Nonconvex Nonseparable Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing
Hyperspectral unmixing is an important step to learn the material categories and corresponding distributions in a scene. Over the past decade, nonnegative matrix factorization (NMF) has been utilized for this task, thanks to its good physical interpretation. The solution space of NMF is very huge du...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9210778/ |
| _version_ | 1819150169841598464 |
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| author | Fengchao Xiong Jun Zhou Jianfeng Lu Yuntao Qian |
| author_facet | Fengchao Xiong Jun Zhou Jianfeng Lu Yuntao Qian |
| author_sort | Fengchao Xiong |
| collection | DOAJ |
| description | Hyperspectral unmixing is an important step to learn the material categories and corresponding distributions in a scene. Over the past decade, nonnegative matrix factorization (NMF) has been utilized for this task, thanks to its good physical interpretation. The solution space of NMF is very huge due to its nonconvex objective function for both variables simultaneously. Many convex and nonconvex sparse regularizations are embedded into NMF to limit the number of trivial solutions. Unfortunately, they either produce biased sparse solutions or unbiased sparse solutions with the sacrifice of the convex objective function of NMF with respect to individual variable. In this article, we enhance NMF by introducing a generalized minimax concave (GMC) sparse regularization. The GMC regularization is nonconvex and nonseparable, enabling promotion of unbiased and sparser results while simultaneously preserving the convexity of NMF for each variable separately. Therefore, GMC-NMF better avoids being trapped into local minimals, and thereby produce physically meaningful and accurate results. Extensive experimental results on synthetic data and real-world data verify its utility when compared with several state-of-the-art approaches. |
| first_indexed | 2024-12-22T14:13:14Z |
| format | Article |
| id | doaj.art-f20daaab4bcb49e2b781b3a2b6c8e936 |
| institution | Directory Open Access Journal |
| issn | 2151-1535 |
| language | English |
| last_indexed | 2024-12-22T14:13:14Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| spelling | doaj.art-f20daaab4bcb49e2b781b3a2b6c8e9362022-12-21T18:23:10ZengIEEEIEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing2151-15352020-01-01136088610010.1109/JSTARS.2020.30281049210778Nonconvex Nonseparable Sparse Nonnegative Matrix Factorization for Hyperspectral UnmixingFengchao Xiong0https://orcid.org/0000-0002-9753-4919Jun Zhou1https://orcid.org/0000-0001-5822-8233Jianfeng Lu2https://orcid.org/0000-0002-9190-507XYuntao Qian3https://orcid.org/0000-0002-7418-5891College of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, ChinaSchool of Information and Communication Technology, Griffith University, Nathan, QLD, AustraliaCollege of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, ChinaCollege of Computer Science, Zhejiang University, Hangzhou, ChinaHyperspectral unmixing is an important step to learn the material categories and corresponding distributions in a scene. Over the past decade, nonnegative matrix factorization (NMF) has been utilized for this task, thanks to its good physical interpretation. The solution space of NMF is very huge due to its nonconvex objective function for both variables simultaneously. Many convex and nonconvex sparse regularizations are embedded into NMF to limit the number of trivial solutions. Unfortunately, they either produce biased sparse solutions or unbiased sparse solutions with the sacrifice of the convex objective function of NMF with respect to individual variable. In this article, we enhance NMF by introducing a generalized minimax concave (GMC) sparse regularization. The GMC regularization is nonconvex and nonseparable, enabling promotion of unbiased and sparser results while simultaneously preserving the convexity of NMF for each variable separately. Therefore, GMC-NMF better avoids being trapped into local minimals, and thereby produce physically meaningful and accurate results. Extensive experimental results on synthetic data and real-world data verify its utility when compared with several state-of-the-art approaches.https://ieeexplore.ieee.org/document/9210778/Generalized minimax concave (GMC) regularizationhyperspectral unmixingnonnegative matrix factorization (NMF)sparse representation |
| spellingShingle | Fengchao Xiong Jun Zhou Jianfeng Lu Yuntao Qian Nonconvex Nonseparable Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing Generalized minimax concave (GMC) regularization hyperspectral unmixing nonnegative matrix factorization (NMF) sparse representation |
| title | Nonconvex Nonseparable Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing |
| title_full | Nonconvex Nonseparable Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing |
| title_fullStr | Nonconvex Nonseparable Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing |
| title_full_unstemmed | Nonconvex Nonseparable Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing |
| title_short | Nonconvex Nonseparable Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing |
| title_sort | nonconvex nonseparable sparse nonnegative matrix factorization for hyperspectral unmixing |
| topic | Generalized minimax concave (GMC) regularization hyperspectral unmixing nonnegative matrix factorization (NMF) sparse representation |
| url | https://ieeexplore.ieee.org/document/9210778/ |
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