{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T13:47:20Z","timestamp":1769608040229,"version":"3.49.0"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,7,22]],"date-time":"2023-07-22T00:00:00Z","timestamp":1689984000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,22]],"date-time":"2023-07-22T00:00:00Z","timestamp":1689984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071060"],"award-info":[{"award-number":["12071060"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12125108"],"award-info":[{"award-number":["12125108"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971466"],"award-info":[{"award-number":["11971466"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11991021"],"award-info":[{"award-number":["11991021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12021001"],"award-info":[{"award-number":["12021001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11688101"],"award-info":[{"award-number":["11688101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018527","name":"Key Research Program of Frontier Science, Chinese Academy of Sciences","doi-asserted-by":"publisher","award":["ZDBS-LY-7022"],"award-info":[{"award-number":["ZDBS-LY-7022"]}],"id":[{"id":"10.13039\/501100018527","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004739","name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004739","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2023,9]]},"DOI":"10.1007\/s10915-023-02289-0","type":"journal-article","created":{"date-parts":[[2023,7,22]],"date-time":"2023-07-22T10:01:56Z","timestamp":1690020116000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stochastic Gauss\u2013Newton Algorithms for Online PCA"],"prefix":"10.1007","volume":"96","author":[{"given":"Siyun","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5705-0805","authenticated-orcid":false,"given":"Xin","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liwei","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,7,22]]},"reference":[{"key":"2289_CR1","doi-asserted-by":"crossref","unstructured":"Allen-Zhu, Z., Li, Y.: First efficient convergence for streaming $$k$$-PCA: a global, gap-free, and near-optimal rate. In: 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pp. 487\u2013492. IEEE (2017)","DOI":"10.1109\/FOCS.2017.51"},{"key":"2289_CR2","unstructured":"Balcan, M.-F., Du, S.S., Wang, Y., Yu, A.W.: An improved gap-dependency analysis of the noisy power method. In: Conference on Learning Theory, pp. 284\u2013309. PMLR (2016)"},{"key":"2289_CR3","unstructured":"Balsubramani, A., Dasgupta, S., Freund, Y.: The fast convergence of incremental PCA. In: Advances in Neural Information Processing Systems, vol. 26, pp. 3174\u20133182 (2013)"},{"issue":"8","key":"2289_CR4","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1109\/JPROC.2018.2847041","volume":"106","author":"L Balzano","year":"2018","unstructured":"Balzano, L., Chi, Y., M Lu, Y.: Streaming PCA and subspace tracking: the missing data case. Proc. IEEE 106(8), 1293\u20131310 (2018)","journal-title":"Proc. IEEE"},{"issue":"1","key":"2289_CR5","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1111\/insr.12220","volume":"86","author":"H Cardot","year":"2018","unstructured":"Cardot, H., Degras, D.: Online principal component analysis in high dimension: which algorithm to choose? Int. Stat. Rev. 86(1), 29\u201350 (2018)","journal-title":"Int. Stat. Rev."},{"key":"2289_CR6","unstructured":"Chen, M., Yang, L., Wang, M., Zhao, T.: Dimensionality reduction for stationary time series via stochastic nonconvex optimization. In: Proceedings of the 32nd International Conference on Neural Information Processing Systems, pp. 3500\u20133510 (2018)"},{"key":"2289_CR7","unstructured":"De\u00a0Sa, C., Re, C., Olukotun, K.: Global convergence of stochastic gradient descent for some non-convex matrix problems. In: International Conference on Machine Learning, pp. 2332\u20132341. PMLR (2015)"},{"key":"2289_CR8","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/s10107-018-1311-3","volume":"178","author":"D Drusvyatskiy","year":"2019","unstructured":"Drusvyatskiy, D., Paquette, C.: Efficiency of minimizing compositions of convex functions and smooth maps. Math. Program. 