{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:40:52Z","timestamp":1740156052932,"version":"3.37.3"},"reference-count":22,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,17]],"date-time":"2020-07-17T00:00:00Z","timestamp":1594944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grants 61773127 and 61727810"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ten Thousand Talent Program","award":["approved in 2018"]},{"name":"Guangdong Province Foundation","award":["Grant 2019B1515120036"]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["Grant 2018A030313306"],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010256","name":"Guangzhou Science and Technology Foundation","doi-asserted-by":"publisher","award":["Grant 201802010037"],"id":[{"id":"10.13039\/501100010256","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Areas of Research and Development Plan Project of Guangdong","award":["Grant 2019B010147001"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"Symmetric nonnegative matrix factorization (SNMF) approximates a symmetric nonnegative matrix by the product of a nonnegative low-rank matrix and its transpose. SNMF has been successfully used in many real-world applications such as clustering. In this paper, we propose an accelerated variant of the multiplicative update (MU) algorithm of He et al. designed to solve the SNMF problem. The accelerated algorithm is derived by using the extrapolation scheme of Nesterov and a restart strategy. The extrapolation scheme plays a leading role in accelerating the MU algorithm of He et al. and the restart strategy ensures that the objective function of SNMF is monotonically decreasing. We apply the accelerated algorithm to clustering problems and symmetric nonnegative tensor factorization (SNTF). The experiment results on both synthetic and real-world data show that it is more than four times faster than the MU algorithm of He et al. and performs favorably compared to recent state-of-the-art algorithms.<\/jats:p>","DOI":"10.3390\/sym12071187","type":"journal-article","created":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T09:10:30Z","timestamp":1595409030000},"page":"1187","source":"Crossref","is-referenced-by-count":2,"title":["An Accelerated Symmetric Nonnegative Matrix Factorization Algorithm Using Extrapolation"],"prefix":"10.3390","volume":"12","author":[{"given":"Peitao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"},{"name":"Guangdong Key Laboratory of IoT Information Technology, Guangzhou 510006, China"}]},{"given":"Zhaoshui","family":"He","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"},{"name":"Guangdong Key Laboratory of IoT Information Technology, Guangzhou 510006, China"}]},{"given":"Jun","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"},{"name":"Guangdong Key Laboratory of IoT Information Technology, Guangzhou 510006, China"},{"name":"Peng Cheng Laboratory, Shenzhen 518055, China"}]},{"given":"Beihai","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"},{"name":"Guangdong Key Laboratory of IoT Information Technology, Guangzhou 510006, China"}]},{"given":"YuLei","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"},{"name":"Guangdong Key Laboratory of IoT Information Technology, Guangzhou 510006, China"}]},{"given":"Ji","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"},{"name":"Guangdong Key Laboratory of IoT Information Technology, Guangzhou 510006, China"}]},{"given":"Taiheng","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"},{"name":"Guangdong Key Laboratory of IoT Information Technology, Guangzhou 510006, China"}]},{"given":"Zhijie","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"},{"name":"Guangdong Key Laboratory of IoT Information Technology, Guangzhou 510006, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,17]]},"reference":[{"unstructured":"Cichocki, A., Jankovic, M., Zdunek, R., and Amari, S.I. (2007, January 13\u201316). Sparse super symmetric tensor factorization. Proceedings of the 2007 International Conference on Neural Information Processing (ICONIP), Kitakyushu, Japan.","key":"ref_1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3120","DOI":"10.1109\/TSP.2017.2679687","article-title":"A nonconvex splitting method for symmetric nonnegative matrix factorization: Convergence analysis and optimality","volume":"65","author":"Lu","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"doi-asserted-by":"crossref","unstructured":"Gao, T., Olofsson, S., and Lu, S. (2016, January 7\u20139). Minimum-volume-regularized weighted symmetric nonnegative matrix factorization for clustering. Proceedings of the 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Washington, DC, USA.","key":"ref_3","DOI":"10.1109\/GlobalSIP.2016.7905841"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"037113","DOI":"10.1063\/1.4914912","article-title":"Considerations on double porosity structure for micropolar bodies","volume":"5","author":"Marin","year":"2015","journal-title":"Aip Adv."