{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T15:43:58Z","timestamp":1787499838552,"version":"build-2736575974"},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642387081","type":"print"},{"value":"9783642387098","type":"electronic"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-40991-2_15","type":"book-chapter","created":{"date-parts":[[2013,8,28]],"date-time":"2013-08-28T01:43:57Z","timestamp":1377654237000},"page":"226-241","source":"Crossref","is-referenced-by-count":13,"title":["A Counterexample for the Validity of Using Nuclear Norm as a Convex Surrogate of Rank"],"prefix":"10.1007","author":[{"given":"Hongyang","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhouchen","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"15_CR1","doi-asserted-by":"crossref","unstructured":"Wang, J.: Geometric Structure of High-Dimensional Data and Dimensionality Reduction. Springer (2012)","DOI":"10.1007\/978-3-642-27497-8"},{"issue":"6","key":"15_CR2","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","volume":"9","author":"E. Cand\u00e8s","year":"2009","unstructured":"Cand\u00e8s, E., Recht, B.: Exact matrix completion via convex optimization. Foundations of Computational Mathematics\u00a09(6), 717\u2013772 (2009)","journal-title":"Foundations of Computational Mathematics"},{"issue":"3","key":"15_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1970392.1970395","volume":"58","author":"E. Cand\u00e8s","year":"2009","unstructured":"Cand\u00e8s, E., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? Journal of the ACM\u00a058(3), 1\u201337 (2009)","journal-title":"Journal of the ACM"},{"issue":"6","key":"15_CR4","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1109\/JPROC.2009.2035722","volume":"98","author":"E. Cand\u00e8s","year":"2010","unstructured":"Cand\u00e8s, E.: Matrix completion with noise. Proceedings of the IEEE\u00a098(6), 925\u2013936 (2010)","journal-title":"Proceedings of the IEEE"},{"key":"15_CR5","unstructured":"Fazel, M.: Matrix Rank Minimization with Applications. PhD thesis, Standford University (2002), \n                    \n                      http:\/\/search.proquest.com\/docview\/305537461"},{"issue":"3","key":"15_CR6","doi-asserted-by":"publisher","first-page":"1548","DOI":"10.1109\/TIT.2011.2104999","volume":"57","author":"D. Gross","year":"2011","unstructured":"Gross, D.: Recovering low-rank matrices from few coefficients in any basis. IEEE Transactions on Information Theory\u00a057(3), 1548\u20131566 (2011)","journal-title":"IEEE Transactions on Information Theory"},{"key":"15_CR7","doi-asserted-by":"crossref","unstructured":"Wright, J., Ganesh, A., Min, K., Ma, Y.: Compressive principal component pursuit. In: IEEE International Symposium on Information Theory Proceedings, pp. 1276\u20131280 (2012)","DOI":"10.1109\/ISIT.2012.6283062"},{"key":"15_CR8","unstructured":"Waters, A.E., Sankaranarayanan, A.C., Baraniuk, R.G.: SpaRCS: Recovering low-rank and sparse matrices from compressive measurements. In: Advances in Neural Information Processing Systems, pp. 1089\u20131097 (2011)"},{"key":"15_CR9","unstructured":"Liu, Y.K.: Universal low-rank matrix recovery from pauli measurements. In: Advances in Neural Information Processing Systems, pp. 1638\u20131646 (2011)"},{"issue":"1","key":"15_CR10","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., Sun, J., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a035(1), 171\u2013184 (2013)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"15_CR11","unstructured":"Liu, G., Lin, Z., Yu, Y.: Robust subspace segmentation by low-rank representation. In: International Conference on Machine Learning, vol.\u00a03, pp. 663\u2013670 (2010)"},{"key":"15_CR12","doi-asserted-by":"crossref","unstructured":"Peng, Y., Ganesh, A., Wright, J., Xu, W., Ma, Y.: RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images. In: IEEE Conference on Computer Vision and Pattern Recognition, vol.