Randomized nonnegative matrix factorization
•A novel randomized hierarchical alternating least squares algorithm for NMF.•The randomized algorithm scales up to big data.•The algorithm outperforms previous compressed NMF algorithms in speed and accuracy.•Both synthetic and real-world data are used for evaluation.•A Python implementation is pro...
Uloženo v:
| Vydáno v: | Pattern recognition letters Ročník 104; s. 1 - 7 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
01.03.2018
Elsevier Science Ltd |
| Témata: | |
| ISSN: | 0167-8655, 1872-7344 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | •A novel randomized hierarchical alternating least squares algorithm for NMF.•The randomized algorithm scales up to big data.•The algorithm outperforms previous compressed NMF algorithms in speed and accuracy.•Both synthetic and real-world data are used for evaluation.•A Python implementation is provided on GitHub.
Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of ‘big data’ has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper presents a randomized hierarchical alternating least squares (HALS) algorithm to compute the NMF. By deriving a smaller matrix from the nonnegative input data, a more efficient nonnegative decomposition can be computed. Our algorithm scales to big data applications while attaining a near-optimal factorization, i.e., the algorithm scales with the target rank of the data rather than the ambient dimension of measurement space. The proposed algorithm is evaluated using synthetic and real world data and shows substantial speedups compared to deterministic HALS. |
|---|---|
| AbstractList | Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of ‘big data’ has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper presents a randomized hierarchical alternating least squares (HALS) algorithm to compute the NMF. By deriving a smaller matrix from the nonnegative input data, a more efficient nonnegative decomposition can be computed. Our algorithm scales to big data applications while attaining a near-optimal factorization, i.e., the algorithm scales with the target rank of the data rather than the ambient dimension of measurement space. The proposed algorithm is evaluated using synthetic and real world data and shows substantial speedups compared to deterministic HALS. •A novel randomized hierarchical alternating least squares algorithm for NMF.•The randomized algorithm scales up to big data.•The algorithm outperforms previous compressed NMF algorithms in speed and accuracy.•Both synthetic and real-world data are used for evaluation.•A Python implementation is provided on GitHub. Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of ‘big data’ has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper presents a randomized hierarchical alternating least squares (HALS) algorithm to compute the NMF. By deriving a smaller matrix from the nonnegative input data, a more efficient nonnegative decomposition can be computed. Our algorithm scales to big data applications while attaining a near-optimal factorization, i.e., the algorithm scales with the target rank of the data rather than the ambient dimension of measurement space. The proposed algorithm is evaluated using synthetic and real world data and shows substantial speedups compared to deterministic HALS. |
| Author | Kutz, J. Nathan Wihlborn, Sophie Mendible, Ariana Erichson, N. Benjamin |
