{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T09:19:01Z","timestamp":1770455941603,"version":"3.49.0"},"publisher-location":"Cham","reference-count":41,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030109271","type":"print"},{"value":"9783030109288","type":"electronic"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-10928-8_21","type":"book-chapter","created":{"date-parts":[[2019,1,24]],"date-time":"2019-01-24T08:19:39Z","timestamp":1548317979000},"page":"344-359","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["MASAGA: A Linearly-Convergent Stochastic First-Order Method for Optimization on Manifolds"],"prefix":"10.1007","author":[{"given":"Reza","family":"Babanezhad","sequence":"first","affiliation":[]},{"given":"Issam H.","family":"Laradji","sequence":"additional","affiliation":[]},{"given":"Alireza","family":"Shafaei","sequence":"additional","affiliation":[]},{"given":"Mark","family":"Schmidt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,23]]},"reference":[{"key":"21_CR1","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"PA Absil","year":"2009","unstructured":"Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2009)"},{"key":"21_CR2","unstructured":"Agarwal, A., Bottou, L.: A lower bound for the optimization of finite sums. arXiv preprint (2014)"},{"key":"21_CR3","unstructured":"Bietti, A., Mairal, J.: Stochastic optimization with variance reduction for infinite datasets with finite sum structure. In: Advances in Neural Information Processing Systems, pp. 1622\u20131632 (2017)"},{"issue":"9","key":"21_CR4","doi-asserted-by":"publisher","first-page":"2217","DOI":"10.1109\/TAC.2013.2254619","volume":"58","author":"S Bonnabel","year":"2013","unstructured":"Bonnabel, S.: Stochastic gradient descent on Riemannian manifolds. IEEE Trans. Autom. Control 58(9), 2217\u20132229 (2013)","journal-title":"IEEE Trans. Autom. Control"},{"key":"21_CR5","first-page":"536","volume":"25","author":"MA Cauchy","year":"1847","unstructured":"Cauchy, M.A.: M\u00e9thode g\u00e9n\u00e9rale pour la r\u00e9solution des syst\u00e8mes d\u2019\u00e9quations simultan\u00e9es. Comptes rendus des s\u00e9ances de l\u2019Acad\u00e9mie des sciences de Paris 25, 536\u2013538 (1847)","journal-title":"Comptes rendus des s\u00e9ances de l\u2019Acad\u00e9mie des sciences de Paris"},{"key":"21_CR6","unstructured":"Defazio, A., Bach, F., Lacoste-Julien, S.: SAGA: a fast incremental gradient method with support for non-strongly convex composite objectives. In: Advances in Neural Information Processing Systems (2014)"},{"key":"21_CR7","unstructured":"Dubey, K.A., Reddi, S.J., Williamson, S.A., Poczos, B., Smola, A.J., Xing, E.P.: Variance reduction in stochastic gradient Langevin dynamics. In: Advances in Neural Information Processing Systems, pp. 1154\u20131162 (2016)"},{"key":"21_CR8","doi-asserted-by":"crossref","unstructured":"Guyon, C., Bouwmans, T., Zahzah, E.h.: Robust principal component analysis for background subtraction: systematic evaluation and comparative analysis. In: Principal Component Analysis. InTech (2012)","DOI":"10.5772\/38267"},{"key":"21_CR9","unstructured":"Harikandeh, R., Ahmed, M.O., Virani, A., Schmidt, M., Kone\u010dn\u1ef3, J., Sallinen, S.: StopWasting my gradients: practical SVRG. In: Advances in Neural Information Processing Systems, pp. 2251\u20132259 (2015)"},{"key":"21_CR10","unstructured":"Hosseini, R., Sra, S.: Matrix manifold optimization for Gaussian mixtures. In: Advances in Neural Information Processing Systems, pp. 910\u2013918 (2015)"},{"key":"21_CR11","unstructured":"Jeuris, B., Vandebril, R., Vandereycken, B.: A survey and comparison of contemporary algorithms for computing the matrix geometric mean. Electron. Trans. Numer. Anal. 39(EPFL-ARTICLE-197637), 379\u2013402 (2012)"},{"key":"21_CR12","unstructured":"Johnson, R., Zhang, T.: Accelerating stochastic gradient descent using predictive variance reduction. In: Advances in Neural Information Processing Systems (2013)"},{"key":"21_CR13","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.laa.2003.12.008","volume":"386","author":"S Kamvar","year":"2004","unstructured":"Kamvar, S., Haveliwala, T., Golub, G.: Adaptive methods for the computation of pagerank. Linear Algebra Appl. 386, 51\u201365 (2004)","journal-title":"Linear Algebra Appl."