\u00a034, pp. 2233\u20132246 (2010)","DOI":"10.1109\/TPAMI.2011.282"},{"issue":"1","key":"15_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11263-012-0515-x","volume":"99","author":"Z. Zhang","year":"2012","unstructured":"Zhang, Z., Ganesh, A., Liang, X., Ma, Y.: TILT: Transform invariant low-rank textures. International Journal of Computer Vision\u00a099(1), 1\u201324 (2012)","journal-title":"International Journal of Computer Vision"},{"key":"15_CR14","doi-asserted-by":"crossref","unstructured":"Cheng, B., Liu, G., Huang, Z., Yan, S.: Multi-task low-rank affinities pursuit for image segmentation. In: IEEE International Conference on Computer Vision, pp. 2439\u20132446 (2011)","DOI":"10.1109\/ICCV.2011.6126528"},{"issue":"3","key":"15_CR15","doi-asserted-by":"publisher","first-page":"1327","DOI":"10.1109\/TIP.2011.2169274","volume":"21","author":"C. Lang","year":"2012","unstructured":"Lang, C., Liu, G., Yu, J., Yan, S.: Saliency detection by multi-task sparsity pursuit. IEEE Transactions on Image Processing\u00a021(3), 1327\u20131338 (2012)","journal-title":"IEEE Transactions on Image Processing"},{"key":"15_CR16","unstructured":"Liu, G., Xu, H., Yan, S.: Exact subspace segmentation and outlier detection by low-rank representation. In: International Conference on Artificial Intelligence and Statistics (2012)"},{"key":"15_CR17","doi-asserted-by":"crossref","unstructured":"Liu, G., Yan, S.: Latent low-rank representation for subspace segmentation and feature extraction. In: IEEE International Conference on Computer Vision, pp. 1615\u20131622 (2011)","DOI":"10.1109\/ICCV.2011.6126422"},{"issue":"2","key":"15_CR18","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1109\/MSP.2010.939739","volume":"28","author":"R. Vidal","year":"2011","unstructured":"Vidal, R.: Subspace clustering. IEEE Signal Processing Magazine\u00a028(2), 52\u201368 (2011)","journal-title":"IEEE Signal Processing Magazine"},{"key":"15_CR19","doi-asserted-by":"crossref","unstructured":"Elhamifar, E., Vidal, R.: Sparse subspace clustering. In: IEEE Conference on Computer Vision and Pattern Recognition, vol.\u00a02, pp. 2790\u20132797 (2009)","DOI":"10.1109\/CVPR.2009.5206547"},{"issue":"1","key":"15_CR20","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1109\/LSP.2012.2229705","volume":"20","author":"A. Adler","year":"2013","unstructured":"Adler, A., Elad, M., Hel-Or, Y.: Probabilistic subspace clustering via sparse representations. IEEE Signal Processing Letters\u00a020(1), 63\u201366 (2013)","journal-title":"IEEE Signal Processing Letters"},{"key":"15_CR21","unstructured":"Liu, R., Lin, Z., Torre, F.D.L., Su, Z.: Fixed-rank representation for unsupervised visual learning. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 598\u2013605 (2012)"},{"issue":"2","key":"15_CR22","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1137\/06065551","volume":"29","author":"S. Friedland","year":"2007","unstructured":"Friedland, S., Torokhti, A.: Generalized rank-constrained matrix approximations. SIAM Journal on Matrix Analysis and Applications\u00a029(2), 656\u2013659 (2007)","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"issue":"4","key":"15_CR23","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1137\/080738970","volume":"20","author":"J. Cai","year":"2010","unstructured":"Cai, J., Cand\u00e8s, E., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM Journal of Optimization\u00a020(4), 1956\u20131982 (2010)","journal-title":"SIAM Journal of Optimization"}],"container-title":["Lecture Notes in Computer Science","Advanced Information Systems Engineering"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-40991-2_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T19:40:39Z","timestamp":1558035639000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-40991-2_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642387081","9783642387098"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-40991-2_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}