Density estimation on Stiefel manifolds using matrix-Fisher model

Muhammad Ali, Michael Antolovich, Boyue Wang

Research output: Book chapter/Published conference paperConference paperpeer-review

Abstract

Our main focus in this paper is on the matrix-variate Fisher distribution for the product case of Stiefel manifolds and perform density estimation or classification via straightforward way of Maximum Likelihood Estimation (MLE) of parameter. The novelty of our proposed method is its strict dependency on normalisation constant appearing in parametric models, i.e., we have implemented our proposed matrix Fisher density function for classification with normalisation constant included in a more general context for Stiefel manifolds. An accurate way of calculating the log-likehood function of matrix based normalising constant and its practicability to matrix variate parametric modelling has been a big hurdle and is treated in this paper for classification on Stiefel manifolds. Instead of ad-hoc approximation of normalisation constant we have considered the method of Saddle Point Approximation (SPA). With the inclusion of calculated normalising constant with matrix-variate Fisher parametric model, the direct MLE with simple Bayesian approach for numerical experiments is employed for classification example using Synthetic and real World dataset, with promising accuracy.
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
Pages66-71
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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