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Asymptotic Dynamic Time Warping calculation with utilizing value repetition

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Abstract

Dynamic Time Warping (DTW) is a popular method for measuring the similarity of time series. It is widely used in various domains. A major drawback of DTW is that it has a high computational complexity. To address this problem, pruning techniques to calculate the exact DTW distance, as well as DTW approximation methods, have become important approaches. In this paper, we introduce Blocked Dynamic Time Warping (BDTW), a new similarity measure which works on run-length encoded time series representation. BDTW utilizes any repetitive values (zero and nonzero) in time series to reduce DTW computation time. BDTW closely approximates DTW distance, and it is significantly faster than traditional DTW for time series with high levels of value repetition. Moreover, BDTW can be combined with time series representation methods which provide constant segments, to serve as a close approximation method even for the time series without value repetition. Constrained BDTW, BDTW upper bound and BDTW lower bound are discussed as variations of BDTW. BDTW upper bound and BDTW lower bound are presented as a new DTW upper bound and lower bound which can be efficiently applied on time series with high levels of value repetition for pruning unhopeful alignments and matches in the exact DTW calculation. We show the effectiveness of BDTW and its variations on different applications using the following datasets: Almanac of Minutely Power, Refit Smart Homes, as well as the 85 datasets from the University of California, Riverside time series classification archive (UCR archive).

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References

  1. Berndt DJ, Clifford J (1994) Using dynamic time warping to find patterns in time series. In: KDD workshop, vol 10, no 16. Seattle, WA, pp 359–370

  2. Shanker AP, Rajagopalan A (2007) Off-line signature verification using dtw. Pattern Recognit Lett 28(12):1407–1414

    Article  Google Scholar 

  3. Kruskal JB, Liberman M (1983) The symmetric time-warping problem: from continuous to discrete. In: Time warps, string edits and macromolecules: the theory and practice of sequence comparison. Addison-Wesley, pp 125–161

  4. Aach J, Church GM (2001) Aligning gene expression time series with time warping algorithms. Bioinformatics 17(6):495–508

    Article  Google Scholar 

  5. Bar-Joseph Z, Gerber G, Gifford DK, Jaakkola TS, Simon I (2002) A new approach to analyzing gene expression time series data. In: Proceedings of the sixth annual international conference on Computational biology. ACM, pp 39–48

  6. Gavrila D, Davis L et al (1995) Towards 3-d model-based tracking and recognition of human movement: a multi-view approach. In: International workshop on automatic face-and gesture-recognition. Citeseer, pp 272–277

  7. Rath TM, Manmatha R (2003) Word image matching using dynamic time warping. In: Proceedings 2003 IEEE computer society conference on computer vision and pattern recognition, vol 2. IEEE

  8. Bagnall A, Lines J, Bostrom A, Large J, Keogh E (2016) The great time series classification bake off: a review and experimental evaluation of recent algorithmic advances. Data Min Knowl Discov 31:606–660

    Article  MathSciNet  Google Scholar 

  9. Wang X, Mueen A, Ding H, Trajcevski G, Scheuermann P, Keogh E (2013) Experimental comparison of representation methods and distance measures for time series data. Data Min Knowl Discov 26(2):275–309 pp. 1–35

    Article  MathSciNet  Google Scholar 

  10. Ding H, Trajcevski G, Scheuermann P, Wang X, Keogh E (2008) Querying and mining of time series data: experimental comparison of representations and distance measures. PVLDB 1(2):1542–1552

    Google Scholar 

  11. Ding H, Trajcevski G, Scheuermann P, Wang X, Keogh E (2008) Querying and mining of time series data: experimental comparison of representations and distance measures. Proc VLDB Endow 1(2):1542–1552

    Article  Google Scholar 

  12. Keogh E, Wei L, Xi X, Vlachos M, Lee S-H, Protopapas P (2009) Supporting exact indexing of arbitrarily rotated shapes and periodic time series under euclidean and warping distance measures. Int J Very Large Data Bases 18(3):611–630