178, 503\u2013558 (2019)","journal-title":"Math. Program."},{"key":"2289_CR9","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316658","volume-title":"Markov Processes: Characterization and Convergence","author":"SN Ethier","year":"1986","unstructured":"Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. Wiley, New York (1986)"},{"issue":"3","key":"2289_CR10","doi-asserted-by":"publisher","first-page":"777","DOI":"10.4310\/CMS.2018.v16.n3.a8","volume":"16","author":"Y Feng","year":"2018","unstructured":"Feng, Y., Li, L., Liu, J.-G.: Semigroups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations. Commun. Math. Sci. 16(3), 777\u2013789 (2018)","journal-title":"Commun. Math. Sci."},{"issue":"3","key":"2289_CR11","doi-asserted-by":"publisher","first-page":"A1949","DOI":"10.1137\/18M1221679","volume":"41","author":"B Gao","year":"2019","unstructured":"Gao, B., Liu, X., Yuan, Y.: Parallelizable algorithms for optimization problems with orthogonality constraints. SIAM J. Sci. Comput. 41(3), A1949\u2013A1983 (2019)","journal-title":"SIAM J. Sci. Comput."},{"key":"2289_CR12","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944","volume-title":"Matrix Computations","author":"GH Golub","year":"2013","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, vol. 3. JHU Press, Baltimore (2013)"},{"key":"2289_CR13","unstructured":"Hardt, M., Price, E.: The noisy power method: a meta algorithm with applications. In: Proceedings of the 27th International Conference on Neural Information Processing Systems, vol. 2, pp. 2861\u20132869 (2014)"},{"key":"2289_CR14","unstructured":"Henriksen, A., Ward, R.: AdaOja: adaptive learning rates for streaming PCA. arXiv preprint arXiv:1905.12115 (2019)"},{"key":"2289_CR15","unstructured":"Huang, D., Niles-Weed, J., Ward, R.: Streaming $$k$$-PCA: efficient guarantees for Oja\u2019s algorithm, beyond rank-one updates. In: Conference on Learning Theory, pp. 2463\u20132498. PMLR (2021)"},{"key":"2289_CR16","unstructured":"Jain, P., Jin, C., Kakade, S.M., Netrapalli, P., Sidford, A.: Streaming PCA: matching matrix Bernstein and near-optimal finite sample guarantees for Oja\u2019s algorithm. In: Conference on Learning Theory, pp. 1147\u20131164. PMLR (2016)"},{"key":"2289_CR17","unstructured":"Johnson, R., Zhang, T.: Accelerating stochastic gradient descent using predictive variance reduction. In: Proceedings of the 26th International Conference on Neural Information Processing Systems, vol. 1, pp. 315\u2013323 (2013)"},{"key":"2289_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1904-8","volume-title":"Principal Component Analysis","author":"IT Jolliffe","year":"1986","unstructured":"Jolliffe, I.T.: Principal Component Analysis. Springer, New York (1986)"},{"issue":"2065","key":"2289_CR19","doi-asserted-by":"publisher","first-page":"20150202","DOI":"10.1098\/rsta.2015.0202","volume":"374","author":"IT Jolliffe","year":"2016","unstructured":"Jolliffe, I.T., Cadima, J.: Principal component analysis: a review and recent developments. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 374(2065), 20150202 (2016)","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"issue":"2","key":"2289_CR20","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1137\/S1064827500366124","volume":"23","author":"AV Knyazev","year":"2001","unstructured":"Knyazev, A.V.: Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method. SIAM J. Sci. Comput. 