Package: dtaidistance
Time Series DistancesLibrary for time series distances (e.g. Dynamic Time Warping) used in theDTAI Research Group. The library offers a pure
Python implementation and a fast implementation in C. The C implementation
has only Cython as a dependency. It is compatible with Numpy and Pandas and
implemented such that unnecessary data copy operations are avoided.Documentation:http://dtaidistance.readthedocs.ioExample:from dtaidistance import dtw
import numpy as np
s1 = np.array([0.0, 0, 1, 2, 1, 0, 1, 0, 0])
s2 = np.array([0.0, 1, 2, 0, 0, 0, 0, 0, 0])
d = dtw.distance_fast(s1, s2)Citing this work:Wannes Meert, Kilian Hendrickx, Toon Van Craenendonck, Pieter Robberechts, Hendrik Blockeel & Jesse Davis.DTAIDistance (Version v2). Zenodo.http://doi.org/10.5281/zenodo.5901139New in v2:Numpy is now an optional dependency, also to compile the C library
(only Cython is required).Small optimizations throughout the C code to improve speed.The consistent use ofssize_tinstead ofintallows for larger data structures on 64 bit
machines and be more compatible with Numpy.The parallelization is now implemented directly in C (included if OpenMP is installed).Themax_distargument turned out to be similar to Silva and Batista's work
on PrunedDTW [7]. The toolbox now implements a version that is equal to PrunedDTW
since it prunes more partial distances. Additionally, ause_pruningargument
is added to automatically setmax_distto the Euclidean distance, as suggested
by Silva and Batista, to speed up the computation (a new methodub_euclideanis available).Support in the C library for multi-dimensional sequences in thedtaidistance.dtw_ndimpackage.DTW Barycenter Averaging for clustering (v2.2).Subsequence search and local concurrences (v2.3).Support for N-dimensional time series (v2.3.7).Installation$ pip install dtaidistanceor$ conda install -c conda-forge dtaidistanceThe pip installation requires Numpy as a dependency to compile Numpy-compatible
C code (using Cython). However, this dependency is optional and can be removed.The source code is available atgithub.com/wannesm/dtaidistance.If you encounter any problems during compilation (e.g. the C-based implementation or OpenMP
is not available), see thedocumentationfor more options.UsageDynamic Time Warping (DTW) Distance Measurefrom dtaidistance import dtw
from dtaidistance import dtw_visualisation as dtwvis
import numpy as np
s1 = np.array([0., 0, 1, 2, 1, 0, 1, 0, 0, 2, 1, 0, 0])
s2 = np.array([0., 1, 2, 3, 1, 0, 0, 0, 2, 1, 0, 0, 0])
path = dtw.warping_path(s1, s2)
dtwvis.plot_warping(s1, s2, path, filename="warp.png")DTW Distance Measure Between Two SeriesOnly the distance measure based on two sequences of numbers:from dtaidistance import dtw
s1 = [0, 0, 1, 2, 1, 0, 1, 0, 0]
s2 = [0, 1, 2, 0, 0, 0, 0, 0, 0]
distance = dtw.distance(s1, s2)
print(distance)The fastest version (30-300 times) uses c directly but requires an array as input (with the double type),
and (optionally) also prunes computations by settingmax_distto the Euclidean upper bound:from dtaidistance import dtw
import array
s1 = array.array('d',[0, 0, 1, 2, 1, 0, 1, 0, 0])
s2 = array.array('d',[0, 1, 2, 0, 0, 0, 0, 0, 0])
d = dtw.distance_fast(s1, s2, use_pruning=True)Or you can use a numpy array (with dtype double or float):from dtaidistance import dtw
import numpy as np
s1 = np.array([0, 0, 1, 2, 1, 0, 1, 0, 0], dtype=np.double)
s2 = np.array([0.0, 1, 2, 0, 0, 0, 0, 0, 0])
d = dtw.distance_fast(s1, s2, use_pruning=True)Check the__doc__for information about the available arguments:print(dtw.distance.__doc__)A number of options are foreseen to early stop some paths the dynamic programming algorithm is exploring or tune
the distance measure computation:window: Only allow for shifts up to this amount away from the two diagonals.max_dist: Stop if the returned distance measure will be larger than this value.max_step: Do not allow steps larger than this value.max_length_diff: Return infinity if difference in length of two series is larger.penalty: Penalty to add if compression or expansion is applied (on top of the distance).psi: Psi relaxation to ignore begin and/or end of sequences (for cylical sequences) [2].use_pruning: Prune computations based on the Euclidean upper bound.DTW Distance Measure all warping pathsIf, next to the distance, you also want the full matrix to see all possible warping paths:from dtaidistance import dtw
s1 = [0, 0, 1, 2, 1, 0, 1, 0, 0]
s2 = [0, 1, 2, 0, 0, 0, 0, 0, 0]
distance, paths = dtw.warping_paths(s1, s2)
print(distance)
print(paths)The matrix with all warping paths can be visualised as follows:from dtaidistance import dtw
from dtaidistance import dtw_visualisation as dtwvis
import random
import numpy as np
x = np.arange(0, 20, .5)
s1 = np.sin(x)
s2 = np.sin(x - 1)
random.seed(1)
for idx in range(len(s2)):
    if random.random() < 0.05:
        s2[idx] += (random.random() - 0.5) / 2
d, paths = dtw.warping_paths(s1, s2, window=25, psi=2)
best_path = dtw.best_path(paths)
dtwvis.plot_warpingpaths(s1, s2, paths, best_path)Notice thepsiparameter that relaxes the matching at the beginning and end.