},{"key":"21_CR14","unstructured":"Kasai, H., Sato, H., Mishra, B.: Riemannian stochastic variance reduced gradient on Grassmann manifold. arXiv preprint arXiv:1605.07367 (2016)"},{"key":"21_CR15","unstructured":"Kone\u010dn\u1ef3, J., Richt\u00e1rik, P.: Semi-stochastic gradient descent methods. arXiv preprint (2013)"},{"key":"21_CR16","unstructured":"Le Roux, N., Schmidt, M., Bach, F.: A stochastic gradient method with an exponential convergence rate for strongly-convex optimization with finite training sets. In: Advances in Neural Information Processing Systems (2012)"},{"issue":"11","key":"21_CR17","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","volume":"86","author":"Y LeCun","year":"1998","unstructured":"LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278\u20132324 (1998)","journal-title":"Proc. IEEE"},{"issue":"1","key":"21_CR18","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1109\/TPAMI.2009.112","volume":"32","author":"V Mahadevan","year":"2010","unstructured":"Mahadevan, V., Vasconcelos, N.: Spatiotemporal saliency in dynamic scenes. IEEE Trans. Pattern Anal. Mach. Intell. 32(1), 171\u2013177 (2010). https:\/\/doi.org\/10.1109\/TPAMI.2009.112","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"21_CR19","doi-asserted-by":"crossref","unstructured":"Mahdavi, M., Jin, R.: MixedGrad: an $$o(1\/t$$) convergence rate algorithm for stochastic smooth optimization. In: Advances in Neural Information Processing Systems (2013)","DOI":"10.1155\/2013\/908602"},{"key":"21_CR20","unstructured":"Mairal, J.: Optimization with first-order surrogate functions. arXiv preprint arXiv:1305.3120 (2013)"},{"key":"21_CR21","unstructured":"Needell, D., Ward, R., Srebro, N.: Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. In: Advances in Neural Information Processing Systems, pp. 1017\u20131025 (2014)"},{"issue":"4","key":"21_CR22","doi-asserted-by":"publisher","first-page":"1574","DOI":"10.1137\/070704277","volume":"19","author":"A Nemirovski","year":"2009","unstructured":"Nemirovski, A., Juditsky, A., Lan, G., Shapiro, A.: Robust stochastic approximation approach to stochastic programming. SIAM J. Optim. 19(4), 1574\u20131609 (2009)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"21_CR23","first-page":"543","volume":"269","author":"Y Nesterov","year":"1983","unstructured":"Nesterov, Y.: A method for unconstrained convex minimization problem with the rate of convergence $${O}(1\/k^2)$$. Doklady AN SSSR 269(3), 543\u2013547 (1983)","journal-title":"Doklady AN SSSR"},{"issue":"23","key":"21_CR24","doi-asserted-by":"publisher","first-page":"8577","DOI":"10.1073\/pnas.0601602103","volume":"103","author":"ME Newman","year":"2006","unstructured":"Newman, M.E.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. 103(23), 8577\u20138582 (2006)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"21_CR25","unstructured":"Nguyen, L., Liu, J., Scheinberg, K., Tak\u00e1\u010d, M.: SARAH: a novel method for machine learning problems using stochastic recursive gradient. arXiv preprint arXiv:1703.00102 (2017)"},{"key":"21_CR26","unstructured":"Nutini, J., Laradji, I., Schmidt, M.: Let\u2019s Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence. ArXiv e-prints, December 2017"},{"key":"21_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-26654-1","volume-title":"Riemannian Geometry","author":"P Petersen","year":"2016","unstructured":"Petersen, P., Axler, S., Ribet, K.: Riemannian Geometry, vol. 171. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-26654-1"},{"issue":"4","key":"21_CR28","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1137\/0330046","volume":"30","author":"BT Polyak","year":"1992","unstructured":"Polyak, B.T., Juditsky, A.B.: Acceleration of stochastic approximation by averaging. SIAM J. Contr. Optim. 30(4), 838\u2013855 (1992)","journal-title":"SIAM J. Contr. Optim."},{"issue":"3","key":"21_CR29","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1214\/aoms\/1177729586","volume":"22","author":"H Robbins","year":"1951","unstructured":"Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Statist. 22(3), 400\u2013407 (1951). https:\/\/doi.org\/10.1214\/aoms\/1177729586","journal-title":"Ann. Math. Statist."