K-Shape: Efficient and Accurate Clustering of Time Series

SIGMOD Record

Volumn 45, Issue 1, 2016, Pages 69-76

  Paparrizos, John ^a   Gravano, Luis ^a  

^a Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTERING ALGORITHMS; DATA MINING; HIERARCHICAL CLUSTERING; ITERATIVE METHODS; TIME SERIES;

CLUSTERING APPROACH; DATA MINING METHODS; DOMAIN INDEPENDENTS; EXPERIMENTAL EVALUATION; ITERATIVE REFINEMENT; PRE-PROCESSING STEP; SPECTRAL CLUSTERING METHODS; TIME SERIES CLUSTERING;

TIME SERIES ANALYSIS;

EID: 85112863727     PISSN: 01635808     EISSN: None     Source Type: Journal    
DOI: 10.1145/2949741.2949758     Document Type: Article

References (71)

1. The UCR Time Series Classification/Clustering Homepage. http://www.cs.ucr.edu/eamonn/time_series_data. Accessed: May 2014.
2. R. Agrawal, C. Faloutsos, and A. N. Swami. Efficient similarity search in sequence databases. In FODO, pages 69-84, 1993.
3. J. Alon, S. Sclaroff, G. Kollios, and V. Pavlovic. Discovering clusters in motion time-series data. In CVPR, pages 375-381, 2003.
4. A. J. Bagnall and G. J. Janacek. Clustering time series from ARMA models with clipped data. In KDD, pages 49-58, 2004.
5. Z. Bar-Joseph, G. Gerber, D. K. Gifford, T. S. Jaakkola, and I. Simon. A new approach to analyzing gene expression time series data. In RECOMB, pages 39-48, 2002.
6. G. E. Batista, E. J. Keogh, O. M. Tataw, and V. M. de Souza. CID: An efficient complexity-invariant distance for time series. Data Mining and Knowledge Discovery, pages 1-36, 2013.
7. D. J. Berndt and J. Clifford. Using dynamic time warping to find patterns in time series. In AAAI Workshop on KDD, pages 359-370, 1994.
8. Y. Cai and R. Ng. Indexing spatio-temporal trajectories with Chebyshev polynomials. In SIGMOD, pages 599-610, 2004.
9. L. Chen and R. Ng. On the marriage of Lp-norms and edit distance. In VLDB, pages 792-803, 2004.
10. L. Chen, M. T. Özsu, and V. Oria. Robust and fast similarity search for moving object trajectories. In SIGMOD, pages 491-502, 2005.
11. Q. Chen, L. Chen, X. Lian, Y. Liu, and J. X. Yu. Indexable PLA for efficient similarity search. In VLDB, pages 435-446, 2007.
12. Y. Chen, M. A. Nascimento, B. C. Ooi, and A. K. Tung. Spade: On shape-based pattern detection in streaming time series. In ICDE, pages 786-795, 2007.
13. J. W. Cooley and J. W. Tukey. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90):297-301, 1965.
14. G. Das, K.-I. Lin, H. Mannila, G. Renganathan, and P. Smyth. Rule discovery from time series. In KDD, pages 16-22, 1998.
15. H. Ding, G. Trajcevski, P. Scheuermann, X. Wang, and E. Keogh. Querying and mining of time series data: Experimental comparison of representations and distance measures. PVLDB, 1(2):1542-1552, 2008.
16. C. Faloutsos, M. Ranganathan, and Y. Manolopoulos. Fast subsequence matching in time-series databases. In SIGMOD, pages 419-429, 1994.
17. M. Filippone, F. Camastra, F. Masulli, and S. Rovetta. A survey of kernel and spectral methods for clustering. Pattern Recognition, 41(1):176-190, 2008.
18. E. Frentzos, K. Gratsias, and Y. Theodoridis. Index-based most similar trajectory search. In ICDE, pages 816-825, 2007.
19. M. Friedman. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association, 32:675-701, 1937.
20. M. Frigo and S. G. Johnson. The design and implementation of FFTW3. Proceedings of the IEEE, 93(2):216-231, 2005.
21. M. Gavrilov, D. Anguelov, P. Indyk, and R. Motwani. Mining the stock market: Which measure is best? In KDD, pages 487-496, 2000.
