Dynamic Time Warp: find the optimal alignment between two time series.
Comprehensive implementation of Dynamic Time Warping (DTW) algorithms in R.
The DTW algorithm computes the stretch of the time axis which optimally maps one given timeseries (query) onto whole or part of another (reference). It yields the remaining cumulative distance after the alignment and the point-by-point correspondence (warping function). DTW is widely used e.g. for classification and clustering tasks in econometrics, chemometrics and general timeseries mining.
Please see documentation for function
dtw, which is the
main entry point to the package.
The R implementation in dtw provides:
arbitrary windowing functions (global constraints), eg. the Sakoe-Chiba band; see
arbitrary transition types (also known as step patterns, slope constraints, local constraints, or DP-recursion rules). This includes dozens of well-known types; see
all step patterns classified by Rabiner-Juang, Sakoe-Chiba, and Rabiner-Myers;
symmetric and asymmetric;
Rabiner's smoothed variants;
arbitrary, user-defined slope constraints
partial matches: open-begin, open-end, substring matches
proper, pattern-dependent, normalization (exact average distance per step)
the Minimum Variance Matching (MVM) algorithm (Latecki et al.)
Multivariate timeseries can be aligned with arbitrary local distance
definitions, leveraging the
dist function of
package proxy. DTW itself becomes a distance function with the
In addition to computing alignments, the package provides:
methods for plotting alignments and warping functions in several classic styles (see plot gallery);
graphical representation of step patterns;
functions for applying a warping function, either direct or inverse; and more.
If you use this software, please cite it according to
citation("dtw"). The package home page is at
To get the latest stable version from CRAN, use
install.packages("dtw"). To get the development version
(possibly unstable), use
Toni Giorgino, Copyright (c) 2007-2013
Istituto di Ingegneria Biomedica (ISIB-CNR)
National Research Council of Italy
Toni Giorgino. Computing and Visualizing Dynamic Time Warping
Alignments in R: The dtw Package. Journal of Statistical
Software, 31(7), 1-24. http://www.jstatsoft.org/v31/i07/
Tormene, P.; Giorgino, T.; Quaglini, S. & Stefanelli, M. Matching incomplete time series with dynamic time warping: an algorithm and an application to post-stroke rehabilitation. Artif Intell Med, 2009, 45, 11-34
Rabiner, L. R., & Juang, B.-H. (1993). Chapter 4 in Fundamentals of speech recognition. Englewood Cliffs, NJ: Prentice Hall.
dtw for the main entry point to the package;
dtwWindowingFunctions for global constraints;
stepPattern for local constraints;
building a local cost matrix with multivariate
timeseries and custom distance functions.