23(2), 517\u2013541 (2001)","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"2289_CR21","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/0041-5553(69)90135-9","volume":"9","author":"TP Krasulina","year":"1969","unstructured":"Krasulina, T.P.: The method of stochastic approximation for the determination of the least eigenvalue of a symmetrical matrix. USSR Comput. Math. Math. Phys. 9(6), 189\u2013195 (1969)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"2289_CR22","unstructured":"Krizhevsky, A., Hinton, G.: Learning multiple layers of features from tiny images. Technical report, Department of Computer Science, University of Toronto (2009)"},{"issue":"11","key":"2289_CR23","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":"2289_CR24","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s10107-017-1182-z","volume":"167","author":"CJ Li","year":"2016","unstructured":"Li, C.J., Wang, M., Han, L., Tong, Z.: Near-optimal stochastic approximation for online principal component estimation. Math. Program. 167(1), 75\u201397 (2016)","journal-title":"Math. Program."},{"key":"2289_CR25","unstructured":"Li, C.J., Wang, M., Liu, H., Zhang, T.: Diffusion approximations for online principal component estimation and global convergence. In: Advances in Neural Information Processing Systems, vol.\u00a030 (2017)"},{"key":"2289_CR26","unstructured":"Li, C.-L., Lin, H.-T., Lu, C.-J.: Rivalry of two families of algorithms for memory-restricted streaming PCA. In: Artificial Intelligence and Statistics, pp. 473\u2013481. PMLR (2016)"},{"issue":"3","key":"2289_CR27","doi-asserted-by":"publisher","first-page":"A1641","DOI":"10.1137\/120871328","volume":"35","author":"X Liu","year":"2013","unstructured":"Liu, X., Wen, Z., Zhang, Y.: Limited memory block Krylov subspace optimization for computing dominant singular value decompositions. SIAM J. Sci. Comput. 35(3), A1641\u2013A1668 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"2289_CR28","doi-asserted-by":"publisher","first-page":"1571","DOI":"10.1137\/140971464","volume":"25","author":"X Liu","year":"2015","unstructured":"Liu, X., Wen, Z., Zhang, Y.: An efficient Gauss\u2013Newton algorithm for symmetric low-rank product matrix approximations. SIAM J. Optim. 25(3), 1571\u20131608 (2015)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"2289_CR29","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1016\/j.tcs.2006.07.012","volume":"367","author":"JC Lv","year":"2006","unstructured":"Lv, J.C., Yi, Z., Tan, K.K.: Global convergence of Oja\u2019s PCA learning algorithm with a non-zero-approaching adaptive learning rate. Theoret. Comput. Sci. 367(3), 286\u2013307 (2006)","journal-title":"Theoret. Comput. Sci."},{"issue":"3","key":"2289_CR30","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/BF00275687","volume":"15","author":"E Oja","year":"1982","unstructured":"Oja, E.: Simplified neuron model as a principal component analyzer. J. Math. Biol. 15(3), 267\u2013273 (1982)","journal-title":"J. Math. Biol."},{"issue":"11","key":"2289_CR31","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1080\/14786440109462720","volume":"2","author":"K Pearson","year":"1901","unstructured":"Pearson, K.: LIII. On lines and planes of closest fit to systems of points in space. Lond. Edinb. Dublin Philos. Mag. J. Sci. 2(11), 559\u2013572 (1901)","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. Sci."},{"key":"2289_CR32","doi-asserted-by":"crossref","unstructured":"Raychaudhuri, S., Stuart, J.M., Altman, R.B.: Principal components analysis to summarize microarray experiments: application to sporulation time series. In: Biocomputing 2000, pp. 455\u2013466. World Scientific (1999)","DOI":"10.1142\/9789814447331_0043"},{"issue":"3","key":"2289_CR33","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. Stat. 22(3), 400\u2013407 (1951)","journal-title":"Ann. Math. Stat."},{"issue":"3","key":"2289_CR34","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/BF02219773","volume":"16","author":"H Rutishauser","year":"1970","unstructured":"Rutishauser, H.: Simultaneous iteration method for symmetric matrices. Numer. Math. 16(3), 205\u2013223 (1970)","journal-title":"Numer. Math."},{"issue":"5","key":"2289_CR35","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1137\/0717059","volume":"17","author":"Y Saad","year":"1980","unstructured":"Saad, Y.: On the rates of convergence of the Lanczos and the block-Lanczos methods. SIAM J. Numer. Anal. 17(5), 687\u2013706 (1980)","journal-title":"SIAM J. Numer. Anal."