Eberly College of Arts and Sciences
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.
Digital Commons Citation
Li, Shengqiao; Mnatsakanov, Robert M.; and Andrew, Michael E., "k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions" (2011). Faculty & Staff Scholarship. 2737.
Li, S., Mnatsakanov, R. M., & Andrew, M. E. (2011). k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions. Entropy, 13(3), 650–667. https://doi.org/10.3390/e13030650