E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Knowledge and Information Systems 3(3), 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....3. It should require a small space overhead 4. It should be dynamic. It should be easy to insert and delete sequences, as well as to append new measurements at the end of a given data sequence. 5. It should handle data sequences as well as queries of varying length. To the above, authors in [17] add the following properties: 1. It should be possible to build the index in reasonable time . 2. The index should be able to handle different distance measures, where appropriate. A very important result in [8] is that in order for the correctness to be guaranteed, the signature extraction ....

....The reconstruction error, that is the distance (measured by some distance metric, usually the Euclidian dis tance) between the original and the reconstructed objects is a metric of the fidelity of the transformation. The general method for dimensionality reduction may be summed up as follows [17]: 1. Establish a distance metric Dob t from a domain expert (e.g. Euclidian distance) 2. Produce a dimensionality reduction technique (i.e. define the signature extraction function F) that produces signatures of length k, where k can be efficiently handled by a standard Spatial Access Method. ....

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrota. Dimensionality reduction for fast similarity search in large time series databases. In Journal of Knowledge and In- jrmation Systems, Volume 3, Number 3, 2001.

....Prefix Search performs a database search using a prefix of a prespecified length of the query sequence. Multipiece Search splits the query sequence to nonoverlapping subsequences of prespecified length and performs queries for each of these subsequences. Keogh, Chakrabarti, Pazzani and Mehrotra [13] proposed to split the time sequence into equal sized windows. The average of the values in each window is used to represent all the entries in the window. This compression technique is called the PAA (Piecewise Aggregate Approximation) technique. The experimental results in this paper show that ....

....did not get any improvements with these basis functions. Haar wavelet performed slightly better than DFT. DB2 performed poor for lower dimensions, but its performance was comparable to Haar for higher dimensions. Note that one can consider using other dimensionality reduction techniques like PAA [13] instead of DFT or wavelets. However, the experiments in [18] show that PAA is worse than DFT, Haar wavelets, and Daubechies wavelets. Our experiments with string data [8] also confirm that wavelets perform better than other techniques for our sliding window based index structure. There is no ....

E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality reduction for fast similarity search in large time series databases. Knowledge and Information Systems Journal, 2000.

....matching and similarity search in time series databases [1, 2, 3] Mannila et al. 4] introduce an efficient solution to the discovery of frequent patterns in a sequence database. Chan et al. 5] study the use of wavelets in time series matching and Faloutsos et al. in [6] and Keogh et al. in [7] propose indexing methods for fast sequence matching using R trees, the Discrete Fourier Transform and the Discrete Wavelet Transform. Toroslu et al. 8] introduce the problem of mining cyclically repeated patterns. Han et al. 9] introduce the concept of partial periodic patterns and propose a ....

E. Keogh, K. Chakrabarti, M. Pazzani and S. Mehrotra. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Springer-Verlag, Knowledge and Information Systems (2001) p. 263--286.

....little space overhead; 3. it should allow queries of various length; 4. it should allow insertions and deletions without rebuilding the index; and 5. it should be correct: No false dismissals must occur. To achieve high performance, the number of false alarms should also be low. Keogh et al. [14] add the following criteria to the list above: 6. It should be possible to build the index in reasonable time; and 7. the index should preferrably be able to handle more than one distance measure. 3 Signature Based Similarity Search A time sequence #x of length n can be considered a vector or ....

....assuming (4) holds, if two signatures are far apart, we know the corresponding [se quences] must also be far apart [7, p. 7] To minimise the number of false alarms, we want d sig to approximate d as closely as possible. This general method of dimensionality reducion may be summed up as follows [14]: 1. Establish a distance metric d from a domain expert. 2. Produce a dimensionality reduction technique to produce signatures of length k, where k can be efficiently handled by a standard spatial access method. 3. Produce a distance measure d sig over the k dimensional signature space, and ....

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Eamonn J. Keogh, K. Chakrabarti, and M. Pazzani. Dimensionality reduction for fast similarity search in large time series databases, 2000.

....also as a component inside data mining algorithms like clustering, classification and association rule mining. Time series databases convert time series segments to multidimensional points using some transformation (e.g. Discrete Fourier Transform (DFT) 5, 46] Discrete Wavelet Transform (DWT) [29, 79], Singular Value Decomposition (SVD) 79, 76, 81] Similarity search is then performed on the transformed data. Example applications include a doctor searching for a particular pattern (that implies a heart irregularity) in the ECG database for diagnosis, a stock analyst searching for a ....