},{"key":"2289_CR36","unstructured":"Shamir, O.: A stochastic PCA and SVD algorithm with an exponential convergence rate. In: International Conference on Machine Learning, pp. 144\u2013152. PMLR (2015)"},{"key":"2289_CR37","unstructured":"Shamir, O.: Convergence of stochastic gradient descent for PCA. In: International Conference on Machine Learning, pp. 257\u2013265. PMLR (2016)"},{"key":"2289_CR38","unstructured":"Shamir, O.: Fast stochastic algorithms for SVD and PCA: convergence properties and convexity. In: International Conference on Machine Learning, pp. 248\u2013256. PMLR (2016)"},{"issue":"2","key":"2289_CR39","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1137\/S0036144599363084","volume":"42","author":"GLG Sleijpen","year":"2000","unstructured":"Sleijpen, G.L.G., Van\u00a0der Vorst, H.A.: A Jacobi\u2013Davidson iteration method for linear eigenvalue problems. SIAM Rev. 42(2), 267\u2013293 (2000)","journal-title":"SIAM Rev."},{"key":"2289_CR40","doi-asserted-by":"crossref","unstructured":"Sorensen, D.C.: Implicitly restarted Arnoldi\/Lanczos methods for large scale eigenvalue calculations. In: Parallel Numerical Algorithms, pp. 119\u2013165. Springer (1997)","DOI":"10.1007\/978-94-011-5412-3_5"},{"issue":"2","key":"2289_CR41","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/0010-4655(94)90073-6","volume":"79","author":"A Stathopoulos","year":"1994","unstructured":"Stathopoulos, A., Fischer, C.F.: A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix. Comput. Phys. Commun. 79(2), 268\u2013290 (1994)","journal-title":"Comput. Phys. Commun."},{"key":"2289_CR42","volume-title":"Matrix Perturbation Theory","author":"GW Stewart","year":"1990","unstructured":"Stewart, G.W., Sun, J.: Matrix Perturbation Theory. Academic Press, Cambridge (1990)"},{"issue":"12","key":"2289_CR43","doi-asserted-by":"publisher","first-page":"8659","DOI":"10.1016\/j.eswa.2010.06.065","volume":"37","author":"A Subasi","year":"2010","unstructured":"Subasi, A., Gursoy, M.I.: EEG signal classification using PCA, ICA, LDA and support vector machines. Expert Syst. Appl. 37(12), 8659\u20138666 (2010)","journal-title":"Expert Syst. Appl."},{"key":"2289_CR44","unstructured":"Tang, C.: Exponentially convergent stochastic $$k$$-PCA without variance reduction. In: Advances in Neural Information Processing Systems, pp. 12393\u201312404 (2019)"},{"issue":"1\u20132","key":"2289_CR45","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000048","volume":"8","author":"JA Tropp","year":"2015","unstructured":"Tropp, J.A.: An introduction to matrix concentration inequalities. Found. Trends Mach. Learn. 8(1\u20132), 1\u2013230 (2015)","journal-title":"Found. Trends Mach. Learn."},{"issue":"1","key":"2289_CR46","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1162\/jocn.1991.3.1.71","volume":"3","author":"M Turk","year":"1991","unstructured":"Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cogn. Neurosci. 3(1), 71\u201386 (1991)","journal-title":"J. Cogn. Neurosci."},{"issue":"5","key":"2289_CR47","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1103\/PhysRev.36.823","volume":"36","author":"GE Uhlenbeck","year":"1930","unstructured":"Uhlenbeck, G.E.: On the theory of the Brownian motion. Phys. Rev. 36(5), 823 (1930)","journal-title":"Phys. Rev."},{"issue":"6","key":"2289_CR48","doi-asserted-by":"publisher","first-page":"2905","DOI":"10.1214\/13-AOS1151","volume":"41","author":"VQ Vu","year":"2013","unstructured":"Vu, V.Q., Lei, J.: Minimax sparse principal subspace estimation in high dimensions. Ann. Stat. 41(6), 2905\u20132947 (2013)","journal-title":"Ann. Stat."},{"issue":"1","key":"2289_CR49","first-page":"4599","volume":"23","author":"B Wang","year":"2022","unstructured":"Wang, B., Ma, S., Xue, L.: Riemannian stochastic proximal gradient methods for nonsmooth optimization over the Stiefel manifold. J. Mach. Learn. Res. 23(1), 4599\u20134631 (2022)","journal-title":"J. Mach. Learn. Res."