Classification on Stiefel and Grassmann manifolds via maximum Likelihood estimation of matrix distributions

Ali, M; Gao, J; Antolovich, M

Classification on Stiefel and Grassmann manifolds via maximum Likelihood estimation of matrix distributions

Ali, M Gao, J Antolovich, M

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Publication Type:: Conference Proceeding
Citation:: Proceedings of the International Joint Conference on Neural Networks, 2016, 2016-October pp. 3751 - 3757
Issue Date:: 2016-10-31

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Field	Value	Language
dc.contributor.author	Ali, M	en_US
dc.contributor.author	Gao, J	en_US
dc.contributor.author	Antolovich, M https://orcid.org/0000-0003-2601-8332	en_US
dc.date.issued	2016-10-31	en_US
dc.identifier.citation	Proceedings of the International Joint Conference on Neural Networks, 2016, 2016-October pp. 3751 - 3757	en_US
dc.identifier.isbn	9781509006199	en_US
dc.identifier.uri	http://hdl.handle.net/10453/98471
dc.description.abstract	© 2016 IEEE. Matrix manifolds such as Stiefel and Grassmann manifolds have been widely used in modern computer vision. This paper is concerned with the problem of classifying such manifold-valued data, based on the maximum likelihood estimation for the parametric probability density functions defined on the manifolds. By using a new way of computing normalisation constants for the matrix Langevin distribution function, defined for the data on Stiefel manifold, and the Fisher-Bingham density function on Grassmann manifold, we proposed a simple way to estimate the parameters in the distribution and demonstrated on real world datasets that the proposed method is efficient and more accurate. Our method uses asymptotic and Taylor series approximations, with good accuracy estimate.	en_US
dc.relation.ispartof	Proceedings of the International Joint Conference on Neural Networks	en_US
dc.relation.isbasedon	10.1109/IJCNN.2016.7727683	en_US
dc.title	Classification on Stiefel and Grassmann manifolds via maximum Likelihood estimation of matrix distributions	en_US
dc.type	Conference Proceeding
utslib.citation.volume	2016-October	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US
pubs.volume	2016-October	en_US

Abstract:

© 2016 IEEE. Matrix manifolds such as Stiefel and Grassmann manifolds have been widely used in modern computer vision. This paper is concerned with the problem of classifying such manifold-valued data, based on the maximum likelihood estimation for the parametric probability density functions defined on the manifolds. By using a new way of computing normalisation constants for the matrix Langevin distribution function, defined for the data on Stiefel manifold, and the Fisher-Bingham density function on Grassmann manifold, we proposed a simple way to estimate the parameters in the distribution and demonstrated on real world datasets that the proposed method is efficient and more accurate. Our method uses asymptotic and Taylor series approximations, with good accuracy estimate.

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http://hdl.handle.net/10453/98471