# Improving the efficiency of traditional DTW accelerators

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## Abstract

Dynamic time warping (DTW) is the most popular approach for evaluating the similarity of time series, but its computation is costly. Therefore, simple functions lower bounding DTW distances have been designed, accelerating searches by quickly pruning sequences that could not possibly be best matches. The tighter the bounds, the more they prune and the better the performance. Designing new functions that are even tighter is difficult because their computation is likely to become complex, canceling the benefits of their pruning. It is possible, however, to design simple functions with a higher pruning power by relaxing the *no false dismissal* assumption, resulting in approximate lower bound functions. This paper describes how very popular approaches accelerating DTW such as \(\text {LB}\_\text {Keogh}{}\) and \(\text {LB}\_\text {PAA}{}\) can be made more efficient via approximations. The accuracy of approximations can be tuned, ranging from no false dismissal to potential losses when aggressively set for great response time savings. At very large scale, indexing time series is mandatory. This paper also describes how approximate lower bound functions can be used with *i*SAX. Furthermore, it shows that a \(k\)-means-based quantization step for *i*SAX gives significant performance gains.

## Keywords

Dynamic time warping Indexing Lower bounds Upper bounds Indexing trees## References

- 1.Aach J, Church G (2001) Aligning gene expression time series with time warping algorithms. Bioinformatics 17(6):495CrossRefGoogle Scholar
- 2.Camerra A, Palpanas T, Shieh J, Keogh EJ (2010) iSAX 2.0: indexing and mining one billion time series. In: Proceedings of the IEEE international conference on data miningGoogle Scholar
- 3.Chu S, Keogh E, Hart D, Pazzani M et al (2002) Iterative deepening dynamic time warping for time series. In: Proceedings of the SIAM international conference on data miningGoogle Scholar
- 4.Faloutsos C, Ranganathan M, Manolopoulos Y (1994) Fast subsequence matching in time-series databases. In: Proceedings of the ACM SIGMOD conference on management of dataGoogle Scholar
- 5.Gavrila D, Davis L (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
- 6.Itakura F (1975) Minimum prediction residual principle applied to speech recognition. IEEE Trans Acoust Speech Signal Process 23(1):67–72CrossRefGoogle Scholar
- 7.Kashyap S, Karras P (2011) Scalable knn search on vertically stored time series. In: Proceedings of the ACM SIGKDD conference on knowledge discovery and data mining, ACM, pp 1334–1342Google Scholar
- 8.Keogh E, Ratanamahatana C (2005) Exact indexing of dynamic time warping. Knowl Inform Syst 7(3):358–386CrossRefGoogle Scholar
- 9.Keogh E, Xi X, Wei L, Ratanamahatana CA (2006) The ucr time series classification/clustering homepage. www.cs.ucr.edu/~eamonn/time_series_data/
- 10.Lin J, Keogh E, Wei L, Lonardi S (2007) Experiencing SAX: a novel symbolic representation of time series. Data Mining Knowl Discov 15(2):107–144CrossRefMathSciNetGoogle Scholar
- 11.Munich M, Perona P (1999) Continuous dynamic time warping for translation-invariant curve alignment with applications to signature verification. In: Proceedings of the IEEE international conference on computer vision, vol 1, pp 108–115Google Scholar
- 12.Nistér D, Stewénius H (2006) Scalable recognition with a vocabulary tree. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 2161–2168Google Scholar
- 13.Paulevé L, Jégou H, Amsaleg L (2010) Locality sensitive hashing: a comparison of hash function types and querying mechanisms. Pattern Recogn Lett 31(11):1348–1358CrossRefGoogle Scholar
- 14.Sakoe H, Chiba S (1978) Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans Acoust Speech Signal Process 26:43–49CrossRefMATHGoogle Scholar
- 15.Shieh J, Keogh E (2008) iSAX: indexing and mining terabyte sized time series. In: Proceedings of the ACM SIGKDD conference on knowledge discovery and data miningGoogle Scholar
- 16.Sivic J, Zisserman A (2003) Video google: a text retrieval approach to object matching in videos. In: Proceedings of the IEEE international conference on computer vision, pp 1470–1477Google Scholar
- 17.Tavenard R, Jégou H, Amsaleg L (2011) Balancing clusters to reduce response time variability in large scale image search. In: Proceedings of the IEEE workshop on content-based multimedia indexingGoogle Scholar
- 18.Vlachos M, Hadjieleftheriou M, Gunopulos D, Keogh EJ (2003) Indexing multi-dimensional time-series with support for multiple distance measures. In: Proceedings of the ACM SIGKDD conference on knowledge discovery and data mining, pp 216–225Google Scholar
- 19.Yi B, Jagadish HV, Faloutsos C (1998) Efficient retrieval of similar time sequences under time warping. In: Proceedings of the IEEE international conference on data engineeringGoogle Scholar