},{"key":"2289_CR50","doi-asserted-by":"crossref","unstructured":"Wang, C., Lu, Y.M.: Online learning for sparse PCA in high dimensions: exact dynamics and phase transitions. In: 2016 IEEE Information Theory Workshop (ITW), pp. 186\u2013190. IEEE (2016)","DOI":"10.1109\/ITW.2016.7606821"},{"key":"2289_CR51","doi-asserted-by":"publisher","first-page":"508","DOI":"10.4208\/csiam-am.SO-2020-0008","volume":"2","author":"L Wang","year":"2021","unstructured":"Wang, L., Gao, B., Liu, X.: Multipliers correction methods for optimization problems over the Stiefel manifold. CSIAM Trans. Appl. Math. 2, 508\u2013531 (2021)","journal-title":"CSIAM Trans. Appl. Math."},{"issue":"2","key":"2289_CR52","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1287\/ijoo.2021.0064","volume":"4","author":"Z Wang","year":"2022","unstructured":"Wang, Z., Liu, B., Chen, S., Ma, S., Xue, L., Zhao, H.: A manifold proximal linear method for sparse spectral clustering with application to single-cell RNA sequencing data analysis. INFORMS J. Optim. 4(2), 200\u2013214 (2022)","journal-title":"INFORMS J. Optim."},{"key":"2289_CR53","unstructured":"Ward, R., Wu, X., Bottou, L.: AdaGrad stepsizes: sharp convergence over nonconvex landscapes. In: International Conference on Machine Learning, pp. 6677\u20136686. PMLR (2019)"},{"issue":"3","key":"2289_CR54","doi-asserted-by":"publisher","first-page":"1175","DOI":"10.1007\/s10915-015-0061-0","volume":"66","author":"Z Wen","year":"2016","unstructured":"Wen, Z., Yang, C., Liu, X., Zhang, Y.: Trace-penalty minimization for large-scale eigenspace computation. J. Sci. Comput. 66(3), 1175\u20131203 (2016)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"2289_CR55","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1137\/16M1058534","volume":"38","author":"Z Wen","year":"2017","unstructured":"Wen, Z., Zhang, Y.: Accelerating convergence by augmented Rayleigh\u2013Ritz projections for large-scale eigenpair computation. SIAM J. Matrix Anal. Appl. 38(2), 273\u2013296 (2017)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"2289_CR56","unstructured":"Xiao, H., Rasul, K., Vollgraf, R.: Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747 (2017)"},{"key":"2289_CR57","doi-asserted-by":"crossref","unstructured":"Xiao, N., Liu, X., Yuan, Y.: A class of smooth exact penalty function methods for optimization problems with orthogonality constraints. Optim. Methods Softw. 1\u201337 (2020)","DOI":"10.1080\/10556788.2020.1852236"},{"key":"2289_CR58","unstructured":"Yang, W., Xu, H.: Streaming sparse principal component analysis. In: International Conference on Machine Learning, pp. 494\u2013503. PMLR (2015)"},{"issue":"4","key":"2289_CR59","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1007\/s11425-018-9554-4","volume":"64","author":"S Zhou","year":"2021","unstructured":"Zhou, S., Bai, Y.: Convergence analysis of Oja\u2019s iteration for solving online PCA with nonzero-mean samples. Sci. China Math. 64(4), 849\u2013868 (2021)","journal-title":"Sci. China Math."},{"issue":"2","key":"2289_CR60","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1137\/21M1433812","volume":"4","author":"P Zilber","year":"2022","unstructured":"Zilber, P., Nadler, B.: GNMR: a provable one-line algorithm for low rank matrix recovery. SIAM J. Math. Data Sci. 4(2), 909\u2013934 (2022)","journal-title":"SIAM J. Math. Data Sci."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02289-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-023-02289-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02289-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,24]],"date-time":"2024-10-24T20:54:12Z","timestamp":1729803252000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-023-02289-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,22]]},"references-count":60,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["2289"],"URL":"https:\/\/doi.org\/10.1007\/s10915-023-02289-0","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,22]]},"assertion":[{"value":"24 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 June 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declared no potential conflicts of interest with respect to the research, authorship, or publication of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"72"}}