Abstract
Fast and scalable analysis techniques are becoming increasingly important in the era of big data, because they are the enabling techniques to create real-time and interactive experiences in data analysis. Time series are widely available in diverse application areas. Due to the large number of time series instances (e.g., millions) and the high dimensionality of each time series instance (e.g., thousands), it is challenging to conduct clustering on large-scale time series, and it is even more challenging to do so in real-time to support interactive exploration.
In this paper, we propose a novel end-to-end time series clustering algorithm, YADING, which automatically clusters large-scale time series with fast performance and quality results. Specifically, YADING consists of three steps: sampling the input dataset, conducting clustering on the sampled dataset, and assigning the rest of the input data to the clusters generated on the sampled dataset. In particular, we provide theoretical proof on the lower and upper bounds of the sample size, which not only guarantees YADING's high performance, but also ensures the distribution consistency between the input dataset and the sampled dataset. We also select L1 norm as similarity measure and the multi-density approach as the clustering method. With theoretical bound, this selection ensures YADING's robustness to time series variations due to phase perturbation and random noise.
Evaluation results have demonstrated that on typical-scale (100,000 time series each with 1,000 dimensions) datasets, YADING is about 40 times faster than the state-of-the-art, sampling-based clustering algorithm DENCLUE 2.0, and about 1,000 times faster than DBSCAN and CLARANS. YADING has also been used by product teams at Microsoft to analyze service performance. Two of such use cases are shared in this paper.
- Debregeas, A., and Hebrail, G. 1998. Interactive interpretation of Kohonen maps applied to curves. In Proc. of KDD'98. 179--183.Google Scholar
- Derrick, K., Bill, K., and Vamsi, C. 2012.
Large scale/big data federation & virtualization: a case study .Google Scholar - D. A. Patterson. 2002. A simple way to estimate the cost of downtime. In Proc. of LISA' 02, pp. 185--188. Google ScholarDigital Library
- Eamonn, K., and Shruti, K. 2002. On the need for time series data mining benchmarks: a survey and empirical demonstration. In Proc. of KDD'02, July 23--26.Google Scholar
- T. W. Liao. 2005. Clustering of time series data---A survey Pattern Recognit., vol. 38, no. 11, pp. 1857--1874, Nov. Google ScholarDigital Library
- X. Golay, S. Kollias, G. Stoll, D. Meier, A. Valavanis, P. Boesiger. 1998. A new correlation-based fuzzy logic clustering algorithm for fMRI, Mag. Resonance Med.Google Scholar
- B. K. Yi, H. V. Jagadish, and C. Faloutsos. 1998. Efficient retrieval of similar time sequences under time warping. In IEEE Proc. of ICDE, Feb. Google ScholarDigital Library
- J. Han, M. Kamber. 2001. Data Mining: Concepts and Techniques, Morgan Kaufmann, San Francisco, pp. 346--389. Google ScholarDigital Library
- Chu, K. & Wong, M. 1999. Fast time-series searching with scaling and shifting. In proc. of PODS. pp 237--248. Google ScholarDigital Library
- Popivanov, I. & Miller, R. J. 2002. Similarity search over time series data using wavelets. In proc. of ICDE. Google ScholarDigital Library
- Keogh, E., Chakrabarti, K., Pazzani, M. & Mehrotra, S. 2001. Locally adaptive dimensionality reduction for indexing large time series databases. In proc. of ACM SIGMOD. Google ScholarDigital Library
- Yi, B. & Faloutsos, C. 2000. Fast time sequence indexing for arbitrary lp norms. In proc. of the VLDB. pp 385--394. Google ScholarDigital Library
- E. J. Keogh, K. Chakrabarti, M. J. Pazzani, and S. Mehrotra. 2001. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Knowl. Inf. Syst., 3(3).Google Scholar
- G. Kollios, D. Gunopulos, N. Koudas, and S. Berchtold. 2003. Efficient biased sampling for approximate clustering and outlier detection in large datasets. IEEE TKDE, 15(5). Google ScholarDigital Library
