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Sparse density estimation on the multinomial manifold

Hong, X., Gao, J., Chen, S. and Zia, T. (2015) Sparse density estimation on the multinomial manifold. IEEE Transactions on Neural Networks and Learning Systems, 26 (11). pp. 2972-2977. ISSN 2162-237X

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To link to this item DOI: 10.1109/TNNLS.2015.2389273


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.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
ID Code:39718
Uncontrolled Keywords:Minimum integrated square error (MISE), multinomial manifold, probability density function (pdf), sparse modeling.
Publisher:IEEE Computational Intelligence Society
Publisher Statement:© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.


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