{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T18:26:04Z","timestamp":1773771964946,"version":"3.50.1"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"8-10","license":[{"start":{"date-parts":[[2018,5,10]],"date-time":"2018-05-10T00:00:00Z","timestamp":1525910400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-16-CE23-0016-01"],"award-info":[{"award-number":["ANR-16-CE23-0016-01"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"name":"CPER Nord-Pas de Calais\/FEDER DATA Advanced data science and technologies"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2018,9]]},"DOI":"10.1007\/s10994-018-5713-5","type":"journal-article","created":{"date-parts":[[2018,5,10]],"date-time":"2018-05-10T18:12:26Z","timestamp":1525975946000},"page":"1457-1475","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A distributed Frank\u2013Wolfe framework for learning low-rank matrices with the trace norm"],"prefix":"10.1007","volume":"107","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2814-4837","authenticated-orcid":false,"given":"Wenjie","family":"Zheng","sequence":"first","affiliation":[]},{"given":"Aur\u00e9lien","family":"Bellet","sequence":"additional","affiliation":[]},{"given":"Patrick","family":"Gallinari","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,5,10]]},"reference":[{"key":"5713_CR1","doi-asserted-by":"crossref","unstructured":"Amit, Y., Fink, M., Srebro, N., & Ullman, S. (2007). Uncovering shared structures in multiclass classification. In ICML.","DOI":"10.1145\/1273496.1273499"},{"issue":"3","key":"5713_CR2","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/s10994-007-5040-8","volume":"73","author":"A Argyriou","year":"2008","unstructured":"Argyriou, A., Evgeniou, T., & Pontil, M. (2008). Convex multi-task feature learning. Machine Learning, 73(3), 243\u2013272.","journal-title":"Machine Learning"},{"key":"5713_CR3","first-page":"1019","volume":"9","author":"FR Bach","year":"2008","unstructured":"Bach, F. R. (2008). Consistency of trace norm minimization. Journal of Machine Learning Research, 9, 1019\u20131048.","journal-title":"Journal of Machine Learning Research"},{"key":"5713_CR4","doi-asserted-by":"crossref","unstructured":"Bellet, A., Liang, Y., Garakani, A. B., Balcan, M. F., & Sha, F. (2015). A distributed Frank\u2013Wolfe algorithm for communication-efficient sparse learning. In SDM.","DOI":"10.1137\/1.9781611974010.54"},{"key":"5713_CR5","unstructured":"Bhojanapalli, S., Neyshabur, B., & Srebro, N. (2016). Global optimality of local search for low rank matrix recovery. In NIPS."},{"issue":"2","key":"5713_CR6","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1002\/cem.1122","volume":"22","author":"R Bro","year":"2008","unstructured":"Bro, R., Acar, E., & Kolda, T. G. (2008). Resolving the sign ambiguity in the singular value decomposition. Journal of Chemometrics, 22(2), 135\u2013140.","journal-title":"Journal of Chemometrics"},{"key":"5713_CR7","unstructured":"Cabral, R. S., De\u00a0la Torre, F., Costeira, J. P., & Bernardino, A. (2011). Matrix completion for multi-label image classification. In NIPS."},{"key":"5713_CR8","doi-asserted-by":"crossref","unstructured":"Cabral, R., De\u00a0La\u00a0Torre, F., Costeira, J. P., & Bernardino, A. (2013). Unifying nuclear norm and bilinear factorization approaches for low-rank matrix decomposition. In ICCV.","DOI":"10.1109\/ICCV.2013.309"},{"issue":"4","key":"5713_CR9","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1137\/080738970","volume":"20","author":"JF Cai","year":"2010","unstructured":"Cai, J. F., Cand\u00e8s, E. J., & Shen, Z. (2010). A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 20(4), 1956\u20131982.","journal-title":"SIAM Journal on Optimization"},{"issue":"2","key":"5713_CR10","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1137\/151005099","volume":"57","author":"EJ Candes","year":"2015","unstructured":"Candes, E. J., Eldar, Y. C., Strohmer, T., & Voroninski, V. (2015). Phase retrieval via matrix completion. SIAM Review, 57(2), 225\u2013251.","journal-title":"SIAM