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A Wasserstein Subsequence Kernel for Time Series.
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Wasserstein Time Series Kernel

A preprint version of the paper accepted at ICDM 2019 can be found here.


WTK relies on the following dependencies:

  • numpy
  • scikit-learn
  • POT
  • cython


The easiest way is to install WTK from the Python Package Index (PyPI) via

$ pip install cython numpy wtk


The package provides functions to transform a set of n training time series and o test time series into an n x n distance matrix for training and an o x n distance matrix for testing. Additionally, we provide a way to run a grid search for a krein space SVM. krein_svm_grid_search runs a 5-fold cross-validation on the training set to determine the best hyperparameters. Then, its classification accuracy is computed on the test set.

from wtk import transform_to_dist_matrix
from wtk.utilities import get_ucr_dataset, krein_svm_grid_search

# Read UCR data
X_train, y_train, X_test, y_test = get_ucr_dataset('../data/UCR/raw_data/', 'DistalPhalanxTW')

# Compute wasserstein distance matrices with subsequence length k=10
D_train, D_test = transform_to_dist_matrix(X_train, X_test, 10)

# Run the grid search
svm_clf = krein_svm_grid_search(D_train, D_test, y_train, y_test)

Alternatively, you can get the kernel matrices computed from the distance matrices and train your own classifier.

from sklearn.svm import SVC
from wtk import get_kernel_matrix
from sklearn.metrics import accuracy_score
from sklearn.svm import SVC

# Get the kernel matrices
K_train = get_kernel_matrix(D_train, psd=True, gamma=0.2)
K_test = get_kernel_matrix(D_test, psd=False, gamma=0.2)

# Train your classifier
clf = SVC(C=5, kernel='precomputed'), y_train)

y_pred = clf.predict(K_test)
print(accuracy_score(y_test, y_pred))


You can find some simple examples on our examples page and an examples jupyter notebook. In case the notebook cannot be rendered, please visit it on nbviewer.


If you have questions concerning WTK or you encounter problems when trying to build the tool under your own system, please open an issue in the issue tracker. Try to describe the issue in sufficient detail in order to make it possible for us to help you.


WTK is developed and maintained by members of the Machine Learning and Computational Biology Lab:


Please use the following BibTeX citation when using our method or comparing to it:

  author    = {Bock, Christian and Togninalli, Matteo and Ghisu, Elisabetta and Gumbsch, Thomas and Rieck, Bastian and Borgwardt, Karsten},
  title     = {A Wasserstein Subsequence Kernel for Time Series},
  booktitle = {Proceedings of the 19th IEEE International Conference on Data Mining~(ICDM)},
  year      = {2019},
  pubstate  = {inpress},
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