k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions
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 a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2011-03-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/13/3/650/ |
| _version_ | 1818013112342675456 |
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| author | Michael E. Andrew Shengqiao Li Robert M. Mnatsakanov |
| author_facet | Michael E. Andrew Shengqiao Li Robert M. Mnatsakanov |
| author_sort | Michael E. Andrew |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T06:28:20Z |
| format | Article |
| id | doaj.art-d289111d042244f39f23b52adfd8584a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T06:28:20Z |
| publishDate | 2011-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d289111d042244f39f23b52adfd8584a2022-12-22T02:07:42ZengMDPI AGEntropy1099-43002011-03-0113365066710.3390/e13030650k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical DistributionsMichael E. AndrewShengqiao LiRobert M. MnatsakanovA 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.http://www.mdpi.com/1099-4300/13/3/650/hyperspherical distributiondirectional datadifferential entropycross entropyKullback-Leibler divergencek-nearest neighbor |
| spellingShingle | Michael E. Andrew Shengqiao Li Robert M. Mnatsakanov k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions Entropy hyperspherical distribution directional data differential entropy cross entropy Kullback-Leibler divergence k-nearest neighbor |
| title | k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions |
| title_full | k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions |
| title_fullStr | k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions |
| title_full_unstemmed | k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions |
| title_short | k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions |
| title_sort | k nearest neighbor based consistent entropy estimation for hyperspherical distributions |
| topic | hyperspherical distribution directional data differential entropy cross entropy Kullback-Leibler divergence k-nearest neighbor |
| url | http://www.mdpi.com/1099-4300/13/3/650/ |
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