| Author_xml | – sequence: 1 givenname: N. Benjamin orcidid: 0000-0003-0667-3516 surname: Erichson fullname: Erichson, N. Benjamin email: erichson@uw.edu, nbe@st-andrews.ac.uk organization: Department of Applied Mathematics, University of Washington, Seattle, USA – sequence: 2 givenname: Ariana surname: Mendible fullname: Mendible, Ariana organization: Department of Applied Mathematics, University of Washington, Seattle, USA – sequence: 3 givenname: Sophie orcidid: 0000-0001-8675-0264 surname: Wihlborn fullname: Wihlborn, Sophie organization: Fidelity International, London, UK – sequence: 4 givenname: J. Nathan surname: Kutz fullname: Kutz, J. Nathan organization: Department of Applied Mathematics, University of Washington, Seattle, USA |
| BookMark | eNqFkE9LAzEQxYNUsK1-Aw8Fj7LrJNlNsh4EKfUPFATRc8gmWcnSbmo2LdpPb-p68qBzGRh-7w3vTdCo851F6BxDjgGzqzbfqBiszglgkQPOAfgRGmPBScZpUYzQOGE8E6wsT9Ck71sAYLQSY3T5rDrj125vzSy5dvZNRbezs3UydB-zRunog9uno-9O0XGjVr09-9lT9Hq3eJk_ZMun-8f57TLTVEDMTE1qbCvGSkUbUwqhMQFeAyXMljhtVlWYUBBFQzhwjEldG61NWTGhQJV0ii4G303w71vbR9n6bejSS0mApSkYrxJVDJQOvu-DbeQmuLUKnxKDPNQiWznUIg-1SMAy1ZJk179k2sXveDEot_pPfDOIbYq_czbIXjvbaWtcQqM03v1t8AUPpIFd |
| CitedBy_id | crossref_primary_10_1007_s10015_023_00875_x crossref_primary_10_1007_s10898_022_01167_7 crossref_primary_10_1162_neco_a_01157 crossref_primary_10_1002_nme_6009 crossref_primary_10_5194_gmd_18_2891_2025 crossref_primary_10_1109_ACCESS_2019_2933845 crossref_primary_10_1137_18M118966X crossref_primary_10_1007_s40305_020_00322_9 crossref_primary_10_1109_ACCESS_2019_2933877 crossref_primary_10_1109_TSP_2021_3066258 crossref_primary_10_1137_20M1352405 crossref_primary_10_1016_j_is_2024_102379 crossref_primary_10_1109_TMI_2019_2923466 crossref_primary_10_1109_TSP_2024_3469830 crossref_primary_10_1109_TIT_2025_3529680 crossref_primary_10_1016_j_cmpb_2025_108866 crossref_primary_10_1371_journal_pone_0225265 crossref_primary_10_1007_s10915_025_02976_0 crossref_primary_10_1109_ACCESS_2022_3197291 crossref_primary_10_1109_TETCI_2020_3042268 crossref_primary_10_1137_24M1638355 crossref_primary_10_1109_TMTT_2022_3208917 crossref_primary_10_1145_3432185 crossref_primary_10_1371_journal_pone_0207579 |
| Cites_doi | 10.1002/env.3170050203 10.1007/BF02288367 10.1137/140977898 10.1007/s10107-015-0892-3 10.1109/JSTARS.2012.2194696 10.1073/pnas.0803205106 10.1109/TSP.2016.2516971 10.1038/44565 10.1145/2842602 10.1587/transfun.E92.A.708 10.1137/090771806 10.1109/34.41390 10.1109/5.726791 10.1088/2632-2153/ab8240 10.1137/12086755X 10.1137/130938700 10.1016/j.csda.2006.11.006 10.1109/34.927464 10.1162/NECO_a_00256 10.1109/LSP.2014.2374838 10.1007/s10898-013-0035-4 10.1137/080736417 |
| ContentType | Journal Article |
| Copyright | 2018 Elsevier B.V. Copyright Elsevier Science Ltd. Mar 1, 2018 |
| Copyright_xml | – notice: 2018 Elsevier B.V. – notice: Copyright Elsevier Science Ltd. Mar 1, 2018 |
| DBID | AAYXX CITATION 7SC 7TK 8FD JQ2 L7M L~C L~D |
| DOI | 10.1016/j.patrec.2018.01.007 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Neurosciences Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest Computer Science Collection Computer and Information Systems Abstracts Neurosciences Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EISSN | 1872-7344 |
| EndPage | 7 |
| ExternalDocumentID | 10_1016_j_patrec_2018_01_007 S0167865518300138 |
