A Haar Wavelet-based Multi-resolution Representation Method of Time Series Data

Muhammad Marwan Muhammad Fuad

2015

Abstract

Similarity search of time series can be efficiently handled through a multi-resolution representation scheme which offers the possibility to use pre-computed distances that are calculated and stored at indexing time and then utilized at query time together with filters in the form of exclusion conditions which speed up the search. In this paper we introduce a new multi-resolution representation and search framework of time series. Compared with our previous multi-resolution methods which use first degree polynomials to reduce the dimensionality of the time series at different resolution levels, the novelty of this work is that it applies Haar wavelets to represent the time series. This representation is particularly adapted to our multi-resolution approach as discrete wavelet transforms have the ability of reflecting the local and global information content at every resolution level thus enhancing the performance of the similarity search algorithm, which is what we have shown in this paper through extensive experiments on different datasets.

References

  1. Bergeron, R. D., and Foulks, A., 2006: Interactive out-ofcore visualization of multiresolution time series data, numerical modeling of space plasma flows: ASTRONUM-2006. Proceedings of the 1st IGPPCalSpace International Conference, Palm Springs, California.
  2. Castro, N., and Azevedo, P., 2010: Multiresolution motif discovery in time series. Proceedings of the SIAM International Conference on Data Mining, SDM 2010, , Columbus, Ohio, USA. SIAM.
  3. Chan, K., and Wai-chee Fu, A., 1999: Efficient time series matching by wavelets. In Proc. 15th. Int. Conf. on Data Engineering.
  4. DeVore, R., Jawerth, B. and Lucier, B., 1992: Image compression through wavelet transform coding. IEEE Transactions on Information Theory.
  5. Faloutsos, C., Ranganathan, M., and Manolopoulos, Y., 1994: Fast subsequence matching in time-series databases. In Proc. ACM SIGMOD Conf., Minneapolis.
  6. Figueras i Ventura R. M., Frossard P., and Vandergheynst P., 2002: Evolutionary multiresolution matching pursuit and its relations with the human visual system. In Proceedings of the European Signal Processing Conference, Toulouse, France.
  7. Hao, M., Dayal, U., Keim, D. A., Schreck, T., 2007: Multi-resolution techniques for visual exploration of large time-series data. Proc. of Eurographics/IEEEVGTC Symposium on Visualization.
  8. Jacobs, C. E., Finkelstein, A., and Salesin, D. H., 1995: Fast multiresolution image querying. In Proceedings of SIGGRAPH 95, ACM, New York.
  9. Keogh, E., Chakrabarti, K., Pazzani, M., and Mehrotra, 2000. Dimensionality reduction for fast similarity search in large time series databases. J. of Know. and Inform. Sys.
  10. Keogh, E., Chakrabarti, K,. Pazzani, M., and Mehrotra, S., 2001: locally adaptive dimensionality reduction for similarity search in large time series databases. SIGMOD.
  11. 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/
  12. Lin, J., Vlachos, M., Gunopulos, D., Keogh, E., 2007: Multi-Resolution Time Series Clustering and Application to Images. Multimedia Data Mining and Knowledge Discovery, Springer.
  13. Lin, J., Vlachos, M., Keogh, E., and Gunopulos, D., 2005: A MPAA-based iterative clustering algorithm augmented by nearest neighbors search for time-series data streams. Proceedings of the 9th Pacic-Asia Conference on Knowledge Discovery and Data Mining (PAKDD'05), Springer.
  14. Megalooikonomou, C., 2005: Multiresolution symbolic representation of time series. In Proceedings of the 21st IEEE International Conference on Data Engineering (ICDE). Tokyo, Japan.
  15. Morinaka, Y., Yoshikawa, M., Amagasa, T., and Uemura, S., 2001: The L-index: An indexing structure for efficient subsequence matching in time sequence databases. In Proc. 5th Pacific Asia Conf. on Knowledge Discovery and Data Mining.