Review"},{"issue":"6","key":"5713_CR11","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","volume":"9","author":"EJ Cand\u00e8s","year":"2009","unstructured":"Cand\u00e8s, E. J., & Recht, B. (2009). Exact matrix completion via convex optimization. Foundations of Computational mathematics, 9(6), 717\u2013772.","journal-title":"Foundations of Computational mathematics"},{"issue":"5","key":"5713_CR12","doi-asserted-by":"publisher","first-page":"2053","DOI":"10.1109\/TIT.2010.2044061","volume":"56","author":"EJ Cand\u00e8s","year":"2010","unstructured":"Cand\u00e8s, E. J., & Tao, T. (2010). The power of convex relaxation: Near-optimal matrix completion. IEEE Transactions on Information Theory, 56(5), 2053\u20132080.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"5713_CR13","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1023\/A:1007379606734","volume":"28","author":"R Caruana","year":"1997","unstructured":"Caruana, R. (1997). Multitask Learning. Machine Learning, 28(1), 41\u201375.","journal-title":"Machine Learning"},{"issue":"4","key":"5713_CR14","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1145\/1824777.1824783","volume":"6","author":"KL Clarkson","year":"2010","unstructured":"Clarkson, K. L. (2010). Coresets, sparse greedy approximation, and the Frank\u2013Wolfe algorithm. ACM Transactions on Algorithms, 6(4), 63.","journal-title":"ACM Transactions on Algorithms"},{"issue":"1","key":"5713_CR15","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1145\/1327452.1327492","volume":"51","author":"J Dean","year":"2008","unstructured":"Dean, J., & Ghemawat, S. (2008). Mapreduce: Simplified data processing on large clusters. Communications of the ACM, 51(1), 107\u2013113.","journal-title":"Communications of the ACM"},{"key":"5713_CR16","doi-asserted-by":"crossref","unstructured":"Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., & Li, F. F. (2009). ImageNet: A large-scale hierarchical image database. In CVPR.","DOI":"10.1109\/CVPR.2009.5206848"},{"issue":"1\u20132","key":"5713_CR17","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1002\/nav.3800030109","volume":"3","author":"M Frank","year":"1956","unstructured":"Frank, M., & Wolfe, P. (1956). An algorithm for quadratic programming. Naval research logistics quarterly, 3(1\u20132), 95\u2013110.","journal-title":"Naval research logistics quarterly"},{"issue":"1\u20132","key":"5713_CR18","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s10107-014-0841-6","volume":"155","author":"RM Freund","year":"2016","unstructured":"Freund, R. M., & Grigas, P. (2016). New analysis and results for the Frank\u2013Wolfe method. Mathematical Programming, 155(1\u20132), 199\u2013230.","journal-title":"Mathematical Programming"},{"key":"5713_CR19","unstructured":"Garber, D., & Hazan, E. (2015). Faster rates for the Frank\u2013Wolfe method over strongly-convex sets. In ICML."},{"key":"5713_CR20","unstructured":"Goldberg, A., Recht, B., Xu, J., Nowak, R., & Zhu, X. (2010). Transduction with matrix completion: Three birds with one stone. In NIPS."},{"issue":"3","key":"5713_CR21","doi-asserted-by":"publisher","first-page":"1548","DOI":"10.1109\/TIT.2011.2104999","volume":"57","author":"D Gross","year":"2011","unstructured":"Gross, D. (2011). Recovering low-rank matrices from few coefficients in any basis. IEEE Transactions on Information Theory, 57(3), 1548\u20131566.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"15","key":"5713_CR22","doi-asserted-by":"publisher","first-page":"150,401","DOI":"10.1103\/PhysRevLett.105.150401","volume":"105","author":"D Gross","year":"2010","unstructured":"Gross, D., Liu, Y. K., Flammia, S. T., Becker, S., & Eisert, J. (2010). Quantum state tomography via compressed sensing. Physical Review Letters, 105(15), 150,401.","journal-title":"Physical Review Letters"},{"key":"5713_CR23","doi-asserted-by":"crossref","unstructured":"Harchaoui, Z., Douze, M., Paulin, M., Dudik, M., & Malick, J. (2012). Large-scale image classification with trace-norm regularization. In