{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T20:16:11Z","timestamp":1768680971789,"version":"3.49.0"},"reference-count":56,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,23]],"date-time":"2024-10-23T00:00:00Z","timestamp":1729641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12161020"],"award-info":[{"award-number":["12161020"]}]},{"name":"National Natural Science Foundation of China","award":["12061025"],"award-info":[{"award-number":["12061025"]}]},{"name":"National Natural Science Foundation of China","award":["61966006"],"award-info":[{"award-number":["61966006"]}]},{"name":"National Natural Science Foundation of China","award":["QKHJC-ZK[2024]YB528"],"award-info":[{"award-number":["QKHJC-ZK[2024]YB528"]}]},{"name":"National Natural Science Foundation of China","award":["QIANKEHEJICHU-ZK [2021] Key 038"],"award-info":[{"award-number":["QIANKEHEJICHU-ZK [2021] Key 038"]}]},{"name":"Guizhou Provincial Basis Research Program (Natural Science)","award":["12161020"],"award-info":[{"award-number":["12161020"]}]},{"name":"Guizhou Provincial Basis Research Program (Natural Science)","award":["12061025"],"award-info":[{"award-number":["12061025"]}]},{"name":"Guizhou Provincial Basis Research Program (Natural Science)","award":["61966006"],"award-info":[{"award-number":["61966006"]}]},{"name":"Guizhou Provincial Basis Research Program (Natural Science)","award":["QKHJC-ZK[2024]YB528"],"award-info":[{"award-number":["QKHJC-ZK[2024]YB528"]}]},{"name":"Guizhou Provincial Basis Research Program (Natural Science)","award":["QIANKEHEJICHU-ZK [2021] Key 038"],"award-info":[{"award-number":["QIANKEHEJICHU-ZK [2021] Key 038"]}]},{"name":"Guizhou Provincial Science and Technology Projects","award":["12161020"],"award-info":[{"award-number":["12161020"]}]},{"name":"Guizhou Provincial Science and Technology Projects","award":["12061025"],"award-info":[{"award-number":["12061025"]}]},{"name":"Guizhou Provincial Science and Technology Projects","award":["61966006"],"award-info":[{"award-number":["61966006"]}]},{"name":"Guizhou Provincial Science and Technology Projects","award":["QKHJC-ZK[2024]YB528"],"award-info":[{"award-number":["QKHJC-ZK[2024]YB528"]}]},{"name":"Guizhou Provincial Science and Technology Projects","award":["QIANKEHEJICHU-ZK [2021] Key 038"],"award-info":[{"award-number":["QIANKEHEJICHU-ZK [2021] Key 038"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The Nonnegative Matrix Factorization (NMF) algorithm and its variants have gained widespread popularity across various domains, including neural networks, text clustering, image processing, and signal analysis. In the context of hyperspectral unmixing (HU), an important task involving the accurate extraction of endmembers from mixed spectra, researchers have been actively exploring different regularization techniques within the traditional NMF framework. These techniques aim to improve the precision and reliability of the endmember extraction process in HU. In this study, we propose a novel HU algorithm called KMBNMF, which introduces an average kurtosis regularization term based on endmember spectra to enhance endmember extraction, additionally, it integrates a manifold regularization term into the average kurtosis-constrained NMF by constructing a symmetric weight matrix. This combination of these two regularization techniques not only optimizes the extraction process of independent endmembers but also improves the part-based representation capability of hyperspectral data. Experimental results obtained from simulated and real-world hyperspectral datasets demonstrate the competitive performance of the proposed KMBNMF algorithm when compared to state-of-the-art algorithms.<\/jats:p>","DOI":"10.3390\/sym16111414","type":"journal-article","created":{"date-parts":[[2024,10,23]],"date-time":"2024-10-23T09:07:04Z","timestamp":1729674424000},"page":"1414","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Non-Negative Matrix Factorization with Averaged Kurtosis and Manifold Constraints for Blind Hyperspectral Unmixing"],"prefix":"10.3390","volume":"16","author":[{"given":"Chunli","family":"Song","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China"},{"name":"Laboratory of Electrical Power Big Data of Guizhou Province, School of Big Data, Guizhou Institute of Technology, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linzhang","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China"},{"name":"School of Mathematical Sciences, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0726-8849","authenticated-orcid":false,"given":"Chengbin","family":"Zeng","sequence":"additional","affiliation":[{"name":"Department of Automation, Moutai Institute, Renhuai 564507, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1109\/TGRS.2005.844293","article-title":"A fast algorithm to unmix hyperspectral data","volume":"43","author":"Nascimento","year":"2005","journal-title":"IEEE Trans. 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