Software Open Access

Transfer Entropy With Partitioning

Published: March 4, 2016. Version: 1.0.0

When using this resource, please cite the original publication:

Lee et al. Transfer Entropy Estimation and Directional Coupling Change Detection in Biomedical Time Series. Biomedical Engineering Online 2012 11:19.

Please include the standard citation for PhysioNet:

Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals (2003). Circulation. 101(23):e215-e220.


This is a repository of MATLAB functions that can estimate transfer entropy (information flow) from one time series to another using a non-parametric partitioning algorithm. Also included is an example data set that the implemented algorithms can be applied to.

The functions have been tested in MATLAB R2016b on 03 March 2016.



There are three functions used to calculate transfer entropy between time series using different methods of probability density estimation:

  • [T] = transferEntropyKDE(X,Y,t,w,N,bw_coeff)
    • Based on Guassian kernel density estimation.
    • Calls function mdKDE
  • [T nPar dimPar]=transferEntropyPartition(X,Y,t,w)
    • Based on the Darbellay-Vajda partitioning algorithm
    • Calls function DVpartition3D
  • [T] = transferEntropyRank(X,Y,l,k,t,w,Q)
    • Based on bin counting with fixed and equally-spaced bins.
    • Calls function quantentr

The MAT file 'example_data.mat' contains a 1-D structure array of example data that harnesses an information flow from X to Y at a lag of 2 according to: y(i)=[(1+a)*x(i-2)]^2
Different values of the coupling constant 'a' were simulated, along with associated levels of Laplacian noise given by SNR levels.

  • For a demonstration, run 'demoscript.m'. The plotted results should look like figure 1.
  • See the individual .m function files for information on how to call them.
  • See readme_example_data.txt for information on the example data parameters.
  • See Measuring Information Transfer, Physical Review Letters, 85(2):461-464, 2000 for more details on the methods.



This package was developed by J. Lee, S. Nemati, and I. Silvia.


Access Policy:
Anyone can access the files, as long as they conform to the terms of the specified license.

License (for files):
Open Data Commons Attribution License v1.0

Corresponding Author
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Total uncompressed size: 152.1 KB.

Folder Navigation: <base>
Name Size Modified
COPYING 34.3 KB 2019-04-12
DVpartition3D.m 3.7 KB 2019-04-12
demoresults.jpg 18.1 KB 2019-04-12
demoscript.m 606 B 2019-04-12
example_data.mat 84.4 KB 2019-04-12
mdKDE.m 1.6 KB 2019-04-12
quantentr.m 1.3 KB 2019-04-12
readme_example_data.txt 703 B 2019-04-12
transferEntropyKDE.m 2.5 KB 2019-04-12
transferEntropyPartition.m 2.4 KB 2019-04-12
transferEntropyRank.m 2.4 KB 2019-04-12