CVPR.","DOI":"10.1109\/CVPR.2012.6248078"},{"issue":"1\u20132","key":"5713_CR24","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s10107-014-0778-9","volume":"152","author":"Z Harchaoui","year":"2015","unstructured":"Harchaoui, Z., Juditsky, A., & Nemirovski, A. (2015). Conditional gradient algorithms for norm-regularized smooth convex optimization. Mathematical Programming, 152(1\u20132), 75\u2013112.","journal-title":"Mathematical Programming"},{"key":"5713_CR25","doi-asserted-by":"crossref","unstructured":"Hazan, E. (2008). Sparse approximate solutions to semidefinite programs. In Latin American symposium on theoretical informatics.","DOI":"10.1007\/978-3-540-78773-0_27"},{"key":"5713_CR26","unstructured":"Hazan, E., & Kale, S. (2012). Projection-free online learning. In ICML."},{"key":"5713_CR27","unstructured":"Hazan, E., & Luo, H. (2016). Variance-reduced and projection-free stochastic optimization. In ICML."},{"key":"5713_CR28","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. In CVPR.","DOI":"10.1109\/CVPR.2016.90"},{"key":"5713_CR29","unstructured":"Jaggi, M. (2013). Revisiting Frank\u2013Wolfe: Projection-free sparse convex optimization. In ICML."},{"key":"5713_CR30","unstructured":"Jaggi, M., Sulovsk, M., et\u00a0al. (2010). A simple algorithm for nuclear norm regularized problems. In ICML."},{"key":"5713_CR31","doi-asserted-by":"crossref","unstructured":"Ji, H., Liu, C., Shen, Z., & Xu, Y. (2010). Robust video denoising using low rank matrix completion. In CVPR.","DOI":"10.1109\/CVPR.2010.5539849"},{"issue":"5","key":"5713_CR32","doi-asserted-by":"publisher","first-page":"2302","DOI":"10.1214\/11-AOS894","volume":"39","author":"V Koltchinskii","year":"2011","unstructured":"Koltchinskii, V., Lounici, K., & Tsybakov, A. B. (2011). Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. The Annals of Statistics, 39(5), 2302\u20132329.","journal-title":"The Annals of Statistics"},{"issue":"8","key":"5713_CR33","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1109\/MC.2009.263","volume":"42","author":"Y Koren","year":"2009","unstructured":"Koren, Y., Bell, R., Volinsky, C., et al. (2009). Matrix factorization techniques for recommender systems. Computer, 42(8), 30\u201337.","journal-title":"Computer"},{"issue":"4","key":"5713_CR34","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.1137\/0613066","volume":"13","author":"J Kuczy\u0144ski","year":"1992","unstructured":"Kuczy\u0144ski, J., & Wo\u017aniakowski, H. (1992). Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start. SIAM Journal on Matrix Analysis and Applications, 13(4), 1094\u20131122.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"5713_CR35","unstructured":"Lacoste-Julien, S., & Jaggi, M. (2015). On the global linear convergence of Frank\u2013Wolfe optimization variants. In NIPS."},{"key":"5713_CR36","unstructured":"Lacoste-Julien, S., Jaggi, M., Schmidt, M., & Pletscher, P. (2013). Block-coordinate Frank\u2013Wolfe optimization for structural SVMs. In ICML."},{"issue":"2","key":"5713_CR37","doi-asserted-by":"publisher","first-page":"1379","DOI":"10.1137\/140992382","volume":"26","author":"G Lan","year":"2016","unstructured":"Lan, G., & Zhou, Y. (2016). Conditional gradient sliding for convex optimization. SIAM Journal on Optimization, 26(2), 1379\u20131409.","journal-title":"SIAM Journal on Optimization"},{"key":"5713_CR38","doi-asserted-by":"crossref","unstructured":"Liu, Z., & Tsang, I. (2017). Approximate conditional gradient descent on multi-class classification. In AAAI.","DOI":"10.1609\/aaai.v31i1.10915"},{"issue":"1\u20132","key":"5713_CR39","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s10107-009-0306-5","volume":"128","author":"S Ma","year":"2011","unstructured":"Ma, S., Goldfarb, D., & Chen, L. (2011). Fixed point and Bregman iterative methods for matrix rank minimization. Mathematical Programming, 128(1\u20132), 321\u2013353.","journal-title":"Mathematical Programming"},{"key":"5713_CR40","unstructured":"Mackey, L.W., Jordan, M.I., & Talwalkar, A. (2011). Divide-and-conquer matrix factorization. In Advances in neural information processing systems (pp. 1134\u20131142)."