| GroupedDBID | --M .DC .~1 0R~ 123 1RT 1~. 1~5 4.4 457 4G. 53G 5VS 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXUO AAYFN ABBOA ABFNM ABFRF ABJNI ABMAC ABYKQ ACDAQ ACGFO ACGFS ACRLP ACZNC ADBBV ADEZE ADTZH AEBSH AECPX AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD AXJTR BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EO8 EO9 EP2 EP3 F5P FDB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ J1W JJJVA KOM LG9 LY1 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 RIG RNS ROL SDF SDG SDP SES SPC SPCBC SST SSV SSZ T5K TN5 UNMZH WH7 XPP ZMT ~G- --K 1B1 29O 9DU AAQXK AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADJOM ADMUD ADMXK ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS EJD FEDTE FGOYB HLZ HVGLF HZ~ IHE R2- RPZ SBC SDS SEW VOH WUQ Y6R ~HD 7SC 7TK 8FD AFXIZ AGCQF AGRNS JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c380t-db2b1e9665a3fd588c1207b0326e51b03699123084f2707112bbdccd5968a0a53 |
| ISICitedReferencesCount | 33 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000425990600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0167-8655 |
| IngestDate | Sat Jul 26 03:14:21 EDT 2025 Sat Nov 29 07:22:52 EST 2025 Tue Nov 18 21:51:59 EST 2025 Fri Feb 23 02:24:34 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Randomized algorithm Dimension reduction NMF |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c380t-db2b1e9665a3fd588c1207b0326e51b03699123084f2707112bbdccd5968a0a53 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-0667-3516 0000-0001-8675-0264 |
| OpenAccessLink | https://doi.org/10.1016/j.patrec.2018.01.007 |
| PQID | 2066664679 |
| PQPubID | 2047552 |
| PageCount | 7 |
| ParticipantIDs | proquest_journals_2066664679 crossref_primary_10_1016_j_patrec_2018_01_007 crossref_citationtrail_10_1016_j_patrec_2018_01_007 elsevier_sciencedirect_doi_10_1016_j_patrec_2018_01_007 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-03-01 2018-03-00 20180301 |
| PublicationDateYYYYMMDD | 2018-03-01 |
| PublicationDate_xml | – month: 03 year: 2018 text: 2018-03-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Pattern recognition letters |
| PublicationYear | 2018 |
| Publisher | Elsevier B.V Elsevier Science Ltd |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier Science Ltd |
| References | Cohen, Farias, Comon (bib0007) 2015; 22 Gillis, Glineur (bib0015) 2012; 24 N.B. Erichson, K. Manohar, S.L. Brunton, J.N. Kutz, Randomized CP tensor decomposition, Preprint arXiv A. Szlam, Y. Kluger, M. Tygert, An implementation of a randomized algorithm for principal component analysis, Preprint arXiv N.B. Erichson, S. Voronin, S.L. Brunton, J.N. Kutz, Randomized matrix decompositions using r, arXiv preprint arXiv Georghiades, Belhumeur, Kriegman (bib0012) 2001; 23 Boutsidis, Drineas, Magdon-Ismail (bib0004) 2014; 43 Boutsidis, Woodruff (bib0005) 2017; 46 Pedregosa, Varoquaux, Gramfort, Michel, Thirion, Grisel, Blondel, Prettenhofer, Weiss, Dubourg, Vanderplas, Passos, Cournapeau, Brucher, Perrot, Duchesnay (bib0029) 2011; 12 Kirby, Sirovich (bib0020) 1990; 12 Gillis (bib0013) 2014 Lee, Seung (bib0024) 2001 Arora, Ge, Kannan, Moitra (bib0001) 2012 Drineas, Mahoney (bib0008) 2016; 59 Zhou, Bian, Tao (bib0039) 2013 N. Gillis, Introduction to nonnegative matrix factorization, arXiv preprint arXiv Halko, Martinsson, Tropp (bib0017) 2011; 53 A.N. Langville, C.D. Meyer, R. Albright, J. Cox, D. Duling, Algorithms, initializations, and convergence for the nonnegative matrix factorization, arXiv preprint arXiv Kim, He, Park (bib0018) 2014; 58 Berry, Browne, Langville, Pauca, Plemmons (bib0002) 2007; 52 Paatero, Tapper (bib0028) 1994; 5 (2014) 1–13. Rokhlin, Szlam, Tygert (bib0030) 2009; 31 Zhou, Tao (bib0040) 2012 Mahoney, Drineas (bib0026) 2009; 106 M. Udell, A. Townsend, Nice latent variable models have log-rank, arXiv preprint arXiv Kimura, Tanaka, Kudo (bib0019) 2015; 39 (2016) 1–55. Wright (bib0038) 2015; 151 (2014). (2017) 1–29. (2015) 1–15. Wang, Zhang, Zhang (bib0037) 2016; 17 Lee, Seung (bib0023) 1999; 401 Mahoney (bib0025) 2011; 3 Bioucas-Dias, Plaza, Dobigeon, Parente, Du, Gader, Chanussot (bib0003) 2012; 5 Lecun, Bottou, Bengio, Haffner (bib0022) 1998; 86 Cichocki, Anh-Huy (bib0006) 2009; 92 Wang, Zhang (bib0036) 2013; 14 P.