- Zhou, S., Zhou, A., Cao, J., Wen, J., Fan, Y., Hu. Y. 2000. Combining sampling technique with DBSCAN algorithm for clustering large spatial databases. In Proc. of the PAKDD. Google ScholarDigital Library
- Stuart, Alan. 1962. Basic Ideas of Scientific Sampling, Hafner Publishing Company, New York.Google Scholar
- M. Ester, H. P. Kriegel, and X. Xu. A density-based algorithm for discovering clusters in large spatial databases with noise. ACM SIGKDD 1996, pages 226--231.Google Scholar
- M. Steinbach, L. Ertoz, and V. Kumar. 2003. Challenges of clustering high dimensional data. In L. T. Wille, editor, New Vistas in Statistical Physics -- Applications in Econophysics, Bioinformatics, and Pattern Recognition. Springer-Verlag.Google Scholar
- Ng R. T., and Han J. 1994. Efficient and Effective Clustering Methods for Spatial Data Mining, In proc. of VLDB. Google ScholarDigital Library
- S. Guha, R. Rastogi, K. Shim. 1998. CURE: an efficient clustering algorithm for large databases. SIGMOD. Google ScholarDigital Library
- W. Wang, J. Yang, R. Muntz, R. 1997. STING: a statistical information grid approach to spatial data mining, VLDB'97. Google ScholarDigital Library
- Hans-Peter Kriegel, Peer Kröger, Jörg Sander, Arthur Zimek 2011. Density-based Clustering. WIREs Data Mining and Knowledge Discovery 1 (3): 231--240. doi:10.1002/widm.30.Google ScholarCross Ref
- Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel, Jörg Sander. 1999. OPTICS: Ordering Points To Identify the Clustering Structure. ACM SIGMOD. pp. 49--60. Google ScholarDigital Library
- Tao Pei, Ajay Jasra, David J. Hand, A. X. Zhu, C. Zhou. 2009. DECODE: a new method for discovering clusters of different densities in spatial data, Data Min Knowl Disc. Google ScholarDigital Library
- C. Guo, H. Li, and D. Pan. 2010. An improved piecewise aggregate approximation based on statistical features for time series mining. KSEM'10, pages 234--244. Google ScholarDigital Library
- Beckmann, N.; Kriegel, H. P.; Schneider, R.; Seeger, B. 1990. "The R-tree: an efficient and robust access method for points and rectangles". In proc. of SIGMOD. p. 322. Google ScholarDigital Library
- X. Golay, S. Kollias, G. Stoll, D. Meier, A. Valavanis, P. Boesiger, A new correlation-based fuzzy logic clustering algorithm for fMRI, Mag. Resonance Med. 40 (1998).Google Scholar
- T. W. Liao, B. Bolt, J. Forester, E. Hailman, C. Hansen, R. C. Kaste, J. O'May, Understanding and projecting the battle state, 23rd Army Science Conference, Orlando, FL, 2002.Google Scholar
- D. Piccolo, A distance measure for classifying ARMA models, J. Time Ser. Anal. 11 (2) (1990) 153--163.Google Scholar
- D. Tran, M. Wagner, Fuzzy c-means clustering-based speaker verification, in: N. R. Pal, M. Sugeno (Eds.), AFSS 2002, Lecture Notes in Artificial Intelligence, 2275, 2002. Google ScholarDigital Library
- Danon L, Díaz-Guilera A, Duch J and Arenas A 2005 J. Stat. Mech. P09008.Google Scholar
- M. Datar, N. Immorlica, P. Indyk, V. S. Mirrokni. 2004. Locality-sensitive hashing scheme based on p-stable distributions, Computational Geometry, pp. 253--262. Google ScholarDigital Library
- Berchthold S., Keim D., Kriegel H. P. 1996. The X-Tree: An Index Structure for High-Dimensional Data, VLDB. Google ScholarDigital Library
- Keogh, E., Zhu, Q., Hu, B., Hao. Y., Xi, X., Wei, L. & Ratanamahatana, C. A. (2011). The UCR Time Series Classification/Clustering Homepage: www.cs.ucr.edu/~eamonn/time_series_data/Google Scholar
- http://research.microsoft.com/en-us/people/juding/yading.aspxGoogle Scholar
- A. Hinneburg and H. H. Gabriel. DENCLUE 2.0: Fast Clustering Based on Kernel Density Estimation. In IDA, 2007. Google ScholarDigital Library
- Sheih, J., Keogh, E., 2009. iSAX: disk-aware mining and indexing of massive time series data sets. Data Mining and Knowledge Discovery 19 (1), 24--57. Google ScholarDigital Library
- D. Barbara. Requirements for clustering data streams. SIGKDD Explorations, 3(2): 23--27, January 2002. Google ScholarDigital Library
- P. Liu, D. Zhou, N. Wu. 2007. Varied Density Based Spatial Clustering of Application with Noise, In proc. of ICSSSM. 528--531Google ScholarCross Ref
Index Terms
- YADING: fast clustering of large-scale time series data
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