{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T09:42:28Z","timestamp":1775554948319,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T00:00:00Z","timestamp":1573084800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T00:00:00Z","timestamp":1573084800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["World Wide Web"],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1007\/s11280-019-00731-8","type":"journal-article","created":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T09:04:32Z","timestamp":1573117472000},"page":"1969-1988","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":69,"title":["Spectral clustering via half-quadratic optimization"],"prefix":"10.1007","volume":"23","author":[{"given":"Xiaofeng","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiangzhang","family":"Gan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangquan","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaye","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shichao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,7]]},"reference":[{"issue":"5","key":"731_CR1","doi-asserted-by":"publisher","first-page":"1571","DOI":"10.1093\/nar\/gkj515","volume":"34","author":"P Alberto","year":"2006","unstructured":"Alberto, P., Casbon, J.A., Saqi, M.A.S.: Spectral clustering of protein sequences. Nucleic Acids Res. 34(5), 1571\u20131580 (2006)","journal-title":"Nucleic Acids Res."},{"issue":"11","key":"731_CR2","doi-asserted-by":"publisher","first-page":"1859","DOI":"10.1109\/TAC.2006.884922","volume":"51","author":"V Boyd","year":"2006","unstructured":"Boyd, V., Faybusovich, L.: Convex optimization. IEEE Trans. Autom. Control 51(11), 1859\u20131859 (2006)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"731_CR3","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1109\/83.551699","volume":"6","author":"P Charbonnier","year":"1997","unstructured":"Charbonnier, P., Blancfraud, L., Aubert, G., Barlaud, M.: Deterministic edge-preserving regularization in computed imaging. IEEE Trans. Image Process. 6(2), 298\u2013311 (1997)","journal-title":"IEEE Trans. Image Process."},{"issue":"19","key":"731_CR4","doi-asserted-by":"publisher","first-page":"2460","DOI":"10.1093\/bioinformatics\/btq461","volume":"26","author":"RC Edgar","year":"2010","unstructured":"Edgar, R.C.: Search and clustering orders of magnitude faster than blast. Bioinformatics 26(19), 2460 (2010)","journal-title":"Bioinformatics"},{"issue":"11","key":"731_CR5","doi-asserted-by":"publisher","first-page":"2765","DOI":"10.1109\/TPAMI.2013.57","volume":"35","author":"E Elhamifar","year":"2013","unstructured":"Elhamifar, E., Vidal, R.: Sparse subspace clustering: Algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11), 2765\u20132781 (2013)","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"731_CR6","unstructured":"Goh, A., Vidal, R.: Locally linear manifold clustering. Journal of Machine Learning Research (2009)"},{"issue":"1","key":"731_CR7","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1109\/TPAMI.2012.88","volume":"35","author":"L Guangcan","year":"2013","unstructured":"Guangcan, L., Zhouchen, L., Shuicheng, Y., Ju, S., Yu, Y., Yi, M.: Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 171\u2013184 (2013)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"731_CR8","unstructured":"Hartigan, J.A., Wong, M.A.: A k-means clustering algorithm. In: ECCV, pp. 492\u2013503 (2008)"},{"key":"731_CR9","doi-asserted-by":"crossref","unstructured":"He, R., Hu, B., Yuan, X., Wang, L.: M-Estimators and Half-Quadratic minimization (2014)","DOI":"10.1007\/978-3-319-07416-0_2"},{"key":"731_CR10","doi-asserted-by":"crossref","unstructured":"Hu, H., Lin, Z., Feng, J., Zhou, J.: Smooth representation clustering. In: CVPR, pp. 3834\u20133841 (2014)","DOI":"10.1109\/CVPR.2014.484"},{"issue":"6","key":"731_CR11","doi-asserted-by":"publisher","first-page":"2770","DOI":"10.1109\/TIP.2018.2890144","volume":"28","author":"Mengqiu Hu","year":"2019","unstructured":"Hu, M., Yang, Y., Shen, F., Xie, N., Hong, R., Shen, H.T.: Collective reconstructive embeddings for cross-modal