    Article  Google Scholar 

  13. Keog E, Ratanamahatana CA (2005) Exact indexing of dynamic time warping. Knowl Inf Syst 7(3):358–386

    Article  Google Scholar 

  14. Tavenard R, Amsaleg L (2015) Improving the efficiency of traditional DTW accelerators. Knowl Inf Syst 42(1):215–243

    Article  Google Scholar 

  15. Silva DF, Batista GE (2016) Speeding up all-pairwise dynamic time warping matrix calculation. In: Proceedings of the 2016 SIAM international conference on data mining. SIAM, pp 837–845

  16. Salvador S, Chan P (2007) Toward accurate dynamic time warping in linear time and space. Intell Data Anal 11(5):561–580

    Google Scholar 

  17. Keogh E, Pazzani MJ (2000) Scaling up dynamic time warping for datamining applications. In: Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 285–289

  18. Chu S, Keogh E, Hart DM, Pazzani MJ (2002) Iterative deepening dynamic time warping for time series. In: SDM. SIAM, pp 195–212

  19. Sharabiani A, Darabi H, Rezaei A, Harford S, Johnson H, Karim F (2017) Efficient classification of long time series by 3-dimensional dynamic time warping. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2017.2699333

    Google Scholar 

  20. Mueen A, Chavoshi N, Abu-El-Rub N, Hamooni H, Minnich A (2016) Awarp: fast warping distance for sparse time series. In: Data Mining (ICDM). IEEE, pp 350–359

  21. Keogh E, Folias T (2002) The UCR time series data mining archive. Computer Science and Engineering Department, University of California, Riverside, CA. http://www.cs.ucr.edu/eamonn/TSDMA/index.html. Accessed 10 May 2016

  22. Megalooikonomou V, Wang Q, Li G, Faloutsos C (2005) A multiresolution symbolic representation of time series. In: Proceedings 21st international conference on data engineering. ICDE 2005. IEEE

  23. Ratanamahatana CA, Keogh E (2005) Three myths about dynamic time warping data mining. In: Proceedings of the SIAM international conference on data mining. SDM 05. SIAM, pp 506–510

  24. Keogh E, Chakrabarti K, Pazzani M, Mehrotra S (2001) Dimensionality reduction for fast similarity search in large time series databases. Knowl Inf Syst 3(3):263–286

    Article  MATH  Google Scholar 

  25. Keogh E, Chakrabarti K, Pazzani M, Mehrotra S (2001) Locally adaptive dimensionality reduction for indexing large time series databases. ACM SIGMOD Rec 30(2):151–162

    Article  MATH  Google Scholar 

  26. Kim SW, Park S, Chu WW (2001) An index-based approach for similarity search supporting time warping in large sequence databases. IEEE, pp 607–614

  27. Fu A, Keogh E, Lau LY (2008) Scaling and time warping in time series querying. Int J Very Large Data Bases 17(4):899–921

    Article  Google Scholar 

  28. Rakthanmanon T, Campana B, Mueen A, Batista G, Westover B, Zhu Q, Zakaria J, Keogh J (2012) Searching and mining trillions of time series subsequences under dynamic time warping. In: Proceedings of the 18th ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 262–270

  29. Batista GE, Wang X, Keogh E (2011) A complexity-invariant distance measure for time series. In: SDM, vol 11. SIAM, pp 699–710

  30. Makonin S (2016) Electricity, water, and natural gas consumption of a residential house in Canada from 2012 to 2014. Sci Data 3:160037. https://doi.org/10.1038/sdata.2016.37

    Article  Google Scholar 

  31. Murray D, Stankovic L Refit: electrical load measurements. http://www.refitsmarthomes.org/. Accessed 15 May 2017

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Anooshiravan Sharabiani, Houshang Darabi, Samuel Harford, Elnaz Douzali, Fazle Karim, Hereford Johnson & Shun Chen

Authors
  1. Anooshiravan Sharabiani
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  2. Houshang Darabi
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  3. Samuel Harford
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  4. Elnaz Douzali
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  5. Fazle Karim
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  6. Hereford Johnson
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  7. Shun Chen
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Correspondence to Houshang Darabi.

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Sharabiani, A., Darabi, H., Harford, S. et al. Asymptotic Dynamic Time Warping calculation with utilizing value repetition. Knowl Inf Syst 57, 359–388 (2018). https://doi.org/10.1007/s10115-018-1163-4

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  • DOI: https://doi.org/10.1007/s10115-018-1163-4

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