Knowledge and Information Systems

, Volume 7, Issue 3, pp 358–386 | Cite as

Exact indexing of dynamic time warping

  • Eamonn KeoghEmail author
  • Chotirat Ann Ratanamahatana


The problem of indexing time series has attracted much interest. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However, it has been forcefully shown that the Euclidean distance is a very brittle distance measure. Dynamic time warping (DTW) is a much more robust distance measure for time series, allowing similar shapes to match even if they are out of phase in the time axis. Because of this flexibility, DTW is widely used in science, medicine, industry and finance. Unfortunately, however, DTW does not obey the triangular inequality and thus has resisted attempts at exact indexing. Instead, many researchers have introduced approximate indexing techniques or abandoned the idea of indexing and concentrated on speeding up sequential searches. In this work, we introduce a novel technique for the exact indexing of DTW. We prove that our method guarantees no false dismissals and we demonstrate its vast superiority over all competing approaches in the largest and most comprehensive set of time series indexing experiments ever undertaken.


Dynamic time warping Indexing Lower bounding Time series 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aach J, Church G (2001) Aligning gene expression time series with time warping algorithms. Bioinformatics 17:495–508CrossRefGoogle Scholar
  2. 2.
    Agrawal R, Lin KI, Sawhney HS, Shim K (1995) Fast similarity search in the presence of noise, scaling, and translation in times-series databases. In: Proceedings of the 21st international conference on very large databases, pp 490–501Google Scholar
  3. 3.
    Bar-Joseph Z, Gerber G, Gifford D, Jaakkola T, Simon I (2002) A new approach to analyzing gene expression time series data. In: Proceedings of the 6th annual international conference on research in computational molecular biology, pp 39–48Google Scholar
  4. 4.
    Berndt D, Clifford J (1994) Using dynamic time warping to find patterns in time series. AAAI-94 workshop on knowledge discovery in databases, pp 229–248Google Scholar
  5. 5.
    Caiani EG, Porta A, Baselli G, Turiel M, Muzzupappa S, Pieruzzi F, Crema C, Malliani A, Cerutti S (1998) Warped-average template technique to track on a cycle-by-cycle basis the cardiac filling phases on left ventricular volume. IEEE Comput Cardiol 25:73–76Google Scholar
  6. 6.
    Chan KP, Fu A, Yu C (2003) Haar wavelets for efficient similarity search of time-series: with and without time warping. IEEE Trans Knowl Data Eng 15(3):686–705CrossRefGoogle Scholar
  7. 7.
    Chu S, Keogh E, Hart D, Pazzani M (2002) Iterative deepening dynamic time warping for time series. In: Proceedings of the 2nd SIAM international conference on data miningGoogle Scholar
  8. 8.
    Das G, Lin K, Mannila H, Renganathan G, Smyth P (1998) Rule discovery form time series. Proceedings of the 4th international conference of knowledge discovery and data mining. AAAI Press, pp 16–22Google Scholar
  9. 9.
    Debregeas A, Hebrail G (1998) Interactive interpretation of Kohonen maps applied to curves. Proceedings of the 4th international conference of knowledge discovery and data mining, pp 179–183Google Scholar
  10. 10.
    Diez JJR, Gonzalez CA (2000) Applying boosting to similarity literals for time series classification. Multiple classifier systems, 1st international workshop, pp 210–219Google Scholar
  11. 11.
    Faloutsos C, Ranganathan M, Manolopoulos Y (1994) Fast subsequence matching in time-series databases. In: Proceedings of the ACM SIGMOD conference, Minneapolis, MN, pp 419–429Google Scholar
  12. 12.
    Faloutsos C, Lin K (1995) FastMap: A fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets. SIGMOD conference, pp 163–174Google Scholar
  13. 13.
    Gavrila DM, Davis LS (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, pp 272–277Google Scholar
  14. 14.
    Gollmer K, Posten C (1995) Detection of distorted pattern using dynamic time warping algorithm and application for supervision of bioprocesses. On-line fault detection and supervision in chemical process industriesGoogle Scholar
  15. 15.
    Guttman A (1984) R-trees: A dynamic index structure for spatial searching. In: Proceedings ACM SIGMOD conference, pp 47–57Google Scholar
  16. 16.
    Hellerstein JM, Papadimitriou CH, Koutsoupias E (1997) Towards an analysis of indexing schemes. 16th ACM symposium on principles of database systems, pp 249–256Google Scholar
  17. 17.
    Itakura F (1975) Minimum prediction residual principle applied to speech recognition. IEEE Trans Acoustics Speech Signal Process ASSP 23:52–72Google Scholar
  18. 18.
    Kadous MW (1999) Learning comprehensible descriptions of multivariate time series. In: Proceedings of the 16th international machine learning conference, pp 454–463Google Scholar
  19. 19.
