{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:43:35Z","timestamp":1740120215301,"version":"3.37.3"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["U1501251","61333013"],"award-info":[{"award-number":["U1501251","61333013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Pearl River S and T Nova Program of Guangzhou","award":["201610010196"],"award-info":[{"award-number":["201610010196"]}]},{"name":"the Guangdong Natural Science Funds for Distinguished Young Scholar","award":["2014A030306037"],"award-info":[{"award-number":["2014A030306037"]}]},{"name":"the Program for New Century Excellent Talents in University","award":["NCET-13-0740"],"award-info":[{"award-number":["NCET-13-0740"]}]},{"name":"the Guangdong program for support of top-notch young professionals","award":["2014TQ01X144"],"award-info":[{"award-number":["2014TQ01X144"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Patt. Recogn. Artif. Intell."],"published-print":{"date-parts":[[2017,9]]},"abstract":"<jats:p> With the development of the detection technology using multispectra sensors, spectral decomposition (SD) attracts more and more attention in the biomedical signal processing and image processing. In this paper, a local smoothness constrained nonnegative matrix factorization (NMF) with nonlinear convergence rate (NMF-NCR) is proposed to solve SD problem and our contributions are as follows. First, it proves that the gradients of the cost function with respect to each variable matrix are Lipschitz continuous. Then, a proximal function is constructed for optimizing the cost function. As a result, our method can achieve an NCR much faster than the traditional methods. Simulations show the advantage in solving SD of our algorithm over the compared methods. <\/jats:p>","DOI":"10.1142\/s0218001417500306","type":"journal-article","created":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T02:01:27Z","timestamp":1487296887000},"page":"1750030","source":"Crossref","is-referenced-by-count":2,"title":["Local Smoothness Constrained Nonnegative Matrix Factorization with Nonlinear Convergence Rate for Spectral Decomposition"],"prefix":"10.1142","volume":"31","author":[{"given":"Kan","family":"Xie","sequence":"first","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangdong Key Laboratory of IoT Information Technology, Guangzhou, 510006, P. R. China"}]},{"given":"Yue","family":"Lai","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangdong Key Laboratory of IoT Information Technology, Guangzhou, 510006, P. R. China"}]},{"given":"Sihui","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangdong Key Laboratory of IoT Information Technology, Guangzhou, 510006, P. R. China"}]},{"given":"Jie","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangdong Key Laboratory of IoT Information Technology, Guangzhou, 510006, P. R. 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