22. R. Giusti and G. E. Batista. An empirical comparison of dissimilarity measures for time series classification. In BRACIS, pages 82-88, 2013.
23. S. Goddard, S. K. Harms, S. E. Reichenbach, T. Tadesse, and W. J. Waltman. Geospatial decision support for drought risk management. Communications of the ACM, 46(1):35-37, 2003.
24. D. Q. Goldin and P. C. Kanellakis. On similarity queries for time-series data: Constraint specification and implementation. In CP, pages 137-153, 1995.
25. G. H. Golub and C. F. Van Loan. Matrix computations, volume 3. JHU Press, 2012.
26. L. Gupta, D. L. Molfese, R. Tammana, and P. G. Simos. Nonlinear alignment and averaging for estimating the evoked potential. IEEE Transactions on Biomedical Engineering, 43(4):348-356, 1996.
27. M. Halkidi, Y. Batistakis, and M. Vazirgiannis. On clustering validation techniques. Journal of Intelligent Information Systems, 17(2-3):107-145, 2001.
28. J. Han, M. Kamber, and J. Pei. Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers Inc., 3rd edition, 2011.
29. R. Honda, S. Wang, T. Kikuchi, and O. Konishi. Mining of moving objects from time-series images and its application to satellite weather imagery. Journal of Intelligent Information Systems, 19(1):79-93, 2002.
30. B. Hu, Y. Chen, and E. Keogh. Time series classification under more realistic assumptions. In SDM, pages 578-586, 2013.
31. K. Kalpakis, D. Gada, and V. Puttagunta. Distance measures for effective clustering of ARIMA time-series. In ICDM, pages 273-280, 2001.
32. Y. Katznelson. An introduction to harmonic analysis. Cambridge University Press, 2004.
33. L. Kaufman and P. J. Rousseeuw. Finding groups in data: An introduction to cluster analysis, volume 344. John Wiley & Sons, 2009.
34. E. Keogh. A decade of progress in indexing and mining large time series databases. In VLDB, pages 1268-1268, 2006.
35. E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra. Locally adaptive dimensionality reduction for indexing large time series databases. In SIGMOD, pages 151-162, 2001.
36. E. Keogh and J. Lin. Clustering of time-series subsequences is meaningless: Implications for previous and future research. Knowledge and Information Systems, 8(2):154-177, 2005.
37. E. Keogh and C. A. Ratanamahatana. Exact indexing of dynamic time warping. Knowledge and Information Systems, 7(3):358-386, 2005.
38. C. Kin-pong and F. Ada. Efficient time series matching by wavelets. In ICDE, pages 126-133, 1999.
39. F. Korn, H. V. Jagadish, and C. Faloutsos. Efficiently supporting ad hoc queries in large datasets of time sequences. In SIGMOD, pages 289-300, 1997.
40. C.-S. Li, P. S. Yu, and V. Castelli. MALM: A framework for mining sequence database at multiple abstraction levels. In CIKM, pages 267-272, 1998.
41. X. Lian, L. Chen, J. X. Yu, G. Wang, and G. Yu. Similarity match over high speed time-series streams. In ICDE, pages 1086-1095, 2007.
42. J. MacQueen. Some methods for classification and analysis of multivariate observations. In BSMSP, pages 281-297, 1967.
43. R. N. Mantegna. Hierarchical structure in financial markets. The European Physical Journal B-Condensed Matter and Complex Systems, 11(1):193-197, 1999.
44. W. Meesrikamolkul, V. Niennattrakul, and C. A. Ratanamahatana. Shape-based clustering for time series data. In PAKDD, pages 530-541. 2012.
45. V. Megalooikonomou, Q. Wang, G. Li, and C. Faloutsos. A multiresolution symbolic representation of time series. In ICDE, pages 668-679, 2005.
46. M. D. Morse and J. M. Patel. An efficient and accurate method for evaluating time series similarity. In SIGMOD, pages 569-580, 2007.
