Non-isometric transforms in time series classification using DTW

Over recent years the popularity of time series has soared. As a consequence there has been a dramatic increase in the amount of interest in querying and mining such data. In particular, many new distance measures between time series have been introduced. In this paper we propose a new distance function based on derivatives and transforms of time series. In contrast to well-known measures from the literature, our approach combines three distances: DTW distance between time series, DTW distance between derivatives of time series, and DTW distance between transforms of time series. The new distance is used in classification with the nearest neighbor rule. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 47 time series data sets from a wide variety of application domains. Our experiments show that this new method provides a significantly more accurate classification on the examined data sets.

[1]  Daniel Lemire,et al.  Faster retrieval with a two-pass dynamic-time-warping lower bound , 2008, Pattern Recognit..

[2]  G. Hommel,et al.  Improvements of General Multiple Test Procedures for Redundant Systems of Hypotheses , 1988 .

[3]  Hui Ding,et al.  Querying and mining of time series data: experimental comparison of representations and distance measures , 2008, Proc. VLDB Endow..

[4]  Eamonn J. Keogh,et al.  A Complexity-Invariant Distance Measure for Time Series , 2011, SDM.

[5]  Eamonn J. Keogh,et al.  CID: an efficient complexity-invariant distance for time series , 2013, Data Mining and Knowledge Discovery.

[6]  Eamonn Keogh.  Exact Indexing of Dynamic Time Warping , 2002, VLDB.

[7]  J. Joseph,et al.  Fourier transforms , 2012 .

[8]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[9]  Marek Kulbacki,et al.  Unsupervised Learning Motion Models Using Dynamic Time Warping , 2002, Intelligent Information Systems.

[10]  Tomasz Górecki,et al.  Using derivatives in time series classification , 2012, Data Mining and Knowledge Discovery.

[11]  R. Iman,et al.  Approximations of the critical region of the fbietkan statistic , 1980 .

[12]  Donald J. Berndt,et al.  Using Dynamic Time Warping to Find Patterns in Time Series , 1994, KDD Workshop.

[13]  G Hommel,et al.  A rapid algorithm and a computer program for multiple test procedures using logical structures of hypotheses. , 1994, Computer methods and programs in biomedicine.

[14]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[15]  Eamonn J. Keogh,et al.  Derivative Dynamic Time Warping , 2001, SDM.

[16]  Paul L. Rosin,et al.  Assessing the Uniqueness and Permanence of Facial Actions for Use in Biometric Applications , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[17]  Paul L. Rosin,et al.  Facial Dynamics in Biometric Identification , 2008, BMVC.

[18]  Clu-istos Foutsos,et al.  Fast subsequence matching in time-series databases , 1994, SIGMOD '94.

[19]  S. García,et al.  An Extension on "Statistical Comparisons of Classifiers over Multiple Data Sets" for all Pairwise Comparisons , 2008 .