....like clustering, classification and association rule mining. Time series databases convert time series segments to multidimensional points using some transformation (e.g. Discrete Fourier Transform (DFT) 5, 46] Discrete Wavelet Transform (DWT) 29, 79] Singular Value Decomposition (SVD) [79, 76, 81]) Similarity search is then performed on the transformed data. Example applications include a doctor searching for a particular pattern (that implies a heart irregularity) in the ECG database for diagnosis, a stock analyst searching for a particular pattern in the stock database for prediction ....

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality reduction for fast similarity search in large time series databases. Knowledge and Information Systems Journal, 2000.

....1000 1500 2000 2500 Figure 1: Above) An example of a motif that occurs three times in a complex and noisy industrial dataset. Below) a zoom in reveals just how similar the three occurrences are to each other There exists a vast body of work on efficiently locating known patterns in time series [1, 6, 12, 23, 35, 36, 37]. Here, however, we must be able to discover motifs without any prior knowledge about the regularities of the data under study. The obvious, nested loop, brute force approach to motif discovery would require a number of comparisons quadratic in the length of the database. Optimizations based on ....

....subsequence C of T is a sampling of length nn of contiguous position from T, that is, C = tp, tp n for l p m n l. Since all subsequences may be a potential motif, any motif discovery algorithm will eventually have to extract all of them, this can be achieved by use of a sliding window [7, 23, 36]. Definition 3. Sliding Window: Given a time series T of length m, and a user defined subsequence length of n, a matrix S of all possible subsequences can be built by sliding a window of size n across T and placing subsequence Cp in the pth row of . The size of matrix is (m n 1) by n. ....

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Keogh, E,. Chakrabarti, K,. Pazzani, M. & Mehrotm (2000). Dimensionality reduction for fast similarity search in large time series databases. Journal of Knowledge and Information Systems. pp 263-286.

....the transformed space. The technique was introduced in [1] and extended in [39, 31,11] The original work by Agrawal et al. utilizes the Discrete Fourier Transform (DFT) to perform the dimensionality reduction, but other techniques have been suggested, including Singular Value Decomposition (SVD) [28, 24, 23], the Discrete Wavelet Transform (DWT) 9, 49, 22] and Piecewise Aggregate Approximation (PAA) 24, 52] For a given index structure, the efficiency of indexing depends only on the fidelity of the approximation in the reduced dimensionality space. However, in choosing a dimensionality reduction ....

.... Agrawal et al. utilizes the Discrete Fourier Transform (DFT) to perform the dimensionality reduction, but other techniques have been suggested, including Singular Value Decomposition (SVD) 28, 24, 23] the Discrete Wavelet Transform (DWT) 9, 49, 22] and Piecewise Aggregate Approximation (PAA) [24, 52]. For a given index structure, the efficiency of indexing depends only on the fidelity of the approximation in the reduced dimensionality space. However, in choosing a dimensionality reduction technique, we cannot simply choose an arbitrary compression algorithm. What is required is a technique ....

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Keogh, E,. Chakrabarti, K,. Pazzani, M. & Mehrotra (2000) Dimensionality reduction for fast similarity search in large time series databases. Journal of Knowledge and Information Systems.

....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. Several high level representations of time series have been proposed, including Fourier Transforms [1,13], Wavelets [4] Symbolic Mappings [2, 5, 24] and Piecewise Linear Representation (PLR) In this work, we confine our attention to PLR, perhaps the most frequently used representation [8, 10, 12, 14, 15, 16, 17, 18, 20, 21, 22, 25, 27, 28, 30, 31] Intuitively Piecewise Linear Representation ....

....two examples. Because K is typically much smaller that n, this representation makes the storage, transmission and computation of the data more efficient. Specifically, in the context of data mining, the piecewise linear representation has been used to: Support fast exact similarly search [13]. Support novel distance measures for time series, including fuzzy queries [27, 28] weighted queries [15] multiresolution queries [31, 18] dynamic time warping [22] and relevance feedback [14] Support concurrent mining of text and time series [17] Support novel clustering and ....

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Keogh, E,. Chakrabarti, K,. Pazzani, M. & Mehrotra (2000). Dimensionality reduction for fast similarity search in large time series databases. Journal of Knowledge and Information Systems.

