Toward accurate dynamic time warping in linear time and space

Dynamic Time Warping (DTW) has a quadratic time and space complexity that limits its use to small time series. In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity. FastDTW uses a multilevel approach that recursively projects a solution from a coarser resolution and refines the projected solution. We prove the linear time and space complexity of FastDTW both theoretically and empirically. We also analyze the accuracy of FastDTW by comparing it to two other types of existing approximate DTW algorithms: constraints (such as Sakoe-Chiba Bands) and abstraction. Our results show a large improvement in accuracy over existing methods.

[1]  Nicolas Courty,et al.  Temporal alignment of communicative gesture sequences: Research Articles , 2006 .

[2]  S. Chiba,et al.  Dynamic programming algorithm optimization for spoken word recognition , 1978 .

[3]  Shashi Shekhar,et al.  Multilevel hypergraph partitioning: application in VLSI domain , 1997, DAC.

[4]  Wesley W. Chu,et al.  An index-based approach for similarity search supporting time warping in large sequence databases , 2001, Proceedings 17th International Conference on Data Engineering.

[5]  Davide Roverso.  MULTIVARIATE TEMPORAL CLASSIFICATION BY WINDOWED WAVELET DECOMPOSITION AND RECURRENT NEURAL NETWORKS , 2000 .

[6]  Eamonn J. Keogh,et al.  Making Time-Series Classification More Accurate Using Learned Constraints , 2004, SDM.

[7]  Eamonn J. Keogh,et al.  Three Myths about Dynamic Time Warping Data Mining , 2005, SDM.

[8]  Alexis Héloir,et al.  Temporal alignment of communicative gesture sequences , 2006, Comput. Animat. Virtual Worlds.

[9]  Eamonn J. Keogh,et al.  Scaling up dynamic time warping for datamining applications , 2000, KDD '00.

[10]  G. W. Hughes,et al.  Minimum Prediction Residual Principle Applied to Speech Recognition , 1975 .

[11]  Eamonn J. Keogh,et al.  Exact indexing of dynamic time warping , 2002, Knowledge and Information Systems.

[12]  L. Gupta,et al.  Nonlinear alignment and averaging for estimating the evoked potential , 1996, IEEE Transactions on Biomedical Engineering.

[13]  K. Markides,et al.  Chromatographic alignment by warping and dynamic programming as a pre-processing tool for PARAFAC modelling of liquid chromatography-mass spectrometry data. , 2002, Journal of chromatography. A.

[14]  Eamonn J. Keogh,et al.  Relevance feedback retrieval of time series data , 1999, SIGIR '99.

[15]  Stan Weidner Salvador,et al.  Learning states for detecting anomalies in time series , 2004 .

[16]  Joseph B. Kruskall,et al.  The Symmetric Time-Warping Problem : From Continuous to Discrete , 1983 .

[17]  Eamonn J. Keogh,et al.  On the Need for Time Series Data Mining Benchmarks: A Survey and Empirical Demonstration , 2002, Data Mining and Knowledge Discovery.

[18]  Michael Gleicher,et al.  Automated extraction and parameterization of motions in large data sets , 2004, SIGGRAPH 2004.

[19]  Eamonn J. Keogh,et al.  UCR Time Series Data Mining Archive , 1983 .

[20]  Waleed H. Abdulla,et al.  Cross-words reference template for DTW-based speech recognition systems , 2003, TENCON 2003. Conference on Convergent Technologies for Asia-Pacific Region.

[21]  Eamonn J. Keogh,et al.  Iterative Deepening Dynamic Time Warping for Time Series , 2002, SDM.