Subscribe

Issue No.05 - May (2008 vol.20)

pp: 615-627

ABSTRACT

This paper presents and analyzes an incremental system for clustering streaming time series. The Online Divisive-Agglomerative Clustering (ODAC) system continuously maintains a tree-like hierarchy of clusters that evolves with data. ODAC uses a top-down strategy. The splitting criterion is a correlation-based dissimilarity measure among time series, splitting each node by the farthest pair of streams, which defines the diameter of the cluster. In stationary environments expanding the structure leads to a decrease in the diameters of the clusters. The system uses a merge operator, which agglomerates two sibling clusters, in order to react to changes in the correlation structure between time series. The split and merge operators are triggered in response to changes in the diameters of existing clusters. The system is designed to process thousands of data streams that flow at high-rate. The main features of the system include update time and memory consumption that do not depend on the number of examples in the stream. Moreover, the time and memory required to process an example decreases whenever the cluster structure expands. Experimental results on artificial and real data assess the processing qualities of the system, suggesting competitive performance on clustering streaming time series, exploring also its ability to deal with concept drift.

INDEX TERMS

Data mining, Clustering, Correlation and regression analysis, Industrial control, Real time

CITATION

Pedro Pereira Rodrigues, João Gama, João Pedro Pedroso, "Hierarchical Clustering of Time-Series Data Streams",

*IEEE Transactions on Knowledge & Data Engineering*, vol.20, no. 5, pp. 615-627, May 2008, doi:10.1109/TKDE.2007.190727REFERENCES

- [1] P. Domingos and G. Hulten, “Mining High-Speed Data Streams,”
Proc. ACM SIGKDD '00, pp. 71-80, 2000.- [3] E. Keogh and S. Kasetty, “On the Need for Time Series Data Mining Benchmarks: A Survey and Empirical Demonstration,”
Proc. ACM SIGKDD '02, pp. 102-111, July 2002.- [4] M. Halkidi, Y. Batistakis, and M. Varzirgiannis, “On Clustering Validation Techniques,”
J. Intelligent Information Systems, vol. 17, no. 2-3, pp. 107-145, 2001.- [5] T. Hastie, R. Tibshirani, and J. Friedman,
The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer Verlag, 2000.- [6] P.P. Rodrigues, J. Gama, and J.P. Pedroso, “ODAC: Hierarchical Clustering of Time Series Data Streams,”
Proc. Sixth SIAM Int'l Conf. Data Mining (ICDM '06), pp. 499-503, Apr. 2006.- [8] F. Ferrer, J. Aguilar, and J. Riquelme, “Incremental Rule Learning and Border Examples Selection from Numerical Data Streams,”
J.Universal Computer Science, vol. 11, no. 8, pp. 1426-1439, 2005.- [9] A.K. Jain and R.C. Dubes,
Algorithms for Clustering Data. Prentice Hall, 1988.- [10] L. Kaufman and P.J. Rousseeuw,
Finding Groups in Data: An Introduction to Cluster Analysis. John Wiley & Sons, 1990.- [11] M. Ester, H.-P. Kriegel, J. Sander, and X. Xu, “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise,”
Proc. ACM SIGKDD '96, pp. 226-231, 1996.- [12] W. Wang, J. Yang, and R.R. Muntz, “STING: A Statistical Information Grid Approach to Spatial Data Mining,”
Proc. 23rd Int'l Conf. Very Large Data Bases (VLDB '97), pp. 186-195, 1997.- [13] D.H. Fisher, “Knowledge Acquisition via Incremental Conceptual Clustering,”
Machine Learning, vol. 2, no. 2, pp. 139-172, 1987.- [14] P. Bradley, U. Fayyad, and C. Reina, “Scaling Clustering Algorithms to Large Databases,”
Proc. ACM SIGKDD '98, pp. 9-15, 1998.- [17] T.F. Gonzalez, “Clustering to Minimize the Maximum Inter-Cluster Distance,”
Theoretical Computer Science, vol. 38, nos. 2-3, pp.293-306, 1985.- [18] T. Zhang, R. Ramakrishnan, and M. Livny, “BIRCH: An Efficient Data Clustering Method for Very Large Databases,”
Proc. ACM SIGMOD '96, pp. 103-114, 1996.- [19] C. Aggarwal, J. Han, J. Wang, and P. Yu, “A Framework for Clustering Evolving Data Streams,”
Proc. 29th Int'l Conf. Very Large Data Bases (VLDB '03), pp. 81-92, Sept. 2003.- [20] S. Guha, R. Rastogi, and K. Shim, “CURE: An Efficient Clustering Algorithm for Large Databases,”
Proc. ACM SIGMOD '98, pp. 73-84, 1998.- [22] G. Hulten, L. Spencer, and P. Domingos, “Mining Time-Changing Data Streams,”
Proc. ACM SIGKDD '01, pp. 97-106, 2001.- [24] K. Pearson, “Regression, Heredity and Panmixia,”
Philosophical Trans. Royal Soc., vol. 187, pp. 253-318, 1896.- [26] M. Wang and X.S. Wang, “Efficient Evaluation of Composite Correlations for Streaming Time Series,”
Proc. Fourth Int'l Conf. Web-Age Information Management (WAIM '03), pp. 369-380, 2003.- [28] L. Hubert and J. Schultz, “Quadratic Assignment as a General Data-Analysis Strategy,”
British J. Math. and Statistical Psychology, vol. 29, pp. 190-241, 1975.- [30] “R: A Language and Environment for Statistical Computing,”
RFoundation for Statistical Computing. R Development Core Team, http:/www.R-project.org, 2005.- [31] L.A. Zadeh, “Fuzzy Sets,”
Information and Control, vol. 8, no. 3, pp.338-353, 1965. |