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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
Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, WV 26505, USA
2
Department of Statistics, West Virginia University, Morgantown, WV 26506, USA
* Authors to whom correspondence should be addressed.
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
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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 StyleLi S, Mnatsakanov RM, Andrew ME. k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions. Entropy. 2011; 13(3):650-667.
Chicago/Turabian StyleLi, Shengqiao; Mnatsakanov, Robert M.; Andrew, Michael E. 2011. "k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions." Entropy 13, no. 3: 650-667.