Block-Active ADMM to Minimize NMF with Bregman Divergences
Over the last ten years, there has been a significant interest in employing <i>nonnegative matrix factorization</i> (NMF) to reduce dimensionality to enable a more efficient clustering analysis in machine learning. This technique has been applied in various image processing applications...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/23/16/7229 |
| _version_ | 1797583245618970624 |
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| author | Xinyao Li Akhilesh Tyagi |
| author_facet | Xinyao Li Akhilesh Tyagi |
| author_sort | Xinyao Li |
| collection | DOAJ |
| description | Over the last ten years, there has been a significant interest in employing <i>nonnegative matrix factorization</i> (NMF) to reduce dimensionality to enable a more efficient clustering analysis in machine learning. This technique has been applied in various image processing applications within the fields of computer vision and sensor-based systems. Many algorithms exist to solve the NMF problem. Among these algorithms, the <i>alternating direction method of multipliers</i> (ADMM) and its variants are one of the most popular methods used in practice. In this paper, we propose a block-active ADMM method to minimize the NMF problem with general Bregman divergences. The subproblems in the ADMM are solved iteratively by a <i>block-coordinate-descent-type</i> (BCD-type) method. In particular, each block is chosen directly based on the <i>stationary condition</i>. As a result, we are able to use much fewer auxiliary variables and the proposed algorithm converges faster than the previously proposed algorithms. From the theoretical point of view, the proposed algorithm is proved to converge to a stationary point sublinearly. We also conduct a series of numerical experiments to demonstrate the superiority of the proposed algorithm. |
| first_indexed | 2024-03-10T23:36:08Z |
| format | Article |
| id | doaj.art-e8da67166aa64104b72ce5ea7998a24f |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T23:36:08Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-e8da67166aa64104b72ce5ea7998a24f2023-11-19T02:58:37ZengMDPI AGSensors1424-82202023-08-012316722910.3390/s23167229Block-Active ADMM to Minimize NMF with Bregman DivergencesXinyao Li0Akhilesh Tyagi1Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50010, USADepartment of Electrical and Computer Engineering, Iowa State University, Ames, IA 50010, USAOver the last ten years, there has been a significant interest in employing <i>nonnegative matrix factorization</i> (NMF) to reduce dimensionality to enable a more efficient clustering analysis in machine learning. This technique has been applied in various image processing applications within the fields of computer vision and sensor-based systems. Many algorithms exist to solve the NMF problem. Among these algorithms, the <i>alternating direction method of multipliers</i> (ADMM) and its variants are one of the most popular methods used in practice. In this paper, we propose a block-active ADMM method to minimize the NMF problem with general Bregman divergences. The subproblems in the ADMM are solved iteratively by a <i>block-coordinate-descent-type</i> (BCD-type) method. In particular, each block is chosen directly based on the <i>stationary condition</i>. As a result, we are able to use much fewer auxiliary variables and the proposed algorithm converges faster than the previously proposed algorithms. From the theoretical point of view, the proposed algorithm is proved to converge to a stationary point sublinearly. We also conduct a series of numerical experiments to demonstrate the superiority of the proposed algorithm.https://www.mdpi.com/1424-8220/23/16/7229NMFADMMBregman divergenceblock activeimaging sensor |
| spellingShingle | Xinyao Li Akhilesh Tyagi Block-Active ADMM to Minimize NMF with Bregman Divergences Sensors NMF ADMM Bregman divergence block active imaging sensor |
| title | Block-Active ADMM to Minimize NMF with Bregman Divergences |
| title_full | Block-Active ADMM to Minimize NMF with Bregman Divergences |
| title_fullStr | Block-Active ADMM to Minimize NMF with Bregman Divergences |
| title_full_unstemmed | Block-Active ADMM to Minimize NMF with Bregman Divergences |
| title_short | Block-Active ADMM to Minimize NMF with Bregman Divergences |
| title_sort | block active admm to minimize nmf with bregman divergences |
| topic | NMF ADMM Bregman divergence block active imaging sensor |
| url | https://www.mdpi.com/1424-8220/23/16/7229 |
| work_keys_str_mv | AT xinyaoli blockactiveadmmtominimizenmfwithbregmandivergences AT akhileshtyagi blockactiveadmmtominimizenmfwithbregmandivergences |