  16. Muhammad Fuad, M. M., Marteau, P. F., 2010a: Fast retrieval of time series by combining a multiresolution filter with a representation technique. The International Conference on Advanced Data Mining and Applications-ADMA2010, ChongQing, China.
  17. Muhammad Fuad, M. M., Marteau P. F., 2010b: Multiresolution approach to time series retrieval. Fourteenth International Database Engineering & Applications Symposium- IDEAS 2010, Montreal, QC, Canada.
  18. Muhammad Fuad, M. M., Marteau P. F., 2010c: Speedingup the similarity search in time series databases by coupling dimensionality reduction techniques with a fast-and-dirty filter. Fourth IEEE International Conference on Semantic Computing- ICSC 2010, Carnegie Mellon University, Pittsburgh, PA, USA.
  19. Popivanov, I., and Miller, R. J., 2002: Similarity search over time series data using wavelets. ICDE.
  20. Ramella, G., Sanniti di Baja, G., 2010: Multiresolution histogram analysis for color reduction, Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications - 15th Iberoamerican Congress on Pattern Recognition, CIARP 2010, Sao Paulo, Brazil.
  21. Schulte, M. J., Lindberg, M. and Laxminarain, A., 2005: Performance evaluation of decimal floating-point arithmetic In IBM Austin Center for Advanced Studies Conference.
  22. Shieh, J., and Keogh, E., 2009: iSAX: Disk-aware mining and indexing of massive time series datasets. Data Mining and Knowledge Discovery.
  23. Shieh, J., and Keogh, E., 2008: iSAX: Indexing and mining terabyte sized time series. In Proceeding of the 14th ACM SIGKDD international Conference on Knowledge Discovery and Data Mining, Las Vegas, Nevada, USA.
  24. Stollnitz, E., DeRose, T., and Salesin, D., 1995: Wavelets for computer graphics: a primer, part 1. IEEE Computer Graphics and Applications.
  25. Sun, S., and Zhou, X., 2005: Semantic caching for webbased spatial applications. In Proceeding of APWeb 2005, Shanghai, China.
  26. Vlachos, M., Lin, J., Keogh, E., Gunopulos, D., 2003: Multi-resolution k-means clustering of time series and applications to images. Workshop on Multimedia Data Mining (MDM), SIGKDD.
  27. Vogiatzis, D., Tsapatsoulis, N., 2006: Missing value estimation for DNA microarrays with mutliresolution schemes. Lecture Notes in Computer Science, Springer Berlin / Heidelberg. Artificial Neural Networks - ICANN.
  28. Wang, Q., Megalooikonomou, V., and Faloutsos, C., 2010: Time series analysis with multiple resolutions. Inf. Syst. 35, 1.
  29. Wu, Y. L., Agrawal, D., and Abbadi, A. E., 2000: A comparison of DFT and DWT based similarity search in time-series databases. In Proc. 9th Int. Conf. on Information and Knowledge Management.
  30. Yang, Z., 2010: Machine learning approaches to bioinformatics. 1st. World Scientific Printers; Singapore.
  31. Yi, B. K., and Faloutsos, C., 2000: Fast time sequence indexing for arbitrary Lp norms. Proceedings of the 26th International Conference on Very Large Databases, Cairo, Egypt.
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Paper Citation


in Harvard Style

Muhammad Fuad M. (2015). A Haar Wavelet-based Multi-resolution Representation Method of Time Series Data . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-074-1, pages 620-626. DOI: 10.5220/0005307006200626


in Bibtex Style

@conference{icaart15,
author={Muhammad Marwan Muhammad Fuad},
title={A Haar Wavelet-based Multi-resolution Representation Method of Time Series Data},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2015},
pages={620-626},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005307006200626},
isbn={978-989-758-074-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - A Haar Wavelet-based Multi-resolution Representation Method of Time Series Data
SN - 978-989-758-074-1
AU - Muhammad Fuad M.
PY - 2015
SP - 620
EP - 626
DO - 10.5220/0005307006200626