Time Series Distances
=====================

Library for time series distances (e.g. Dynamic Time Warping) used in
the `DTAI Research Group <https://dtai.cs.kuleuven.be>`__. The library
offers a pure Python implementation and a faster implementation in C.

Documentation: http://dtaidistance.readthedocs.io

Citing this work: |DOI|

Installation
------------

This packages is available on PyPI (requires Python 3):

::

   $ pip install dtaidistance

In case the C based version is not available, see the documentation for
alternative installation options. In case OpenMP is not available on
your system add the ``--noopenmp`` global option.

The source code is available at
`github.com/wannesm/dtaidistance <https://github.com/wannesm/dtaidistance>`__.

Usage
-----

Dynamic Time Warping (DTW) Distance Measure
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

::

   from 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")

.. figure:: https://people.cs.kuleuven.be/wannes.meert/dtw/dtw_example.png?v=4
   :alt: Dynamic Time Warping (DTW) Example

   Dynamic Time Warping (DTW) Example

DTW Distance Measure Between Two Series
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Only 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):

::

   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)

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)

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].

DTW Distance Measure all warping paths
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

If, 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 numpy as np
   x = np.arange(0, 20, .5)
   s1 = np.sin(x)
   s2 = np.sin(x - 1)
   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)

.. figure:: https://people.cs.kuleuven.be/wannes.meert/dtw/warping_paths.png?v=2
   :alt: DTW Example

   DTW Example

Notice the ``psi`` parameter 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 Series
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

To compute the DTW distance measures between all sequences in a list of
sequences, use the method ``dtw.distance_matrix``. You can set variables
to use more or less c code (``use_c`` and ``use_nogil``) and parallel or
serial execution (``parallel``).

The ``distance_matrix`` method 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 block
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

You 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]]   # 5

Clustering
----------

A distance matrix can be used for time series clustering. You can use
existing methods such as ``scipy.cluster.hierarchy.linkage`` or 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
(``HierarchicalTree`` or ``LinkageTree``), the tree can be visualised:

::

   model.plot("myplot.png")

.. figure:: https://people.cs.kuleuven.be/wannes.meert/dtw/hierarchy.png?v=2
   :alt: Dynamic Time Warping (DTW) hierarchical clusteringt

   Dynamic Time Warping (DTW) hierarchical clusteringt

Dependencies
------------

-  `Python 3 <http://www.python.org>`__
-  `Numpy <http://www.numpy.org>`__

Optional:

-  `Cython <http://cython.org>`__
-  `tqdm <https://github.com/tqdm/tqdm>`__
-  `matplotlib <https://matplotlib.org>`__

Development:

-  `pytest <http://doc.pytest.org>`__
-  `pytest-benchmark <http://pytest-benchmark.readthedocs.io>`__

Contact
-------

-  `Wannes Meert <https://people.cs.kuleuven.be/wannes.meert>`__
   <Wannes.Meert@cs.kuleuven.be>

References
----------

1. T. K. Vintsyuk, Speech discrimination by dynamic programming.
   Kibernetika, 4:81–88, 1968.
2. 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.
3. 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.
4. Mueen, A and Keogh, E, `Extracting Optimal Performance from Dynamic
   Time Warping <http://www.cs.unm.edu/~mueen/DTW.pdf>`__, Tutorial, KDD
   2016
5. D. F. Silva, G. E. A. P. A. Batista, and E. Keogh. `On the effect of
   endpoints on dynamic time
   warping <http://www-bcf.usc.edu/~liu32/milets16/paper/MiLeTS_2016_paper_7.pdf>`__,
   In SIGKDD Workshop on Mining and Learning from Time Series, II.
   Association for Computing Machinery-ACM, 2016.
6. C. Yanping, K. Eamonn, H. Bing, B. Nurjahan, B. Anthony, M. Abdullah
   and B. Gustavo. `The UCR Time Series Classification
   Archive <www.cs.ucr.edu/~eamonn/time_series_data/>`__, 2015.

License
-------

::

   DTAI distance code.

   Copyright 2016-2019 KU Leuven, DTAI Research Group

   Licensed under the Apache License, Version 2.0 (the "License");
   you may not use this file except in compliance with the License.
   You may obtain a copy of the License at

       http://www.apache.org/licenses/LICENSE-2.0

   Unless required by applicable law or agreed to in writing, software
   distributed under the License is distributed on an "AS IS" BASIS,
   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   See the License for the specific language governing permissions and
   limitations under the License.

.. |DOI| image:: https://zenodo.org/badge/80764246.svg
   :target: https://zenodo.org/badge/latestdoi/80764246
