Abstract
This paper addresses the question of clustering density curves around a unit circle by approximating each such curve by a mixture of an appropriate number of von Mises distributions. This is done first by defining a distance between any two such curves either via \(L^2\) or a symmetrized Kullback–Leibler divergence. We show that both these measures yield similar results. After demonstrating via simulations that the proposed clustering methods work successfully, they are applied on an illustrative sample of Optical Coherence Tomography data.
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Notes
This algorithm and implementation describe fitting the parameters of von Mises-Fisher (vMF) mixture models, a direct higher-dimensional extension of the vM distribution with observations on the unit sphere/hypersphere. In two dimensions, this reduces to the vM distribution.
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Communicated by Ravi Khattree, Sreenivasa Rao Jammalamadaka, and M. B. Rao.
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This article is part of the topical collection “Celebrating the Centenary of Professor C. R. Rao” guest edited by Ravi Khattree, Sreenivasa Rao Jammalamadaka, and M. B. Rao.
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Jammalamadaka, S.R., Wainwright, B. & **, Q. Functional Clustering on a Circle Using von Mises Mixtures. J Stat Theory Pract 15, 38 (2021). https://doi.org/10.1007/s42519-021-00173-4
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DOI: https://doi.org/10.1007/s42519-021-00173-4
Keywords
- Circular curves
- Von mises (vM) distribution
- Mixtures of vM
- \(L^2\) Distance and symmetrized Kullback–Leibler
- Clustering curves
- Optical coherence tomography