},{"key":"21_CR30","unstructured":"Sato, H., Kasai, H., Mishra, B.: Riemannian stochastic variance reduced gradient. arXiv preprint arXiv:1702.05594 (2017)"},{"key":"21_CR31","unstructured":"Schmidt, M., Babanezhad, R., Ahmed, M., Defazio, A., Clifton, A., Sarkar, A.: Non-uniform stochastic average gradient method for training conditional random fields. In: Artificial Intelligence and Statistics, pp. 819\u2013828 (2015)"},{"key":"21_CR32","first-page":"567","volume":"14","author":"S Shalev-Schwartz","year":"2013","unstructured":"Shalev-Schwartz, S., Zhang, T.: Stochastic dual coordinate ascent methods for regularized loss minimization. J. Mach. Learn. Res. 14, 567\u2013599 (2013)","journal-title":"J. Mach. Learn. Res."},{"key":"21_CR33","series-title":"Advances in Computer Vision and Pattern Recognition","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/978-3-319-45026-1_3","volume-title":"Algorithmic Advances in Riemannian Geometry and Applications","author":"S Sra","year":"2016","unstructured":"Sra, S., Hosseini, R.: Geometric optimization in machine learning. In: Minh, H.Q., Murino, V. (eds.) Algorithmic Advances in Riemannian Geometry and Applications. ACVPR, pp. 73\u201391. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-45026-1_3"},{"key":"21_CR34","doi-asserted-by":"crossref","unstructured":"Sun, J., Qu, Q., Wright, J.: Complete dictionary recovery over the sphere. In: 2015 International Conference on Sampling Theory and Applications (SampTA), pp. 407\u2013410. IEEE (2015)","DOI":"10.1109\/SAMPTA.2015.7148922"},{"key":"21_CR35","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8390-9","volume-title":"Convex Functions and Optimization Methods on Riemannian Manifolds","author":"C Udriste","year":"1994","unstructured":"Udriste, C.: Convex Functions and Optimization Methods on Riemannian Manifolds, vol. 297. Springer, Dordrecht (1994). https:\/\/doi.org\/10.1007\/978-94-015-8390-9"},{"issue":"12","key":"21_CR36","doi-asserted-by":"publisher","first-page":"6182","DOI":"10.1109\/TSP.2012.2218241","volume":"60","author":"A Wiesel","year":"2012","unstructured":"Wiesel, A.: Geodesic convexity and covariance estimation. IEEE Trans. Signal Process. 60(12), 6182\u20136189 (2012)","journal-title":"IEEE Trans. Signal Process."},{"key":"21_CR37","unstructured":"Zhang, H., Reddi, S.J., Sra, S.: Riemannian SVRG: fast stochastic optimization on Riemannian manifolds. In: Advances in Neural Information Processing Systems, pp. 4592\u20134600 (2016)"},{"key":"21_CR38","unstructured":"Zhang, H., Sra, S.: First-order methods for geodesically convex optimization. In: Conference on Learning Theory, pp. 1617\u20131638 (2016)"},{"key":"21_CR39","unstructured":"Zhang, T., Yang, Y.: Robust principal component analysis by manifold optimization. arXiv preprint arXiv:1708.00257 (2017)"},{"key":"21_CR40","unstructured":"Zhao, P., Zhang, T.: Stochastic optimization with importance sampling for regularized loss minimization. In: International Conference on Machine Learning, pp. 1\u20139 (2015)"},{"key":"21_CR41","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-319-06373-7_1","volume-title":"Geometry of Manifolds with Non-negative Sectional Curvature","author":"W Ziller","year":"2014","unstructured":"Ziller, W.: Riemannian manifolds with positive sectional curvature. In: Dearricott, O., Galaz-Garcia, F., Kennard, L., Searle, C., Weingart, G., Ziller, W. (eds.) Geometry of Manifolds with Non-negative Sectional Curvature. LNM, vol. 2110, pp. 1\u201319. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-06373-7_1"}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-10928-8_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,14]],"date-time":"2024-07-14T08:51:37Z","timestamp":1720947097000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-10928-8_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030109271","9783030109288"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-10928-8_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"23 January 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Dublin","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Ireland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 September 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 September 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.ecmlpkdd2018.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"CMT","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"535","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"131","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"17","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"24% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}