Generalized Leverage Scores: Geometric Interpretation and Applications

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorOrdozgoiti, Brunoen_US
dc.contributor.authorMatakos, Antonisen_US
dc.contributor.authorGionis, Aristidesen_US
dc.contributor.departmentQueen Mary University of Londonen_US
dc.contributor.departmentDepartment of Computer Scienceen_US
dc.contributor.departmentKTH Royal Institute of Technologyen_US
dc.date.accessioned2023-01-02T09:29:28Z
dc.date.available2023-01-02T09:29:28Z
dc.date.issued2022en_US
dc.description| openaire: EC/H2020/871042/EU//SoBigData-PlusPlus
dc.description.abstractIn problems involving matrix computations, the concept of leverage has found a large number of applications. In particular, leverage scores, which relate the columns of a matrix to the subspaces spanned by its leading singular vectors, are helpful in revealing column subsets to approximately factorize a matrix with quality guarantees. As such, they provide a solid foundation for a variety of machine-learning methods. In this paper we extend the definition of leverage scores to relate the columns of a matrix to arbitrary subsets of singular vectors. We establish a precise connection between column and singular-vector subsets, by relating the concepts of leverage scores and principal angles between subspaces. We employ this result to design approximation algorithms with provable guarantees for two well-known problems: generalized column subset selection and sparse canonical correlation analysis. We run numerical experiments to provide further insight on the proposed methods. The novel bounds we derive improve our understanding of fundamental concepts in matrix approximations. In addition, our insights may serve as building blocks for further contributions.en
dc.description.versionPeer revieweden
dc.format.extent17056-17070
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationOrdozgoiti , B , Matakos , A & Gionis , A 2022 , Generalized Leverage Scores: Geometric Interpretation and Applications . in Proceedings of the 39th International Conference on Machine Learning . Proceedings of Machine Learning Research , vol. 162 , JMLR , pp. 17056-17070 , International Conference on Machine Learning , Baltimore , Maryland , United States , 17/07/2022 . < https://proceedings.mlr.press/v162/ordozgoiti22a.html >en
dc.identifier.issn2640-3498
dc.identifier.otherPURE UUID: bac52340-a566-4872-a742-437bfb520930en_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/bac52340-a566-4872-a742-437bfb520930en_US
dc.identifier.otherPURE LINK: https://proceedings.mlr.press/v162/ordozgoiti22a.htmlen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/95534250/Generalized_Leverage_Scores.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/118695
dc.identifier.urnURN:NBN:fi:aalto-202301021057
dc.language.isoenen
dc.publisherPMLR
dc.relationinfo:eu-repo/grantAgreement/EC/H2020/871042/EU//SoBigData-PlusPlusen_US
dc.relation.ispartofInternational Conference on Machine Learningen
dc.relation.ispartofseriesProceedings of the 39th International Conference on Machine Learningen
dc.relation.ispartofseriesProceedings of Machine Learning Researchen
dc.relation.ispartofseriesVolume 162en
dc.rightsopenAccessen
dc.titleGeneralized Leverage Scores: Geometric Interpretation and Applicationsen
dc.typeConference article in proceedingsfi
dc.type.versionpublishedVersion
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