Parameter Estimation in Spherical Symmetry Groups
| Autor: | Dennis Wei, Marc DeGraef, Jeff Simmons, Yu-Hui Chen, Gregory E. Newstadt, Alfred O. Hero |
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| Rok vydání: | 2015 |
| Předmět: |
FOS: Computer and information sciences
Estimation theory Applied Mathematics Mathematical analysis Estimator Machine Learning (stat.ML) 020206 networking & telecommunications 02 engineering and technology 01 natural sciences 010104 statistics & probability Statistics - Machine Learning Symmetric group Signal Processing Expectation–maximization algorithm 0202 electrical engineering electronic engineering information engineering Probability distribution Circular symmetry 0101 mathematics Electrical and Electronic Engineering Invariant (mathematics) Random variable Mathematics |
| Zdroj: | IEEE Signal Processing Letters. 22:1152-1155 |
| ISSN: | 1558-2361 1070-9908 |
| Popis: | This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of distributions over the sphere that are invariant to the actions of a finite spherical symmetry group $\mathcal G$, a group-invariant extension of the Von Mises Fisher (VMF) distribution is obtained. The $\mathcal G$-invariant VMF is parameterized by location and scale parameters that specify the distribution's mean orientation and its concentration about the mean, respectively. Using the restricted finite mixture representation these parameters can be estimated using an Expectation Maximization (EM) maximum likelihood (ML) estimation algorithm. This is illustrated for the problem of mean crystal orientation estimation under the spherically symmetric group associated with the crystal form, e.g., cubic or octahedral or hexahedral. Simulations and experiments establish the advantages of the extended VMF EM-ML estimator for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample. Comment: 4 pages, 1 page with only references and 1 page for appendices. Accepted to be published in Signal Processing Letters |
| Databáze: | OpenAIRE |
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