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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| Format: | Article |
| Language: | English |
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IEEE
2021-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9576718/ |
| _version_ | 1818479639823122432 |
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| author | Giancarlo Sanchez Erik Skau Boian Alexandrov |
| author_facet | Giancarlo Sanchez Erik Skau Boian Alexandrov |
| author_sort | Giancarlo Sanchez |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-10T11:13:26Z |
| format | Article |
| id | doaj.art-531a2ddaf1c54bc7ad8b933b2127f1d0 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-10T11:13:26Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-531a2ddaf1c54bc7ad8b933b2127f1d02022-12-22T01:51:19ZengIEEEIEEE Access2169-35362021-01-01915224315224910.1109/ACCESS.2021.31206569576718Automatic Model Determination for Quaternion NMFGiancarlo Sanchez0https://orcid.org/0000-0002-8088-1391Erik Skau1Boian Alexandrov2https://orcid.org/0000-0001-8636-4603Department of Mathematics and Statistics, Florida International University, Miami, FL, USALos Alamos National Laboratory, Los Alamos, NM, USALos Alamos National Laboratory, Los Alamos, NM, USANonnegative 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.https://ieeexplore.ieee.org/document/9576718/Blind source separationmodel determinationpolarizationquaternion NMFspectropolarimetric imaging |
| spellingShingle | Giancarlo Sanchez Erik Skau Boian Alexandrov Automatic Model Determination for Quaternion NMF IEEE Access Blind source separation model determination polarization quaternion NMF spectropolarimetric imaging |
| title | 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_short | Automatic Model Determination for Quaternion NMF |
| title_sort | automatic model determination for quaternion nmf |
| topic | Blind source separation model determination polarization quaternion NMF spectropolarimetric imaging |
| url | https://ieeexplore.ieee.org/document/9576718/ |
| work_keys_str_mv | AT giancarlosanchez automaticmodeldeterminationforquaternionnmf AT erikskau automaticmodeldeterminationforquaternionnmf AT boianalexandrov automaticmodeldeterminationforquaternionnmf |