of wavelet transformations (not only orthonormal wavelets but also biorthonormal wavelets)can be used to support similarity search. This class includes the most popular and most effective wavelets being used in image compression. We present a detailed performance study of the effects of using different wavelets on the performance of similarity search for timeseries data. We include several wavelets that outperform both the Haar wavelet and the best known nonwavelet transformations for this application. To ensure our results are usable by an application engineer, we also show how to configure an indexing strategy for the best performing transformations. Finally, we identify classes of data that can be indexed efficiently using these wavelet transformations. 1.