hashing. IEEE Transactions on Image Processing. https:\/\/doi.org\/10.1109\/TIP.2018.2890144 (2019)","journal-title":"IEEE Transactions on Image Processing"},{"key":"731_CR12","doi-asserted-by":"crossref","unstructured":"Huber, P.J.: Robust statistics. Wiley, New York (2011)","DOI":"10.1007\/978-3-642-04898-2_594"},{"issue":"4","key":"731_CR13","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1007\/s11280-013-0218-4","volume":"17","author":"Z Ji","year":"2014","unstructured":"Ji, Z., Tao, X., Wang, H.: Outlier detection from large distributed databases. World Wide Web 17(4), 539\u2013568 (2014)","journal-title":"World Wide Web"},{"key":"731_CR14","unstructured":"Junye, G., Liu, M., Zhang, D.: Spectral clustering algorithm based on effective distance. Journal of Frontiers of Computer Science & Technology (2014)"},{"issue":"9","key":"731_CR15","doi-asserted-by":"publisher","first-page":"1154","DOI":"10.1109\/TPAMI.2004.71","volume":"26","author":"MHC Law","year":"2004","unstructured":"Law, M.H.C., Figueiredo, J., Jain, A.K.: Simultaneous feature selection and clustering using mixture models. IEEE Trans Pattern Anal Mach Intell 26(9), 1154\u20131166 (2004)","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"22","key":"731_CR16","doi-asserted-by":"publisher","first-page":"29605","DOI":"10.1007\/s11042-017-5381-7","volume":"77","author":"C Lei","year":"2018","unstructured":"Lei, C., Zhu, X.: Unsupervised feature selection via local structure learning and sparse learning. Multimed Tools Appl 77(22), 29605\u201329622 (2018)","journal-title":"Multimed Tools Appl"},{"issue":"6","key":"731_CR17","doi-asserted-by":"publisher","first-page":"2988","DOI":"10.1109\/TIP.2017.2691557","volume":"26","author":"CG Li","year":"2017","unstructured":"Li, C.G., You, C., Vidal, R.: Structured sparse subspace clustering: A joint affinity learning and subspace clustering framework. IEEE Trans. Image Process. 26 (6), 2988\u20133001 (2017)","journal-title":"IEEE Trans. Image Process."},{"issue":"9","key":"731_CR18","first-page":"1876","volume":"32","author":"XY Liu","year":"2011","unstructured":"Liu, X.Y., Jing-Wei, L.I., Hong, Y.U., You, Q.Z., Lin, H.F.: Adaptive spectral clustering based on shared nearest neighbors. J. Chin. Comput. Syst. 32(9), 1876\u20131880 (2011)","journal-title":"J. Chin. Comput. Syst."},{"issue":"1","key":"731_CR19","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1109\/TPAMI.2012.88","volume":"35","author":"G Liu","year":"2013","unstructured":"Liu, G., Lin, Z., Yan, S., Ju, S., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell 35(1), 171 (2013)","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"731_CR20","unstructured":"Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: NIPS, pp .849\u2013856 (2001)"},{"key":"731_CR21","doi-asserted-by":"crossref","unstructured":"Nie, F., Wang, X., Jordan, M.I., Huang, H.: The constrained laplacian rank algorithm for graph-based clustering. In: AAAI, pp. 1969\u20131976 (2016)","DOI":"10.1609\/aaai.v30i1.10302"},{"key":"731_CR22","doi-asserted-by":"crossref","unstructured":"Nikolova, M., Ng, MK.: Analysis of Half-Quadratic minimization methods for signal and image recovery. Society for Industrial and Applied Mathematics (2005)","DOI":"10.1137\/030600862"},{"issue":"5","key":"731_CR23","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1016\/j.knosys.2011.01.009","volume":"24","author":"Y Peng","year":"2011","unstructured":"Peng, Y., Zhu, Q., Huang, B.: Spectral clustering with density sensitive similarity function. Knowl.-Based Syst. 24(5), 621\u2013628 (2011)","journal-title":"Knowl.-Based Syst."