Comprehensive implementation of Dynamic Time Warping algorithms in R. Supports arbitrary local (eg symmetric, asymmetric, slope-limited) and global (windowing) constraints, fast native code, several plot styles, and more.

The R Package dtw provides the most complete, freely-available (GPL) implementation of Dynamic Time Warping-type (DTW) algorithms up to date.

The package is described in a companion paper, including detailed instructions and extensive background on things like multivariate matching, open-end variants for real-time use, interplay between recursion types and length normalization, history, etc.

The basic DTW algorithm computes the time axis stretch which optimally maps one timeseries (query) onto another (reference); it outputs the remaining cumulative distance between the two. DTW is widely used e.g. for classification and clustering tasks in econometrics, chemometrics and general timeseries mining.

The R implementation in dtw provides:

- arbitrary windowing functions (global constraints), eg. the Sakoe-Chiba band and the Itakura parallelogram;
- arbitrary transition types (also known as step patterns, slope
constraints, local constraints, or DP-recursion rules). This
includes dozens of well-known types:
- 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 *{proxy}dist*
function. DTW itself becomes a distance function with
the *dist* semantics.

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;
- both fast native (C) and interpreted (R) cores.

The best place to learn how to use the package (and a hopefully a decent deal of background on DTW) is the companion paper Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package, which the Journal of Statistical Software makes available for free.

To have a look at how the *dtw* package is used in domains
ranging from bioinformatics to chemistry to data mining, have a
look at the list
of citing
papers.

A link to prebuilt documentation is here.

If you use *dtw*, do cite it in any publication reporting
results obtained with this software. Please follow the directions
given in `citation("dtw")`

, i.e. cite:

Toni Giorgino (2009).Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package.Journal of Statistical Software, 31(7), 1-24. URL www.jstatsoft.org/v31/i07/.

When using partial matching (unconstrained endpoints via
the `open.begin`

/`open.end`

options) and/or
normalization strategies, please also cite:

Paolo Tormene, Toni Giorgino, Silvana Quaglini, Mario Stefanelli (2008). Matching Incomplete Time Series with Dynamic Time Warping: An Algorithm and an Application to Post-Stroke Rehabilitation. Artificial Intelligence in Medicine, 45(1), 11-34. doi:10.1016/j.artmed.2008.11.007

Go to a gallery of sample plots (straight out of the examples in the documentation).

## A noisy sine wave as query idx<-seq(0,6.28,len=100); query<-sin(idx)+runif(100)/10; ## A cosine is for template; sin and cos are offset by 25 samples template<-cos(idx) ## Find the best match with the canonical recursion formula library(dtw); alignment<-dtw(query,template,keep=TRUE); ## Display the warping curve, i.e. the alignment curve plot(alignment,type="threeway") ## Align and plot with the Rabiner-Juang type VI-c unsmoothed recursion plot( dtw(query,template,keep=TRUE, step=rabinerJuangStepPattern(6,"c")), type="twoway",offset=-2); ## See the recursion relation, as a figure and text plot(rabinerJuangStepPattern(6,"c")) rabinerJuangStepPattern(6,"c") ## And much more!

To install the
latest stable
build of the package (hosted at CRAN), issue the following command
in the R console:

> install.packages("dtw")

To get started, begin from the installed documentation:

> library(dtw)

> ?dtw

> ?plot.dtw

Alas, most likely you haven't. DTW had been "multidimensional" since its conception. Local distances are computed betweenN-dimensional vectors; feature vectors have been extensively used in speech recognition since the '70s (see e.g. things like MFCC, RASTA, cepstrum, etc). Don't worry: several other people have "rediscovered" multivariate DTW already. Thedtwpackage supports the numerous types of multi-dimensional local distances that the proxy package does, as explained in section 3.6 of the paper in JSS.

Alas, most likely you haven't. A natural solution for real-time recognition of timeseries is "unconstrained DTW", which relaxes one or both endpoint boundary conditions. To my knowledge, the algorithm was published as early as 1978 by Rabiner, Rosenberg, and Levinson under the name UE2-1: see e.g. the mini-review in (Tormene and Giorgino, 2008). Feel also free to learn about the clever algorithms or expositions by Sakurai et al. (2007); Latecki (2007); Mori et al. (2006); Smith-Waterman (1981); Rabiner and Schmidt (1980); etc. Open-ended alignments (at one or both ends) are available in thedtwpackage, as described in section 3.5 of the JSS paper.

`symmetric1`

recursion I found in Wikipedia/in another
implementation?An alignment computed with a non-normalizable step pattern has two serious drawbacks:This is discussed in section 3.2 of the JSS paper, section 4.2 of the AIIM paper, Rabiner-Juang's book, and elsewhere. Make sure you familiarize yourself with those references.

- It cannot be meaningfully normalized by timeseries length. Hence, longer timeseries have naturally higher distances, in turn making comparisons impossible.
- It favors diagonal steps, therefore it is not robust: two paths differing for a small local change (eg. horizontal+vertical step rather than diagonal) have very different costs.

TLDR: just stick to the default`symmetric2`

recursion and use the value of`normalizedDistance`

.

Of course. Arrange the timeseries (single-variate) in a matrixas rows. Make sure you use a symmetric pattern. See dtwDist.

`dtwDist`

on timeseries of different lengths?Either loop over the inputs yourself, or pad with NAs and use the following code:dtwOmitNA <-function (x,y) { a<-na.omit(x) b<-na.omit(y) return(dtw(a,b,distance.only=TRUE)$normalizedDistance) } ## create a new entry in the registry with two aliases pr_DB$set_entry(FUN = dtwOmitNA, names = c("dtwOmitNA")) d<-dist(dataset, method = "dtwOmitNA")

You have to handle the loop yourself. Assuming you have data arranged as`x[time,component,series]`

, pseudocode would be:for (i in 1..N) { for (j in 1..N) { result[i,j] <- dtw( dist(x[,,i],x[,,j]), distance.only=T )$normalizedDistance

Yes. See Stefan Novak's version of the quickstart example on Stack Overflow. The mapping is performed through the Python package rpy2, which makes the code natural and readable. It also plays well withnumpyandmultiprocessing.

```
See command
````diff`

.

This software is distributed under the terms of the GNU General
Public License Version 2, June 1991. The terms of this license
are in a file called COPYING which you should have received with
this software and which can be displayed by ```
RShowDoc("COPYING")
```

.

Istituto di Ingegneria Biomedica (ISIB-CNR)

Consiglio Nazionale delle Ricerche

Padova, Italy

Academic institutions interested in a seminar or discussions are welcome to invite me. Please indicate dates, audience type and preferred length.

The Istituto di Ingegneria Biomedica provides on-site and remote consultancy services.

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