....DTW to cluster an agent s sensory outputs [30] Euclidian 1. Introduction The indexing of very large time series databases has attracted the attention of database community in recent years. The vast majority of work in this area has focused on indexing under the Euclidean distance metric [5, 10, 17, 18, 21, 34]. However there is an increasing awareness Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is ....

....aligned with the i th point in the other, will produce a pessimistic dissimilarity measure. The nonlinear Dynamic Time Warped alignment allows a more intuitive distance measure to be calculated More than two dozen techniques have been introduced to index time series under the Euclidean distance [5, 10, 17, 18, 21, 34] (see [18] for a more comprehensive listing) In addition, several researchers have shown techniques to approximately index DTW [33] or introduced methods to reduce its demanding CPU time [6] However only two researchers have claimed to have introduced an exact indexing technique for DTW [19, ....

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Keogh, E,. Chakrabarti, K,. Pazzani, M. & Mehrotra (2000) Dimensionality reduction for fast similarity search in large time series databases. Journal of Knowledge and Information Systems. pp 263-286.

....the utility and efficiency of our approach on several real world datasets. 1. INTRODUCTION The problem of efficiently locating previously deftted pattems in a time series database (i.e. query by content) has received much attention and may now be essentially regarded as a solved problem [1, 8, 13, 21, 22, 23, 35, 40]. However, from a knowledge discovery viewpoint, a more interesting problem is the detection of previously unknown, frequently occurring patterns. We call such patterns motif, because of their close analogy to their discrete counterparts in computation biology [11, 16, 30, 34, 36] Figure 1 ....

....2. Subsequence: Given a time series T of length m, a subsequence C of T is a sampling of length n m of contiguous position from T, that is, C = tp, tp n4 for l p m n 1. A task associated with subsequences is to determine if a given subsequence is similar to other subsequences [1, 2, 3, 8, 13, 19, 21, 22, 23, 24, 25, 27, 29, 35, 40]. This idea is formalized in the definition of a match. Definition 3. Match: Given a positive real number R (called range) and a time series T containing a subsequence C beginning at positionp and a subsequence M beginning at q, ifD(C, M ) R, then M is called a matching subsequence of C. The ....

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Keogh, E,. Chakrabarti, K,. Pazzani, M. & Mehrotra (2000). Dimensionality reduction for fast similarity search in large time series databases. Journal of Knowledge and Information Systems. pp 263-286.

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Knowledge and Information Systems 3(3), 2000.

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Keogh, E., Chakrabarti, K., Pazzani, M., and Mehrotea, S. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases.

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Keogh, E., Chakrabarti, K., Pazzani, M., and Mehrotea, S. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases.

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Eamonn Keogh, Kaushik Chakrabarti, Michael Pazzani, Sharad Mehrotra. "Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases" in Proceedings of ACM SIGMOD Conference on Management of Data, pages 151-162, Santa Barbara, CA, May, 2001

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra, Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases, Knowledge and Information Systems 3(3) (2000), 263--286.

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality reduction for fast similarity search in large time series databases. Knowledge and Information Systems, 3(3):263-286, 2000.

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Knowledge and Information Systems, 3(3):263--286, 2000.

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrota. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. In Journal of Knowledge and Information Systems, Volume 3, Number 3, 2001.

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E. J. Keogh, K. Chakrabarti, M. J. Pazzani, and S. Mehrotra. Dimensionality reduction for fast similarity search in large time series databases. Journal of Knowledge and Information Systems, 3(3):263--286, 2001.

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality reduction for fast similarity search in large time series. In Databases. Knowledge and Information Systems 3(3), pages 263--286, 2000.

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# E. Keogh, K. Chakrabarti, M. Pazzani and S. Mehrotra. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Springer-Verlag, Knowledge and Information Systems (2001) p. 263286.

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality reduction for fast similarity search in large time series. In Databases. Knowledge and Information Systems 3(3), pages 263--286, 2000.

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E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Dimensionality reduction for fast similarity search in large time series. In Databases. Knowledge and Information Systems 3(3), pages 263--286, 2000.

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Keogh, E. J., Chakrabarti, K., Pazzani, M. J., and Mehrotra, S. (2000). Dimensionality reduction for fast similarity search in large time series databases. Knowledge and Information Systems Journal, 3(3):263--286.

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Keogh, E., K. Chakrabarti, M. Pazzani and S. Mehrotra, "Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases", Journal of Knowledge and Information Systems, 2000.

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