This Article 
 Bibliographic References 
 Add to: 
Mining Asynchronous Periodic Patterns in Time Series Data
May/June 2003 (vol. 15 no. 3)
pp. 613-628

Abstract—Periodicy detection in time series data is a challenging problem of great importance in many applications. Most previous work focused on mining synchronous periodic patterns and did not recognize the misaligned presence of a pattern due to the intervention of random noise. In this paper, we propose a more flexible model of asynchronous periodic pattern that may be present only within a subsequence and whose occurrences may be shifted due to disturbance. Two parameters min_rep and max_dis are employed to specify the minimum number of repetitions that is required within each segment of nondisrupted pattern occurrences and the maximum allowed disturbance between any two successive valid segments. Upon satisfying these two requirements, the longest valid subsequence of a pattern is returned. A two-phase algorithm is devised to first generate potential periods by distance-based pruning followed by an iterative procedure to derive and validate candidate patterns and locate the longest valid subsequence. We also show that this algorithm cannot only provide linear time complexity with respect to the length of the sequence but also achieve space efficiency.

[1] R. Agrawal and R. Srikant, “Fast Algorithms for Mining Association Rules,” Proc. 1994 Int'l Conf. Very Large Data Bases, pp. 487-499, Sept. 1994.
[2] R. Agrawal and R. Srikant, “Mining Sequential Patterns,” Proc. 1995 Int'l Conf. Data Eng., pp. 3-14, Mar. 1995.
[3] R. Agrawal, G. Psaila, E.L. Wimmers, and M. Zait, “Querying Shapes of Histories,” Proc. Very Large Data Bases (VLDB) Conf., pp. 502-514, 1995.
[4] R.J. Bayardo, “Efficiently Mining Long Patterns From Databases,” ACM SIGMOD Conf. Management of Data, June 1998.
[5] J. Bentley, “Programming Pearls,” Comm. ACM, vol. 27, no. 2, pp. 865-871, 1984.
[6] D. Berndt and J. Clifford, "Finding Patterns in Time Series: A Dynamic Programming Approach," Advances in Knowledge Discovery and Data Mining, U.M. Fayyad et al., eds., AAAI Press, Menlo Park, Calif., 1996, pp. 229-247.
[7] C. Bettini, X.S. Wang, S. Jajodia, and J.-L. Lin, “Discovering Frequent Event Patterns with Multiple Granularities in Time Sequences,” IEEE Trans. Knowledge and Data Eng., vol. 10, no. 2, 1998.
[8] K.P. Chan and A. Fu, “Efficient Time Series Matching by Wavelets,” Proc. Int'l Conf. Data Eng., 1999.
[9] G. Das, K.-I. Lin, H. Mannila, G. Renganathan, and P. Smyth, “Rule Discovery from Time Series,” Proc. Int'l Conf. Knowledge Discovery and Datamining, pp. 16-22, 1998.
[10] R. Feldman, Y. Aumann, A. Amir, and H. Mannila, “Efficient Algorithms for Discovering Frequent Sets in Incremental Databases,” Proc. ACM SIGMOD Workshop Research Issues on Data Mining and Knowledge Discovery (DMKD), pp. 59-66, 1997.
[11] V. Guralnik and J. Srivastava, “Event Detection from Time Series Data,” Proc. ACM SIGKDD, pp. 33-42, 1999.
[12] J. Han, W. Gong, and Y. Yin, “Mining Segment-Wise Periodic Patterns in Time-Related Databases,” Proc. Int'l Conf. Knowledge Discovery and Data Mining, pp. 214-218, 1998.
[13] J. Han, G. Dong, and Y. Yin, Efficient Mining of Partial Periodic Patterns in Time Series Database Proc. 15th Int'l Conf. Data Eng., pp. 106-115, Mar. 1999.
[14] H.V. Jagadish, N. Koudas, and S. Muthukrishnan, Mining Deviants in a Time Series Database Proc. Very Large Data Bases Conf., 1999.
[15] E.J. Keogh and P. Smyth, “A Probabilistic Approach to Fast Pattern Matching in Time Series Databases,” Proc. Int'l Conf. Knowledge Discovery and Datamining, pp. 24-30, 1997.
[16] F. Korn, H. Jagadish, and C. Faloutsos, “Efficiently Supporting Ad Hoc Queries in Large Datasets of Time Sequences,” Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 289-300, May 1997.
[17] L. Lin and T. Risch, “Querying Continuous Time Sequences,” Proc. 24th Int'l Conf. Very Large Data Base (VLDB), pp. 170-181, 1998.
[18] B. Liu, W. Hsu, and Y. Ma, “Mining Association Rules with Multiple Minimum Supports,” Proc. Fifth ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining, pp. 125-134, Sept. 1999.
[19] H. Mannila, H. Toivonen, and A.I. Verkamo, “Discovery of Frequent Episodes in Event Sequences,” Data Mining and Knowledge Discovery, vol. 1, pp. 259-289, 1997.
[20] T. Oates, “Identifying Distinctive Subsequences in Multivariate Time Series by Clustering,” Proc. ACM SIGKDD, pp. 322-326, 1999.
[21] B. Ozden, S. Ramaswamy, and A. Silberschatz, Cyclic Association Rules Proc. 14th Int'l Conf. Data Eng., Apr. 1998.
[22] Y. Qu, C. Wang, and X.S. Wang, “Supporting Fast Search in Time Series for Movement Patterns in Multiple Scales,” Proc. Int'l Conf. Information and Knowledge Management, pp. 251-258, 1998.
[23] D. Rafiei, “On Similarity-Based Queries for Time Series Data,” Proc. 15th Int'l Conf. Data Eng., pp. 410-417, 1999.
[24] S. Ramaswamy, S. Mahajan, and A. Silbershatz, “On the Discovery of Interesting Patterns in Association Rules,” Proc. 24th Int'l Conf. Very Large Databases, pp. 368–379, Aug. 1998.
[25] R. Srikant and R. Agrawal, “Mining Sequential Patterns: Generalizations and Performance Improvements,” Proc. Fifth Int'l Conf. Extending Database Technology (EDBT), pp. 3-17, 1996.
[26] S. Thomas and S. Sarawagi, “Mining Generalized Association Rules and Sequential Patterns Using SQL Queries,” Proc. Fourth Int'l Conf. Knowledge Discovery and Data Mining (KDD '98), pp. 344-348, 1998.
[27] R. Wetprasit and A. Sattar, “Temporal Reasoning with Qualitative and Quantitative Information about Points and Durations,” Proc. 15th Nat'l Conf. Artificial Intelligence (AAAI '98), pp. 656-663, 1998.
[28] J. Yang, W. Wang, and P. Yu, “Infominer: Mining Surprising Periodic Patterns,” Proc. of Seventh Int'l Conf. Knowledge Discovery and Data Mining (KDD '01), pp. 395-400, 2001.

Index Terms:
Asynchronous periodic pattern, segment-based approach, partial periodicity.
Jiong Yang, Wei Wang, Philip S. Yu, "Mining Asynchronous Periodic Patterns in Time Series Data," IEEE Transactions on Knowledge and Data Engineering, vol. 15, no. 3, pp. 613-628, May-June 2003, doi:10.1109/TKDE.2003.1198394
Usage of this product signifies your acceptance of the Terms of Use.