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Entropy 2015, 17(6), 4173-4201;

Contribution to Transfer Entropy Estimation via the k-Nearest-Neighbors Approach

Institut National de la Santé Et de la Recherche Médicale (INSERM), U 1099, Rennes F-35000, France
Université de Rennes 1, LTSI, Rennes F-35000, France
Centre de Recherche en Information Biomédicale sino-français (CRIBs), Rennes F-35000, France
Laboratory of Image Science and Technology (LIST), School of Computer Science and Engineering, Southeast University, Nanjing 210018, China
Author to whom correspondence should be addressed.
Academic Editor: Deniz Gencaga
Received: 31 December 2014 / Accepted: 10 June 2015 / Published: 16 June 2015
(This article belongs to the Special Issue Transfer Entropy)
Full-Text   |   PDF [750 KB, uploaded 16 June 2015]


This paper deals with the estimation of transfer entropy based on the k-nearest neighbors (k-NN) method. To this end, we first investigate the estimation of Shannon entropy involving a rectangular neighboring region, as suggested in already existing literature, and develop two kinds of entropy estimators. Then, applying the widely-used error cancellation approach to these entropy estimators, we propose two novel transfer entropy estimators, implying no extra computational cost compared to existing similar k-NN algorithms. Experimental simulations allow the comparison of the new estimators with the transfer entropy estimator available in free toolboxes, corresponding to two different extensions to the transfer entropy estimation of the Kraskov–Stögbauer–Grassberger (KSG) mutual information estimator and prove the effectiveness of these new estimators. View Full-Text
Keywords: entropy estimation; k nearest neighbors; transfer entropy; bias reduction entropy estimation; k nearest neighbors; transfer entropy; bias reduction
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Zhu, J.; Bellanger, J.-J.; Shu, H.; Le Bouquin Jeannès, R. Contribution to Transfer Entropy Estimation via the k-Nearest-Neighbors Approach. Entropy 2015, 17, 4173-4201.

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