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Entropy 2011, 13(3), 650-667; doi:10.3390/e13030650
Article

k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions

1,* , 1,2,*  and 1
Received: 22 December 2010; in revised form: 27 January 2011 / Accepted: 28 February 2011 / Published: 8 March 2011
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Abstract: A consistent entropy estimator for hyperspherical data is proposed based on the k-nearest neighbor (knn) approach. The asymptotic unbiasedness and consistency of the estimator are proved. Moreover, cross entropy and Kullback-Leibler (KL) divergence estimators are also discussed. Simulation studies are conducted to assess the performance of the estimators for models including uniform and von Mises-Fisher distributions. The proposed knn entropy estimator is compared with the moment based counterpart via simulations. The results show that these two methods are comparable.
Keywords: hyperspherical distribution; directional data; differential entropy; cross entropy; Kullback-Leibler divergence; k-nearest neighbor hyperspherical distribution; directional data; differential entropy; cross entropy; Kullback-Leibler divergence; k-nearest neighbor
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.

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MDPI and ACS Style

Li, S.; Mnatsakanov, R.M.; Andrew, M.E. k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions. Entropy 2011, 13, 650-667.

AMA Style

Li S, Mnatsakanov RM, Andrew ME. k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions. Entropy. 2011; 13(3):650-667.

Chicago/Turabian Style

Li, Shengqiao; Mnatsakanov, Robert M.; Andrew, Michael E. 2011. "k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions." Entropy 13, no. 3: 650-667.


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