Automatic Model Determination for Quaternion NMF

Nonnegative Matrix Factorization (NMF) is a well-known method for Blind Source Separation (BSS). Recently, BSS for polarized signals in spectropolarimetric data, containing both polarization and spectral information, was introduced. This information was encoded in 4-dimensional Stokes vectors repres...

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Main Authors:	Giancarlo Sanchez, Erik Skau, Boian Alexandrov
Format:	article
Language:	EN
Published:	IEEE 2021
Subjects:	Blind source separation model determination polarization quaternion NMF spectropolarimetric imaging Electrical engineering. Electronics. Nuclear engineering TK1-9971
Online Access:	https://doaj.org/article/531a2ddaf1c54bc7ad8b933b2127f1d0
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id	oai:doaj.org-article:531a2ddaf1c54bc7ad8b933b2127f1d0
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spelling	oai:doaj.org-article:531a2ddaf1c54bc7ad8b933b2127f1d02021-11-20T00:01:35ZAutomatic Model Determination for Quaternion NMF2169-353610.1109/ACCESS.2021.3120656https://doaj.org/article/531a2ddaf1c54bc7ad8b933b2127f1d02021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9576718/https://doaj.org/toc/2169-3536Nonnegative Matrix Factorization (NMF) is a well-known method for Blind Source Separation (BSS). Recently, BSS for polarized signals in spectropolarimetric data, containing both polarization and spectral information, was introduced. This information was encoded in 4-dimensional Stokes vectors represented by quaternion numbers. In the proposed Quaternion NMF (QNMF), the common challenge of determining the (usually) unknown number of quaternion signals remained unaddressed. Estimating the number of signals (aka model determination) is important, since an underestimation of this number results in poor source separation and omission of signals, while overestimation leads to extraction of noisy signals without physical meaning. Here, we introduce a method for determining the number of polarized signals in spectropolarimetric data, named QNMF<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>. QNMF<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> integrates: (a) Quaternion Alternating Direction Method of Multipliers (QADMM) implemented for QNMF, (b) random resampling of the initial quaternion data, and (c) custom clustering of sets of QADMM solutions with same number of sources, <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, needed to estimate the stability of the solutions. The appropriate latent dimension is determined based on the stability of the solutions. We demonstrate that, without any prior information, QNMF<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> accurately extracts the correct number of signals used to generate synthetic quaternion datasets and a benchmark spectropolarimetric data.Giancarlo SanchezErik SkauBoian AlexandrovIEEEarticleBlind source separationmodel determinationpolarizationquaternion NMFspectropolarimetric imagingElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 152243-152249 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Blind source separation model determination polarization quaternion NMF spectropolarimetric imaging Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Blind source separation model determination polarization quaternion NMF spectropolarimetric imaging Electrical engineering. Electronics. Nuclear engineering TK1-9971 Giancarlo Sanchez Erik Skau Boian Alexandrov Automatic Model Determination for Quaternion NMF
description	Nonnegative Matrix Factorization (NMF) is a well-known method for Blind Source Separation (BSS). Recently, BSS for polarized signals in spectropolarimetric data, containing both polarization and spectral information, was introduced. This information was encoded in 4-dimensional Stokes vectors represented by quaternion numbers. In the proposed Quaternion NMF (QNMF), the common challenge of determining the (usually) unknown number of quaternion signals remained unaddressed. Estimating the number of signals (aka model determination) is important, since an underestimation of this number results in poor source separation and omission of signals, while overestimation leads to extraction of noisy signals without physical meaning. Here, we introduce a method for determining the number of polarized signals in spectropolarimetric data, named QNMF<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>. QNMF<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> integrates: (a) Quaternion Alternating Direction Method of Multipliers (QADMM) implemented for QNMF, (b) random resampling of the initial quaternion data, and (c) custom clustering of sets of QADMM solutions with same number of sources, <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, needed to estimate the stability of the solutions. The appropriate latent dimension is determined based on the stability of the solutions. We demonstrate that, without any prior information, QNMF<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> accurately extracts the correct number of signals used to generate synthetic quaternion datasets and a benchmark spectropolarimetric data.
format	article
author	Giancarlo Sanchez Erik Skau Boian Alexandrov
author_facet	Giancarlo Sanchez Erik Skau Boian Alexandrov
author_sort	Giancarlo Sanchez
title	Automatic Model Determination for Quaternion NMF
title_short	Automatic Model Determination for Quaternion NMF
title_full	Automatic Model Determination for Quaternion NMF
title_fullStr	Automatic Model Determination for Quaternion NMF
title_full_unstemmed	Automatic Model Determination for Quaternion NMF
title_sort	automatic model determination for quaternion nmf
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/531a2ddaf1c54bc7ad8b933b2127f1d0
work_keys_str_mv	AT giancarlosanchez automaticmodeldeterminationforquaternionnmf AT erikskau automaticmodeldeterminationforquaternionnmf AT boianalexandrov automaticmodeldeterminationforquaternionnmf
_version_	1718419832106385408

Automatic Model Determination for Quaternion NMF

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