},{"key":"5713_CR41","doi-asserted-by":"crossref","unstructured":"Moharrer, A., & Ioannidis, S. (2017). Distributing Frank\u2013Wolfe via map-reduce. In ICDM.","DOI":"10.1109\/ICDM.2017.41"},{"issue":"3","key":"5713_CR42","first-page":"123","volume":"1","author":"N Parikh","year":"2013","unstructured":"Parikh, N., & Boyd, S. (2013). Proximal algorithms. Foundations and Trends in Optimization, 1(3), 123\u2013231.","journal-title":"Foundations and Trends in Optimization"},{"issue":"6","key":"5713_CR43","doi-asserted-by":"publisher","first-page":"3465","DOI":"10.1137\/090763184","volume":"20","author":"TK Pong","year":"2010","unstructured":"Pong, T. K., Tseng, P., Ji, S., & Ye, J. (2010). Trace norm regularization: Reformulations, algorithms, and multi-task learning. SIAM Journal on Optimization, 20(6), 3465\u20133489.","journal-title":"SIAM Journal on Optimization"},{"key":"5713_CR44","first-page":"3413","volume":"12","author":"B Recht","year":"2011","unstructured":"Recht, B. (2011). A simpler approach to matrix completion. Journal of Machine Learning Research, 12, 3413\u20133430.","journal-title":"Journal of Machine Learning Research"},{"issue":"3","key":"5713_CR45","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/s11263-015-0816-y","volume":"115","author":"O Russakovsky","year":"2015","unstructured":"Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., et al. (2015). ImageNet large scale visual recognition challenge. International Journal of Computer Vision, 115(3), 211\u2013252.","journal-title":"International Journal of Computer Vision"},{"issue":"1\u20134","key":"5713_CR46","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11","author":"JF Sturm","year":"1999","unstructured":"Sturm, J. F. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11(1\u20134), 625\u2013653.","journal-title":"Optimization Methods and Software"},{"issue":"1\u20134","key":"5713_CR47","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1080\/10556789908805762","volume":"11","author":"KC Toh","year":"1999","unstructured":"Toh, K. C., Todd, M. J., & T\u00fct\u00fcnc\u00fc, R. H. (1999). SDPT3a MATLAB software package for semidefinite programming, version 1.3. Optimization Methods and Software, 11(1\u20134), 545\u2013581.","journal-title":"Optimization Methods and Software"},{"key":"5713_CR48","doi-asserted-by":"crossref","unstructured":"Tran, N. L., Peel, T., & Skhiri, S. (2015). Distributed Frank\u2013Wolfe under pipelined stale synchronous parallelism. In IEEE Big Data.","DOI":"10.1109\/BigData.2015.7363755"},{"key":"5713_CR49","doi-asserted-by":"publisher","first-page":"5522","DOI":"10.1109\/TAC.2017.2685559","volume":"62","author":"HT Wai","year":"2017","unstructured":"Wai, H. T., Lafond, J., Scaglione, A., & Moulines, E. (2017). Decentralized Frank\u2013Wolfe algorithm for convex and non-convex problems. IEEE Transactions on Automatic Control, 62, 5522\u20135537.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"5713_CR50","unstructured":"Wang, Y. X., Sadhanala, V., Dai, W., Neiswanger, W., Sra, S., & Xing, E. (2016). Parallel and distributed block-coordinate Frank\u2013Wolfe algorithms. In ICML."},{"key":"5713_CR51","unstructured":"Zaharia, M., Chowdhury, M., Franklin, M. J., Shenker, S., & Stoica, I. (2010). Spark: Cluster computing with working sets. In HotCloud."}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10994-018-5713-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-018-5713-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-018-5713-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,23]],"date-time":"2022-08-23T07:22:49Z","timestamp":1661239369000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10994-018-5713-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,10]]},"references-count":51,"journal-issue":{"issue":"8-10","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["5713"],"URL":"https:\/\/doi.org\/10.1007\/s10994-018-5713-5","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,10]]},"assertion":[{"value":"9 December 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}