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.ymeth.2016.06.017","article-title":"Hessian regularization based symmetric nonnegative matrix factorization for clustering gene expression and microbiome data","volume":"111","author":"Ma","year":"2016","journal-title":"Methods"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2117","DOI":"10.1109\/TNN.2011.2172457","article-title":"Symmetric Nonnegative Matrix Factorization: Algorithms and Applications to Probabilistic Clustering","volume":"22","author":"He","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5571","DOI":"10.1109\/TSP.2016.2591510","article-title":"Efficient and Non-Convex Coordinate Descent for Symmetric Nonnegative Matrix Factorization","volume":"64","author":"Vandaele","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5995","DOI":"10.1109\/TSP.2017.2731321","article-title":"Inexact Block Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization","volume":"65","author":"Shi","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"doi-asserted-by":"crossref","unstructured":"Zass, R., and Shashua, A. (2005, January 17\u201320). A unifying approach to hard and probabilistic clustering. Proceedings of the 2005 International Conference on Computer Vision (ICCV), Beijing, China.","key":"ref_9","DOI":"10.1109\/ICCV.2005.27"},{"doi-asserted-by":"crossref","unstructured":"Kuang, D., Ding, C., and Park, H. (2012, January 26\u201328). Symmetric Nonnegative Matrix Factorization for Graph Clustering. Proceedings of the 2012 SIAM International Conference on Data Mining (SDM), Anaheim, CA, USA.","key":"ref_10","DOI":"10.1137\/1.9781611972825.10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/s10898-014-0247-2","article-title":"SymNMF: Nonnegative Low-Rank Approximation of a Similarity Matrix for Graph Clustering","volume":"62","author":"Kuang","year":"2015","journal-title":"J. Glob. Optim."},{"doi-asserted-by":"crossref","unstructured":"Lu, S., and Wang, Z. (2015, January 8\u201311). Accelerated algorithms for eigen-value decomposition with application to spectral clustering. Proceedings of the 2015 Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, CA, USA.","key":"ref_12","DOI":"10.1109\/ACSSC.2015.7421146"},{"unstructured":"Bo, L., Zhang, Z., Wu, X., and Yu, P.S. (2007, January 20\u201324). Relational clustering by symmetric convex coding. Proceedings of the 2007 International Conference on Machine Learning (ICML), Corvallis, OR, USA.","key":"ref_13"},{"doi-asserted-by":"crossref","unstructured":"Long, B., Zhang, Z., and Yu, P. (2005, January 21\u201324). Co-clustering by block value decomposition. Proceedings of the 2005 SIGKDD Conference on Knowledge Discovery and Data Mining (SIGKDD), Chicago, IL, USA.","key":"ref_14","DOI":"10.1145\/1081870.1081949"},{"key":"ref_15","first-page":"372","article-title":"A method of solving a convex programming problem with convergence rate O(1\/k2)","volume":"27","author":"Nesterov","year":"1983","journal-title":"Sov. Math. Dokl."},{"unstructured":"Sutskever, I., Martens, J., Dahl, G., and Hinton, G. (2013, January 16\u201321). On the importance of initialization and momentum in deep learning. Proceedings of the 2013 International Conference on Machine Learning (ICML), Atlanta Marriott Marquis, Atlanta, GA, USA.","key":"ref_16"},{"doi-asserted-by":"crossref","unstructured":"Botev, A., Lever, G., and Barber, D. (2017, January 14\u201319). Nesterov\u2019s accelerated gradient and momentum as approximations to regularised update descent. Proceedings of the 2017 International Joint Conference on Neural Networks (IJCNN), Anchorage, AK, USA.","key":"ref_17","DOI":"10.1109\/IJCNN.2017.7966082"},{"key":"ref_18","first-page":"3","article-title":"Informational complexity and efficient methods for the solution of convex extremal problems","volume":"13","author":"Yudin","year":"1976","journal-title":"Matekon"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6348","DOI":"10.1109\/TNNLS.2018.2830761","article-title":"Pairwise Constraint Propagation-Induced Symmetric Nonnegative Matrix Factorization","volume":"29","author":"Wu","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1162\/neco_a_01157","article-title":"Accelerating nonnegative matrix factorization algorithms using extrapolation","volume":"31","author":"Ang","year":"2019","journal-title":"Neural Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1624","DOI":"10.1109\/TKDE.2005.198","article-title":"Document clustering using locality preserving indexing","volume":"17","author":"Cai","year":"2005","journal-title":"IEEE Trans. Knowl. Data Eng."},{"unstructured":"Zelnik-Manor, L., and Perona, P. (2004, January 13\u201318). Self-Tuning Spectral Clustering. 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