Using Convolution to Mine Obscure Periodic Patterns in One Pass

  • Mohamed G. Elfeky
  • Walid G. Aref
  • Ahmed K. Elmagarmid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2992)

Abstract

The mining of periodic patterns in time series databases is an interesting data mining problem that can be envisioned as a tool for forecasting and predicting the future behavior of time series data. Existing periodic patterns mining algorithms either assume that the periodic rate (or simply the period) is user-specified, or try to detect potential values for the period in a separate phase. The former assumption is a considerable disadvantage, especially in time series databases where the period is not known a priori. The latter approach results in a multi-pass algorithm, which on the other hand is to be avoided in online environments (e.g., data streams). In this paper, we develop an algorithm that mines periodic patterns in time series databases with unknown or obscure periods such that discovering the period is part of the mining process. Based on convolution, our algorithm requires only one pass over a time series of length n, with O(n log n) time complexity.

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References

  1. 1.
    Abrahamson, K.: Generalized String Matching. SIAM Journal on Computing 16(6), 1039–1051 (1987)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Agrawal, R., Srikant, R.: Fast Algorithms for Mining Association Rules. In: Proc. of the 20th Int. Conf. on Very Large Databases, Santiago, Chile (September 1994)Google Scholar
  3. 3.
    Agrawal, R., Srikant, R.: Mining Sequential Patterns. In: Proc. of the 11th Int. Conf. on Data Engineering, Taipei, Taiwan (March 1995)Google Scholar
  4. 4.
    Aref, W., Elfeky, M., Elmagarmid, A.: Incremental, Online, and Merge Mining of Partial Periodic Patterns in Time-Series Databases. IEEE Transactions on Knowledge and Data Engineering (to appear)Google Scholar
  5. 5.
    Ayres, J., Gehrke, J., Yiu, T., Flannick, J.: Sequential Pattern Mining using A Bitmap Representation. In: Proc. of the 8th Int. Conf. on Knowledge Discovery and Data Mining, Edmonton, Alberta, Canada (July 2002)Google Scholar
  6. 6.
    Berberidis, C., Aref, W., Atallah, M., Vlahavas, I., Elmagarmid, A.: Multiple and Partial Periodicity Mining in Time Series Databases. In: Proc. of the 15th Euro. Conf. on Artificial Intelligence, Lyon, France (July 2002)Google Scholar
  7. 7.
    Bettini, C., Wang, X., Jajodia, S., Lin, J.: Discovering Frequent Event Patterns with Multiple Granularities in Time Sequences. IEEE Transactions on Knowledge and Data Engineering 10(2), 222–237 (1998)CrossRefGoogle Scholar
  8. 8.
    Cormen, T., Leiserson, C., Rivest, R.: Introduction to Algorithms. The MIT Press, Cambridge (1990)MATHGoogle Scholar
  9. 9.
    Daw, C., Finney, C., Tracy, E.: A Review of Symbolic Analysis of Experimental Data. Review of Scientific Instruments 74(2), 915–930 (2003)CrossRefGoogle Scholar
  10. 10.
    Garofalakis, M., Rastogi, R., Shim, K.: SPIRIT: Sequential Pattern Mining with Regular Expression Constraints. In: Proc. of the 25th Int. Conf. on Very Large Databases, Edinburgh, Scotland, UK (September 1999)Google Scholar
  11. 11.
    Han, J., Dong, G., Yin, Y.: Efficient Mining of Partial Periodic Patterns in Time Series Databases. In: Proc. of the 15th Int. Conf. on Data Engineering, Sydney, Australia (March 1999)Google Scholar
  12. 12.
    Han, J., Gong, W., Yin, Y.: Mining Segment-Wise Periodic Patterns in Time Related Databases. In: Proc. of the 4th Int. Conf. on Knowledge Discovery and Data Mining, New York City, New York (August 1998)Google Scholar
  13. 13.
    Indyk, P., Koudas, N., Muthukrishnan, S.: Identifying Representative Trends in Massive Time Series Data Sets Using Sketches. In: Proc. of the 26th Int. Conf. on Very Large Data Bases, Cairo, Egypt (September 2000)Google Scholar
  14. 14.
    Keogh, E., Lonardi, S., Chiu, B.: Finding Surprising Patterns in a Time Series Database in Linear Time and Space. In: Proc. of the 8th Int. Conf. on Knowledge Discovery and Data Mining, Edmonton, Alberta, Canada (July 2002)Google Scholar
  15. 15.
    Knuth, D.: The Art of Computer Programming, vol. 2. Addison-Wesley, Reading (1981)MATHGoogle Scholar
  16. 16.
    Ma, S., Hellerstein, J.: Mining Partially Periodic Event Patterns with Unknown Periods. In: Proc. of the 17th Int. Conf. on Data Engineering, Heidelberg, Germany (April 2001)Google Scholar
  17. 17.
    Ozden, B., Ramaswamy, S., Silberschatz, A.: Cyclic Association Rules. In: Proc. of the 14th Int. Conf. on Data Engineering, Orlando, Florida (February 1998)Google Scholar
  18. 18.
    Srikant, R., Agrawal, R.: Mining Sequential Patterns: Generalizations and Performance Improvements. In: Proc. of the 5th Int. Conf. on Extending Database Technology, Avignon, France (March 1996)Google Scholar
  19. 19.
    Vitter, J.: External Memory Algorithms and Data Structures: Dealing with Massive Data. ACM Computing Surveys 33(2), 209–271 (2001)CrossRefGoogle Scholar
  20. 20.
    Yang, J., Wang, W., Yu, P.: Mining Asynchronous Periodic Patterns in Time Series Data. In: Proc. of the 6th Int. Conf. on Knowledge Discovery and Data Mining, Boston, Massachusetts (August 2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mohamed G. Elfeky
    • 1
  • Walid G. Aref
    • 1
  • Ahmed K. Elmagarmid
    • 1
  1. 1.Department of Computer SciencesPurdue University 

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