    Keogh E, Chakrabarti K, Pazzani M, Mehrotra S (2000) Dimensionality reduction for fast similarity search in large time series databases. J Knowl Inf Syst 3(3):263–286CrossRefGoogle Scholar
  20. 20.
    Keogh E, Chakrabarti K, Pazzani M, Mehrotra S (2001) Locally adaptive dimensionality reduction for indexing large time series databases. In: Proceedings of ACM SIGMOD conference on management of data, May, pp 151–162Google Scholar
  21. 21.
    Keogh E, Pazzani M (2000) Scaling up dynamic time warping for data mining applications. In: 6th ACM SIGKDD international conference on knowledge discovery and data mining, BostonGoogle Scholar
  22. 22.
    Kim S, Park S, Chu W (2001) An index-based approach for similarity search supporting time warping in large sequence databases. In: Proceedings of the 17th international conference on data engineering, pp 607–614Google Scholar
  23. 23.
    Kollios G, Vlachos M, Gunopulos G (2002) Discovering similar multidimensional trajectories. In: Proceedings of the 18th international conference on data engineeringGoogle Scholar
  24. 24.
    Korn F, Jagadish H, Faloutsos C (1997) Efficiently supporting ad hoc queries in large datasets of time sequences. In: Proceedings of SIGMOD ’97, pp 289–300Google Scholar
  25. 25.
    Kovacs-Vajna ZM (2000) A fingerprint verification system based on triangular matching and dynamic time warping. IEEE Trans Pattern Anal Mach Intell 22(11):1266–1276CrossRefGoogle Scholar
  26. 26.
    Kruskall JB, Liberman M (1983) The symmetric time warping algorithm: from continuous to discrete. In: Time warps, string edits and macromolecules. AddisonGoogle Scholar
  27. 27.
    Kwong S, He Q, Man K (1996) Genetic time warping for isolated word recognition. Int J Patt Recogn Artif Intell 10(7):849–865CrossRefGoogle Scholar
  28. 28.
    Munich M, Perona P (1999) Continuous dynamic time warping for translation-invariant curve alignment with applications to signature verification. In: Proceedings of 7th international conference on computer vision, Korfu, Greece, pp 108–115Google Scholar
  29. 29.
    Myers C, Rabiner L, Roseneberg A (1980) Performance tradeoffs in dynamic time warping algorithms for isolated word recognition. IEEE Trans Acoustics Speech Signal Process ASSP-28:623–635Google Scholar
  30. 30.
    Park S, Lee D, Chu W (1999) Fast retrieval of similar subsequences in long sequence databases. In: 3rd IEEE knowledge and data engineering exchange workshopGoogle Scholar
  31. 31.
    Park S, Kim S, Chu W (2001) Segment-based approach for subsequence searches in sequence databases. In: Proceedings of the 16th ACM symposium on applied computing, Las Vegas, NV, pp 248–252Google Scholar
  32. 32.
    Park S, Chu W, Yoon J, Hsu C (2000) Efficient searches for similar subsequences of different lengths in sequence databases. In: Proceedings of the 16th IEEE international conference on data engineering, pp 23–32Google Scholar
  33. 33.
    Rabiner L, Juang B (1993) Fundamentals of speech recognition. Prentice, Englewood Cliffs, NJGoogle Scholar
  34. 34.
    Rabiner L, Rosenberg A, Levinson S (1978) Considerations in dynamic time warping algorithms for discrete word recognition. IEEE Trans Acoustics Speech Signal Process ASSP-26:575–582Google Scholar
  35. 35.
    Rath T, Manmatha R (2002) Word image matching using dynamic time warping, Tec Report MM-38. Center for Intelligent Information Retrieval, University of Massachusetts AmherstGoogle Scholar
  36. 36.
    Roussopoulos N, Kelley S, Vincent F (1995) Nearest neighbor queries. SIGMOD Conference, pp 71–79Google Scholar
  37. 37.
    Sakoe H, Chiba S (1978) Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans Acoustics Speech Signal Process ASSP 26:43–49CrossRefGoogle Scholar
  38. 38.
    Schmill M, Oates T, Cohen P (1999) Learned models for continuous planning. In: 7th international workshop on artificial intelligence and statisticsGoogle Scholar
  39. 39.
    Seidl T, Kriegel H (1998) Optimal multi-step k-nearest neighbor search. SIGMOD Conference, pp 154–165Google Scholar
  40. 40.
    Strik H, Boves L (1988) Averaging physiological signals with the use of a DTW algorithm. In: Proceedings SPEECH’88, 7th FASE symposium, Edinburgh, Book 3, pp 883–890Google Scholar
  41. 41.
    Tappert C, Das S (1978) Memory and time improvements in a dynamic programming algorithm for matching speech patterns. IEEE Trans Acoustics Speech Signal Process ASSP 26:583–586CrossRefGoogle Scholar
  42. 42.
    Walker J (2001) HotBits: genuine random numbers generated by radioactive decay, Scholar
  43. 43.
    Yi B, Jagadish K, Faloutsos H (1998) Efficient retrieval of similar time sequences under time warping. In: ICDE 98, pp 23–27Google Scholar
  44. 44.
    Yi BK, Faloutsos C (2000) Fast time sequence indexing for arbitrary Lp norms. Proceedings of the 26th international conference on very large databases, pp 385–394Google Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Computer Science and Engineering DepartmentUniversity of California–RiversideRiversideUSA

Personalised recommendations