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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Autores principales: Giancarlo Sanchez, Erik Skau, Boian Alexandrov
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Publicado: IEEE 2021
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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
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