},{"key":"731_CR24","unstructured":"Roth, V., Lange, T.: Feature selection in clustering problems. In: NIPS (2003)"},{"issue":"37","key":"731_CR25","doi-asserted-by":"publisher","first-page":"9814","DOI":"10.1073\/pnas.1700770114","volume":"114","author":"SA Shah","year":"2017","unstructured":"Shah, S.A., Koltun, V.: Robust continuous clustering. Proc Natl Acad Sci U SA 114(37), 9814\u20139819 (2017)","journal-title":"Proc Natl Acad Sci U SA"},{"issue":"10","key":"731_CR26","doi-asserted-by":"publisher","first-page":"1595","DOI":"10.1109\/TMI.2009.2023362","volume":"28","author":"H Szu-Hao","year":"2009","unstructured":"Szu-Hao, H., Yi-Hong, C., Shang-Hong, L., Novak, C.L.: Learning-based vertebra detection and iterative normalized-cut segmentation for spinal mri. IEEE Trans. Med. Imaging 28(10), 1595\u20131605 (2009)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"4","key":"731_CR27","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1109\/TKDE.2010.145","volume":"23","author":"X Tao","year":"2010","unstructured":"Tao, X., Li, Y., Zhong, N.: A personalized ontology model for Web information gathering. IEEE Trans Knowl Data Eng 23(4), 496\u2013511 (2010)","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"6","key":"731_CR28","doi-asserted-by":"publisher","first-page":"1745","DOI":"10.1007\/s11280-017-0508-3","volume":"21","author":"R Wang","year":"2018","unstructured":"Wang, R., Zong, M.: Joint self-representation and subspace learning for unsupervised feature selection. World Wide Web 21(6), 1745\u20131758 (2018)","journal-title":"World Wide Web"},{"issue":"8","key":"731_CR29","first-page":"1373","volume":"41","author":"WW Wang","year":"2015","unstructured":"Wang, W.W., Xiao-Ping, L.I., Feng, X.C., Si, Qi W.: A survey on sparse subspace clustering. Acta Autom. Sin. 41(8), 1373\u20131384 (2015)","journal-title":"Acta Autom. Sin."},{"key":"731_CR30","doi-asserted-by":"crossref","unstructured":"Wang, L., Zheng, K., Tao, X., Han, X.: Affinity propagation clustering algorithm based on large-scale data-set. International Journal of Computers & Applications (3), 1\u20136 (2018)","DOI":"10.1080\/1206212X.2018.1425184"},{"key":"731_CR31","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.patrec.2018.01.013","volume":"109","author":"R Wang","year":"2018","unstructured":"Wang, R., Ji, W., Liu, M., Wang, X., Weng, J., Deng, S., Gao, S., Yuan, C.-a.: Review on mining data from multiple data sources. Pattern Recogn. Lett. 109, 120\u2013128 (2018)","journal-title":"Pattern Recogn. Lett."},{"issue":"6","key":"731_CR32","doi-asserted-by":"publisher","first-page":"1575","DOI":"10.1007\/s11280-017-0510-9","volume":"21","author":"R Wang","year":"2018","unstructured":"Wang, R., Ji, W., Song, B.: Durable relationship prediction and description using a large dynamic graph. World Wide Web 21(6), 1575\u20131600 (2018)","journal-title":"World Wide Web"},{"key":"731_CR33","doi-asserted-by":"crossref","unstructured":"Yan, J., Pollefeys, M.: A general framework for motion segmentation Independent, articulated, rigid, non-rigid, degenerate and non-degenerate. In: ECCV, pp. 94\u2013106 (2006)","DOI":"10.1007\/11744085_8"},{"key":"731_CR34","unstructured":"Yi, B., Yang, Y., Shen, F., Xie, N., Shen, H.T., Li, X.: Describing video with attention based bidirectional lstm. IEEE Transactions on Cybernetics (2018)"},{"key":"731_CR35","unstructured":"Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: NIPS, pp. 1601\u20131608 (2005)"},{"issue":"3","key":"731_CR36","first-page":"43","volume":"8","author":"S Zhang","year":"2017","unstructured":"Zhang, S., Li, X., Ming, Z., Zhu, X., Cheng, D.: Learning k for knn classification. Acm Trans Intell Syst Technol 8(3), 43 (2017)","journal-title":"Acm Trans Intell Syst Technol"},{"issue":"5","key":"731_CR37","doi-asserted-by":"publisher","first-page":"1774","DOI":"10.1109\/TNNLS.2017.2673241","volume":"29","author":"S Zhang","year":"2018","unstructured":"Zhang, S., Li, X., Zong, M., Zhu, X., Wang, R.: Efficient knn classification with different numbers of nearest neighbors. IEEE Trans Neural Netw Learn Syst 29 (5), 1774\u20131785 (2018)","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"22","key":"731_CR38","doi-asserted-by":"publisher","first-page":"29739","DOI":"10.1007\/s11042-017-5272-y","volume":"77","author":"W Zheng","year":"2018","unstructured":"Zheng, W., Zhu, X., Zhu, Y., Hu, R., Lei, Cong: Dynamic graph learning for spectral feature selection. Multimed Tools Appl 77(22), 29739\u201329755 (2018)","journal-title":"Multimed Tools Appl"},{"key":"731_CR39","unstructured":"Zhou, X., Shen, F., Liu, Li, Liu, W., Nie, L., Yang, Y., Shen, H.T.: