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Sparse density estimation on the multinomial manifold

Sparse density estimation on the multinomial manifold
Sparse density estimation on the multinomial manifold
A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators
2162-237X
2972-2977
Hong, Xia
e6551bb3-fbc0-4990-935e-43b706d8c679
Gao, Junbin
a3dcab84-9675-402c-a19e-d41ea9973f3a
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Zia, Tanveer
e04be2b8-f392-48f5-935d-acbf512a5d1c
Hong, Xia
e6551bb3-fbc0-4990-935e-43b706d8c679
Gao, Junbin
a3dcab84-9675-402c-a19e-d41ea9973f3a
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Zia, Tanveer
e04be2b8-f392-48f5-935d-acbf512a5d1c

Hong, Xia, Gao, Junbin, Chen, Sheng and Zia, Tanveer (2015) Sparse density estimation on the multinomial manifold. IEEE Transactions on Neural Networks and Learning Systems, 26 (11), 2972-2977. (doi:10.1109/TNNLS.2015.2389273).

Record type: Article

Abstract

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators

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Published date: November 2015
Organisations: Southampton Wireless Group

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Local EPrints ID: 383130
URI: https://eprints.soton.ac.uk/id/eprint/383130
ISSN: 2162-237X
PURE UUID: 2e76f9d9-0504-45af-9fa6-9b6c3bf04c12

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Date deposited: 06 Nov 2015 15:22
Last modified: 16 Nov 2017 17:33

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