Recognition on Grassmann manifolds via parametric modelling

Muhammad Ali, Michael Antolovich, Boyue Wang

Research output: Book chapter/Published conference paperConference paper

Abstract

Applicability of the standard Maximum Likelihood Estimation technique for utilising parametric models to real World applications has been a real hurdle due to the difficult calculation of normalising constant since decades. The aim of this paper is therefore to fill some gape by demonstrating a simple Maximum Likelihood Estimation (MLE) technique for classification on Grassmann manifolds sing the matrix-variate Bingham distributional model. The most challenging task in working with such high dimensional parametric models is the calculation of matrix based normalising constant. For calculating the values of normalising constants we propose some ad-hoc technique for approximating the values of normalising constants. These normalising constants are mostly represented by special functions, e.g., Hypergeometric functions, Confluent Hypergeometric functions and Bessel functions etc. We have approximated these special functions by Taylor series approximation and asymptotic series approximation methods, i.e by considering the first few terms of the series most important for calculating the numerical values of normalising constant. The calculated numerical value then boost the applicability of matrix-variate Bingham model for inferences via a simple Bayesian approach. Although these ad-hoc techniques does not have close-form solutions, but still they can produce very nice results for special cases of concentrated parameters.
Original languageEnglish
Title of host publicationProceedings - 2016 9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI 2016)
EditorsYaoli Wang, Jiancheng An, Lipo Wang, Qingli Li, Gaowei Yan, Qing Chang
Place of PublicationUnited States
PublisherIEEE, Institute of Electrical and Electronics Engineers
Pages2014-2019
Number of pages6
ISBN (Electronic)9781509037100
DOIs
Publication statusPublished - 16 Feb 2017
Event9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics, CISP-BMEI 2016 - Datong, China
Duration: 15 Oct 201617 Oct 2016

Conference

Conference9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics, CISP-BMEI 2016
CountryChina
CityDatong
Period15/10/1617/10/16

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  • Cite this

    Ali, M., Antolovich, M., & Wang, B. (2017). Recognition on Grassmann manifolds via parametric modelling. In Y. Wang, J. An, L. Wang, Q. Li, G. Yan, & Q. Chang (Eds.), Proceedings - 2016 9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI 2016) (pp. 2014-2019). [7853050] IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CISP-BMEI.2016.7853050