Estimating the square root of probability density function on Riemannian manifold

Hong, X. ORCID: https://orcid.org/0000-0002-6832-2298 and Gao, J. (2021) Estimating the square root of probability density function on Riemannian manifold. Expert Systems: International Journal of Knowledge Engineering, 38 (7). e12266. ISSN 1468-0394 doi: 10.1111/exsy.12266

Abstract/Summary

We propose that the square root of a probability density function can be represented as a linear combination of Gaussian kernels. It is shown that if the Gaussian kernel centres and kernel width are known, then the maximum likelihood parameter estimator can be formulated as a Riemannian optimisation problem on sphere manifold. The first order Riemannian geometry of the sphere manifold and vector transport are initially explored, then the well-known Riemannian conjugate gradient algorithm is used to estimate the model parameters. For completeness, the k-means clustering algorithm and a grid search are employed to determine the centres and kernel width, respectively. Simulated examples are employed to demonstrate that the proposed approach is effective in constructing the estimate of the square root of probability density function.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/75374
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
Uncontrolled Keywords	Control and Systems Engineering, Theoretical Computer Science, Computational Theory and Mathematics, Artificial Intelligence
Publisher	Wiley
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