47. A. Mueen, E. Keogh, and N. Young. Logical-shapelets: An expressive primitive for time series classification. In KDD, pages 1154-1162, 2011.
48. P. Nemenyi. Distribution-free Multiple Comparisons. PhD thesis, Princeton University, 1963.
49. A. Y. Ng, M. I. Jordan, and Y. Weiss. On spectral clustering: Analysis and an algorithm. In NIPS, pages 849-856, 2002.
50. V. Niennattrakul and C. A. Ratanamahatana. Shape averaging under time warping. In ECTI-CON, pages 626-629, 2009.
51. T. Oates. Identifying distinctive subsequences in multivariate time series by clustering. In KDD, pages 322-326, 1999.
52. P. Papapetrou, V. Athitsos, M. Potamias, G. Kollios, and D. Gunopulos. Embedding-based subsequence matching in time-series databases. TODS, 36(3):17, 2011.
53. J. Paparrizos and L. Gravano. k-Shape: Efficient and accurate clustering of time series. In SIGMOD, pages 1855-1870, 2015.
54. F. Petitjean, A. Ketterlin, and P. Gançarski. A global averaging method for dynamic time warping, with applications to clustering. Pattern Recognition, 44(3):678-693, 2011.
55. T. Rakthanmanon, B. Campana, A. Mueen, G. Batista, B. Westover, Q. Zhu, J. Zakaria, and E. Keogh. Searching and mining trillions of time series subsequences under dynamic time warping. In KDD, pages 262-270, 2012.
56. T. Rakthanmanon, E. J. Keogh, S. Lonardi, and S. Evans. Time series epenthesis: Clustering time series streams requires ignoring some data. In ICDM, pages 547-556, 2011.
57. W. M. Rand. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336):846-850, 1971.
58. C. A. Ratanamahatana and E. Keogh. Making time-series classification more accurate using learned constraints. In SDM, pages 11-22, 2004.
59. E. J. Ruiz, V. Hristidis, C. Castillo, A. Gionis, and A. Jaimes. Correlating financial time series with micro-blogging activity. In WSDM, pages 513-522, 2012.
60. H. Sakoe and S. Chiba. Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech and Signal Processing, 26(1):43-49, 1978.
61. Y. Shou, N. Mamoulis, and D. Cheung. Fast and exact warping of time series using adaptive segmental approximations. Machine Learning, 58(2-3):231-267, 2005.
62. K. Uehara and M. Shimada. Extraction of primitive motion and discovery of association rules from human motion data. In Progress in Discovery Science, pages 338-348. 2002.
63. M. Vlachos, M. Hadjieleftheriou, D. Gunopulos, and E. Keogh. Indexing multidimensional time-series. The VLDB Journal, 15(1):1-20, 2006.
64. M. Vlachos, G. Kollios, and D. Gunopulos. Discovering similar multidimensional trajectories. In ICDE, pages 673-684, 2002.
65. H. Wang, Y. Cai, Y. Yang, S. Zhang, and N. Mamoulis. Durable queries over historical time series. TKDE, 26(3):595-607, 2014.
66. X. Wang, A. Mueen, H. Ding, G. Trajcevski, P. Scheuermann, and E. Keogh. Experimental comparison of representation methods and distance measures for time series data. Data Mining and Knowledge Discovery, 26(2):275-309, 2013.
67. T. Warren Liao. Clustering of time series data-a survey. Pattern Recognition, 38(11):1857-1874, 2005.
68. Y. Xiong and D.-Y. Yeung. Mixtures of ARMA models for model-based time series clustering. In ICDM, pages 717-720, 2002.
69. J. Yang and J. Leskovec. Patterns of temporal variation in online media. In WSDM, pages 177-186, 2011.
70. L. Ye and E. Keogh. Time series shapelets: A new primitive for data mining. In KDD, pages 947-956, 2009.
71. J. Zakaria, A. Mueen, and E. Keogh. Clustering time series using unsupervised-shapelets. In ICDM, pages 785-794, 2012.