{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:30:53Z","timestamp":1787329853814,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"name":"Moore Foundation"},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["723991"],"award-info":[{"award-number":["723991"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["R01GM090200"],"award-info":[{"award-number":["R01GM090200"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["578\/14"],"award-info":[{"award-number":["578\/14"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>Rank-one update of the spectrum of a matrix is a fundamental problem in classical perturbation theory. In this paper, we consider its variant where only part of the spectrum is known. We address this variant using an efficient scheme for updating the known eigenpairs with guaranteed error bounds. Then, we apply our scheme to the extension of the top eigenvectors of the graph Laplacian to a new data sample. In particular, we model this extension as a perturbation problem and show how to solve it using our rank-one updating scheme. We provide a theoretical analysis of this extension method and back it up with numerical results that illustrate its advantages.<\/jats:p>","DOI":"10.1137\/18m1172120","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T12:59:52Z","timestamp":1565701192000},"page":"973-997","source":"Crossref","is-referenced-by-count":3,"title":["Symmetric Rank-One Updates from Partial Spectrum with an Application to Out-of-Sample Extension"],"prefix":"10.1137","volume":"40","author":[{"given":"Roy","family":"Mitz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nir","family":"Sharon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yoel","family":"Shkolnisky","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,8,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1162\/089976603321780317"},{"key":"atypb2","unstructured":"C. M. Bender and S. A. Orszag,\n                      Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory\n                      , Springer, New York, 2013."},{"key":"atypb3","first-page":"177","author":"Bengio Y.","year":"2004","journal-title":"MA"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2005.07.021"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1198\/106186008X318440"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396012"},{"key":"atypb7","unstructured":"F. W. Byron and R. W. Fuller,\n                      Mathematics of Classical and Quantum Physics\n                      , Courier Corporation, North Chelmsford, MA, 2012."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/16.4.457"},{"key":"atypb9","unstructured":"F. R. Chung,\n                      Spectral Graph Theory\n                      , CBMS Reg. Conf. Ser. Math. 92, American Mathematical Society, Providence, RI, 1997."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2006.04.006"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2008.2002305"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2006.11.016"},{"key":"atypb13","unstructured":"G. H. Golub and C. F. Van Loan,\n                      Matrix Computations\n                      , Vol. 3, The John Hopkins University Press, Baltimore, MD, 2012."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/040619028"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"A. N. Langville and C. D. Meyer,\n                      Google's PageRank and Beyond: The Science of Search Engine Rankings\n                      , Princeton University Press, Princeton, NJ, 2011.","DOI":"10.2307\/j.ctt7t8z9"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600011129"},{"key":"atypb17","first-page":"849","volume":"2","author":"Ng A. Y.","year":"2002","journal-title":"Adv. Neural Inf. Process. Systems"},{"key":"atypb18","unstructured":"L. Page, S. Brin, R. Motwani, and T. Winograd,\n                      The PageRank Citation Ranking: Bringing Order to the Web.\n                      , Technical report, Stanford InfoLab, 1999."},{"key":"atypb19","first-page":"554","author":"Papadopoulo T.","year":"2000","journal-title":"New York"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1126\/science.290.5500.2323"},{"key":"atypb21","unstructured":"J. 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Sun,\n                      Matrix perturbation theory\n                      , Academic Press, New York, 1990."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-007-9033-z"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1172120","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:36:10Z","timestamp":1787326570000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1172120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1172120"],"URL":"https:\/\/doi.org\/10.1137\/18m1172120","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}