Graph convolutional network hashing (2018)"},{"issue":"2","key":"731_CR40","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1109\/TCYB.2015.2403356","volume":"46","author":"X Zhu","year":"2016","unstructured":"Zhu, X., Li, X., Zhang, S.: Block-row sparse multiview multilabel learning for image classification. IEEE Trans Cybern 46(2), 450\u2013461 (2016)","journal-title":"IEEE Trans Cybern"},{"key":"731_CR41","doi-asserted-by":"crossref","unstructured":"Zhu, X., He, W., Li, Y., Yang, Y., Zhang, S., Hu, R., Xhu, Y.: One-step spectral clustering via dynamically learning affinity matrix and subspace, pp. 2963\u20132969 (2017)","DOI":"10.1609\/aaai.v31i1.10780"},{"issue":"6","key":"731_CR42","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.1109\/TNNLS.2016.2521602","volume":"28","author":"X Zhu","year":"2017","unstructured":"Zhu, X., Li, X., Zhang, S., Ju, C., Wu, X.: Robust joint graph sparse coding for unsupervised spectral feature selection. IEEE Trans Neural Netw Learn Syst 28(6), 1263\u20131275 (2017)","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"9","key":"731_CR43","doi-asserted-by":"publisher","first-page":"2033","DOI":"10.1109\/TMM.2017.2703636","volume":"19","author":"X Zhu","year":"2017","unstructured":"Zhu, X., Li, X., Zhang, S., Xu, Z., Yu, L., Wang, C.: Graph pca hashing for similarity search. IEEE Trans Multimed 19(9), 2033\u20132044 (2017)","journal-title":"IEEE Trans Multimed"},{"issue":"8","key":"731_CR44","doi-asserted-by":"publisher","first-page":"1532","DOI":"10.1109\/TKDE.2018.2858782","volume":"31","author":"X Zhu","year":"2019","unstructured":"Zhu, X., Shichao, Z., Li, Y., Jilian, Z., Lifeng, Y., Yue, F.: Low-rank sparse subspace for spectral clustering. IEEE Trans Knowl Data Eng 31(8), 1532\u20131543 (2019)","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"10","key":"731_CR45","doi-asserted-by":"publisher","first-page":"2022","DOI":"10.1109\/TKDE.2018.2873378","volume":"31","author":"Xiaofeng Zhu","year":"2019","unstructured":"Zhu, X., Zhang, S., Hu, R., He, W., Lei, C., Zhu, P.: One-step multi-view spectral clustering. IEEE Transactions on Knowledge and Data Engineering. https:\/\/doi.org\/10.1109\/TKDE.2018.2873378 (2018)","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"issue":"8","key":"731_CR46","doi-asserted-by":"publisher","first-page":"1532","DOI":"10.1109\/TKDE.2018.2858782","volume":"31","author":"Xiaofeng Zhu","year":"2019","unstructured":"Zhu, X., Zhang, S., Li, Y., Zhang, J., Yang, L., Fang, Y.: Low-rank sparse subspace for spectral clustering. IEEE Transactions on Knowledge and Data Engineering. https:\/\/doi.org\/10.1109\/TKDE.2018.2858782","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"key":"731_CR47","doi-asserted-by":"crossref","unstructured":"Zhu, X., Zhu, Y., Zhang, S., Hu, R., He, W.: Adaptive hypergraph learning for unsupervised feature selection, 3581\u20133587, pp. (2018)","DOI":"10.24963\/ijcai.2017\/501"},{"key":"731_CR48","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Zhu, X., Zheng, W.: Robust multi-view learning via half-quadratic minimization, pp. 3278\u20133284 (2018)","DOI":"10.24963\/ijcai.2018\/455"}],"container-title":["World Wide Web"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11280-019-00731-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11280-019-00731-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11280-019-00731-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,3]],"date-time":"2022-10-03T21:50:36Z","timestamp":1664833836000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11280-019-00731-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,7]]},"references-count":48,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["731"],"URL":"https:\/\/doi.org\/10.1007\/s11280-019-00731-8","relation":{},"ISSN":["1386-145X","1573-1413"],"issn-type":[{"value":"1386-145X","type":"print"},{"value":"1573-1413","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,7]]},"assertion":[{"value":"2 June 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 November 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}