{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:34:03Z","timestamp":1750221243368,"version":"3.41.0"},"reference-count":47,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T00:00:00Z","timestamp":1541030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Program for Science and Technology Innovation Talents in Universities of Henan Province","award":["19HASTIT026"],"award-info":[{"award-number":["19HASTIT026"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61871470, 61761130079, U1604153 and 61301230"],"award-info":[{"award-number":["61871470, 61761130079, U1604153 and 61301230"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Key Research and Development Program of China","award":["2018YFB1107400"],"award-info":[{"award-number":["2018YFB1107400"]}]},{"name":"Training Program for the Young-Backbone Teachers in Universities of Henan Province","award":["2017GGJS065"],"award-info":[{"award-number":["2017GGJS065"]}]},{"name":"Key Research Program of Frontier Sciences, CAS","award":["QYZDY-SSW-JSC044"],"award-info":[{"award-number":["QYZDY-SSW-JSC044"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Intell. Syst. Technol."],"published-print":{"date-parts":[[2018,11,30]]},"abstract":"<jats:p>Nonnegative matrix factorization (NMF) is one widely used feature extraction technology in the tasks of image clustering and image classification. For the former task, various unsupervised NMF methods based on the data distribution structure information have been proposed. While for the latter task, the label information of the dataset is one very important guiding. However, most previous proposed supervised NMF methods emphasis on imposing the discriminant constraints on the coefficient matrix. When dealing with new coming samples, the transpose or the pseudoinverse of the basis matrix is used to project these samples to the low dimension space. In this way, the label influence to the basis matrix is indirect. Although, there are also some methods trying to constrain the basis matrix in NMF framework, either they only restrict within-class samples or impose improper constraint on the basis matrix. To address these problems, in this article a novel NMF framework named discriminative and orthogonal subspace constraints-based nonnegative matrix factorization (DOSNMF) is proposed. In DOSNMF, the discriminative constraints are imposed on the projected subspace instead of the directly learned representation. In this manner, the discriminative information is directly connected with the projected subspace. At the same time, an orthogonal term is incorporated in DOSNMF to adjust the orthogonality of the learned basis matrix, which can ensure the orthogonality of the learned subspace and improve the sparseness of the basis matrix at the same time. This framework can be implemented in two ways. The first way is based on the manifold learning theory. In this way, two graphs, i.e., the intrinsic graph and the penalty graph, are constructed to capture the intra-class structure and the inter-class distinctness. With this design, both the manifold structure information and the discriminative information of the dataset are utilized. For convenience, we name this method as the name of the framework, i.e., DOSNMF. The second way is based on the Fisher\u2019s criterion, we name it Fisher\u2019s criterion-based DOSNMF (FDOSNMF). The objective functions of DOSNMF and FDOSNMF can be easily optimized using multiplicative update (MU) rules. The new methods are tested on five datasets and compared with several supervised and unsupervised variants of NMF. The experimental results reveal the effectiveness of the proposed methods.<\/jats:p>","DOI":"10.1145\/3229051","type":"journal-article","created":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T12:18:14Z","timestamp":1541074694000},"page":"1-24","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Discriminative and Orthogonal Subspace Constraints-Based Nonnegative Matrix Factorization"],"prefix":"10.1145","volume":"9","author":[{"given":"Xuelong","family":"Li","sequence":"first","affiliation":[{"name":"Chinese Academy of Sciences, Shaanxi, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guosheng","family":"Cui","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences, Shaanxi, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1965-240X","authenticated-orcid":false,"given":"Yongsheng","family":"Dong","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences, Shaanxi, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,11]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2011.01.012"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61159-9_32"},{"volume-title":"Convex Optimization","author":"Boyd Stephen","key":"e_1_2_1_3_1"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2010.231"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2738050"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2014.2326059"},{"volume-title":"Proceedings of the Conference on Advances in Neural Information Processing Systems. 1141--1148","year":"2004","author":"Donoho David","key":"e_1_2_1_7_1"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/2806416.2806568"},{"volume-title":"Truncated cauchy non-negative matrix factorization for robust subspace learning","year":"2017","author":"Guan Naiyang","key":"e_1_2_1_9_1"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2011.2105496"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-017-9158-x"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2652730"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/NNSP.2002.1030067"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601434"},{"volume-title":"Independent Component Analysis","author":"Hyv\u00e4rinen Aapo","key":"e_1_2_1_15_1"},{"volume-title":"Modern Multivariate Statistical Techniques","author":"Izenman Alan Julian","key":"e_1_2_1_16_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-78189-1"},{"volume-title":"Principal Component Analysis","author":"Jolliffe Ian","key":"e_1_2_1_17_1"},{"volume-title":"Learning the parts of objects by non-negative matrix factorization. Nature 401, 6755","year":"1999","author":"Lee Daniel D.","key":"e_1_2_1_18_1"},{"volume-title":"Proceedings of the Advances in Neural Information Processing Systems. 556--562","author":"Lee Daniel D.","key":"e_1_2_1_19_1"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2001.990477"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2016.2585355"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/3090312"},{"key":"e_1_2_1_23_1","first-page":"1","article-title":"SCE: A manifold regularized set-covering method for data partitioning","volume":"99","author":"Li Xuelong","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst. PP"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2009.12.023"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2011.217"},{"key":"e_1_2_1_26_1","first-page":"2129","article-title":"Large-cone nonnegative matrix factorization","volume":"28","author":"Liu Tongliang","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2015.2458986"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-013-1572-z"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSVT.2016.2539779"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1985.13340"},{"volume-title":"A generalized power iteration method for solving quadratic problem on the stiefel manifold. Sci. China Info. Sci. 60, 11","year":"2017","author":"Nie Feiping","key":"e_1_2_1_31_1"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/JETCAS.2014.2298290"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/2987379"},{"volume-title":"Proceedings of the International Conference on Machine Learning. 1692--1700","year":"2014","author":"Trigeorgis George","key":"e_1_2_1_34_1"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.5555\/3172077.3172296"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2013.2294215"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2016.2624267"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/3078971.3078977"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.217"},{"volume-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 1--8.","year":"2008","author":"Yang Jianchao","key":"e_1_2_1_40_1"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2733200"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2014.02.004"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSVT.2009.2017306"},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2006.873291"},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2015.2499273"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2010.2044788"},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2015.2403356"}],"container-title":["ACM Transactions on Intelligent Systems and Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3229051","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3229051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T02:07:35Z","timestamp":1750212455000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3229051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11]]},"references-count":47,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,11,30]]}},"alternative-id":["10.1145\/3229051"],"URL":"https:\/\/doi.org\/10.1145\/3229051","relation":{},"ISSN":["2157-6904","2157-6912"],"issn-type":[{"type":"print","value":"2157-6904"},{"type":"electronic","value":"2157-6912"}],"subject":[],"published":{"date-parts":[[2018,11]]},"assertion":[{"value":"2017-10-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-11-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}