In this example this results in a perfect match even though the sine waves are slightly shifted.DTW Distance Measures Between Set of SeriesTo compute the DTW distance measures between all sequences in a list of sequences, use the methoddtw.distance_matrix.
You can set variables to use more or less c code (use_canduse_nogil) and parallel or serial execution
(parallel).Thedistance_matrixmethod expects a list of lists/arrays:from dtaidistance import dtw
import numpy as np
series = [
    np.array([0, 0, 1, 2, 1, 0, 1, 0, 0], dtype=np.double),
    np.array([0.0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0]),
    np.array([0.0, 0, 1, 2, 1, 0, 0, 0])]
ds = dtw.distance_matrix_fast(series)or a matrix (in case all series have the same length):from dtaidistance import dtw
import numpy as np
series = np.matrix([
    [0.0, 0, 1, 2, 1, 0, 1, 0, 0],
    [0.0, 1, 2, 0, 0, 0, 0, 0, 0],
    [0.0, 0, 1, 2, 1, 0, 0, 0, 0]])
ds = dtw.distance_matrix_fast(series)DTW Distance Measures Between Set of Series, limited to blockYou can instruct the computation to only fill part of the distance measures matrix.
For example to distribute the computations over multiple nodes, or to only
compare source series to target series.from dtaidistance import dtw
import numpy as np
series = np.matrix([
     [0., 0, 1, 2, 1, 0, 1, 0, 0],
     [0., 1, 2, 0, 0, 0, 0, 0, 0],
     [1., 2, 0, 0, 0, 0, 0, 1, 1],
     [0., 0, 1, 2, 1, 0, 1, 0, 0],
     [0., 1, 2, 0, 0, 0, 0, 0, 0],
     [1., 2, 0, 0, 0, 0, 0, 1, 1]])
ds = dtw.distance_matrix_fast(series, block=((1, 4), (3, 5)))The output in this case will be:#  0     1    2    3       4       5
[[ inf   inf  inf     inf     inf  inf]    # 0
 [ inf   inf  inf  1.4142  0.0000  inf]    # 1
 [ inf   inf  inf  2.2360  1.7320  inf]    # 2
 [ inf   inf  inf     inf  1.4142  inf]    # 3
 [ inf   inf  inf     inf     inf  inf]    # 4
 [ inf   inf  inf     inf     inf  inf]]   # 5ClusteringA distance matrix can be used for time series clustering. You can use existing methods such asscipy.cluster.hierarchy.linkageor one of two included clustering methods (the latter is a
wrapper for the SciPy linkage method).from dtaidistance import clustering
# Custom Hierarchical clustering
model1 = clustering.Hierarchical(dtw.distance_matrix_fast, {})
cluster_idx = model1.fit(series)
# Augment Hierarchical object to keep track of the full tree
model2 = clustering.HierarchicalTree(model1)
cluster_idx = model2.fit(series)
# SciPy linkage clustering
model3 = clustering.LinkageTree(dtw.distance_matrix_fast, {})
cluster_idx = model3.fit(series)For models that keep track of the full clustering tree (HierarchicalTreeorLinkageTree), the
tree can be visualised:model.plot("myplot.png")DependenciesPython 3Optional:CythonNumpytqdmMatplotlibSciPyPyClusteringDevelopment:pytestpytest-benchmarkContacthttps://people.cs.kuleuven.be/wannes.meertReferencesT. K. Vintsyuk,
Speech discrimination by dynamic programming.
Kibernetika, 4:81–88, 1968.H. Sakoe and S. Chiba,
Dynamic programming algorithm optimization for spoken word recognition.
IEEE Transactions on Acoustics, Speech and Signal Processing, 26(1):43–49, 1978.C. S. Myers and L. R. Rabiner,
A comparative study of several dynamic time-warping algorithms for connected-word recognition.
The Bell System Technical Journal, 60(7):1389–1409, Sept 1981.Mueen, A and Keogh, E,Extracting Optimal Performance from Dynamic Time Warping,
Tutorial, KDD 2016D. F. Silva, G. E. A. P. A. Batista, and E. Keogh.On the effect of endpoints on dynamic time warping,
In SIGKDD Workshop on Mining and Learning from Time Series, II. Association for Computing Machinery-ACM, 2016.C. Yanping, K. Eamonn, H. Bing, B. Nurjahan, B. Anthony, M. Abdullah and B. Gustavo.The UCR Time Series Classification Archive, 2015.D. F. Silva and G. E. Batista.Speeding up all-pairwise dynamic time warping matrix calculation,
In Proceedings of the 2016 SIAM International Conference on Data Mining, pages 837–845. SIAM, 2016.LicenseDTAI distance code.

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