-G. Martinsson, Randomized methods for matrix computations and analysis of high dimensional data, Preprint arXiv (2017). (2016). Tepper, Sapiro (bib0032) 2016; 64 Gu (bib0016) 2015; 37 S. Voronin, P.-G. Martinsson, Rsvdpack: subroutines for computing partial singular value decompositions via randomized sampling on single core, multi core, and GPU architectures, Preprint arXiv Eckart, Young (bib0009) 1936; 1 Turk, Pentland (bib0033) 1991 Boutsidis (10.1016/j.patrec.2018.01.007_bib0005) 2017; 46 Wang (10.1016/j.patrec.2018.01.007_bib0037) 2016; 17 Cohen (10.1016/j.patrec.2018.01.007_bib0007) 2015; 22 Rokhlin (10.1016/j.patrec.2018.01.007_bib0030) 2009; 31 Georghiades (10.1016/j.patrec.2018.01.007_bib0012) 2001; 23 Pedregosa (10.1016/j.patrec.2018.01.007_bib0029) 2011; 12 Tepper (10.1016/j.patrec.2018.01.007_bib0032) 2016; 64 Wang (10.1016/j.patrec.2018.01.007_bib0036) 2013; 14 10.1016/j.patrec.2018.01.007_bib0027 Kim (10.1016/j.patrec.2018.01.007_bib0018) 2014; 58 Kimura (10.1016/j.patrec.2018.01.007_bib0019) 2015; 39 10.1016/j.patrec.2018.01.007_bib0021 Berry (10.1016/j.patrec.2018.01.007_bib0002) 2007; 52 Paatero (10.1016/j.patrec.2018.01.007_bib0028) 1994; 5 Gillis (10.1016/j.patrec.2018.01.007_bib0015) 2012; 24 Bioucas-Dias (10.1016/j.patrec.2018.01.007_bib0003) 2012; 5 Wright (10.1016/j.patrec.2018.01.007_bib0038) 2015; 151 Gillis (10.1016/j.patrec.2018.01.007_bib0013) 2014 Gu (10.1016/j.patrec.2018.01.007_bib0016) 2015; 37 Zhou (10.1016/j.patrec.2018.01.007_bib0040) 2012 Drineas (10.1016/j.patrec.2018.01.007_bib0008) 2016; 59 Lecun (10.1016/j.patrec.2018.01.007_bib0022) 1998; 86 Kirby (10.1016/j.patrec.2018.01.007_bib0020) 1990; 12 Arora (10.1016/j.patrec.2018.01.007_bib0001) 2012 Turk (10.1016/j.patrec.2018.01.007_bib0033) 1991 10.1016/j.patrec.2018.01.007_bib0014 Lee (10.1016/j.patrec.2018.01.007_bib0023) 1999; 401 10.1016/j.patrec.2018.01.007_bib0035 Cichocki (10.1016/j.patrec.2018.01.007_bib0006) 2009; 92 10.1016/j.patrec.2018.01.007_bib0010 10.1016/j.patrec.2018.01.007_bib0031 Mahoney (10.1016/j.patrec.2018.01.007_bib0025) 2011; 3 10.1016/j.patrec.2018.01.007_bib0034 10.1016/j.patrec.2018.01.007_bib0011 Zhou (10.1016/j.patrec.2018.01.007_bib0039) 2013 Mahoney (10.1016/j.patrec.2018.01.007_bib0026) 2009; 106 Halko (10.1016/j.patrec.2018.01.007_bib0017) 2011; 53 Eckart (10.1016/j.patrec.2018.01.007_bib0009) 1936; 1 Lee (10.1016/j.patrec.2018.01.007_bib0024) 2001 Boutsidis (10.1016/j.patrec.2018.01.007_bib0004) 2014; 43 |
| References_xml | – volume: 43 start-page: 687 year: 2014 end-page: 717 ident: bib0004 article-title: Near-optimal column-based matrix reconstruction publication-title: SIAM J. Comput. – volume: 1 start-page: 211 year: 1936 end-page: 218 ident: bib0009 article-title: The approximation of one matrix by another of lower rank publication-title: Psychometrika – volume: 37 start-page: 1139 year: 2015 end-page: 1173 ident: bib0016 article-title: Subspace iteration randomization and singular value problems publication-title: SIAM J. Sci. Comput. – start-page: 257 year: 2014 end-page: 291 ident: bib0013 article-title: The Why and How of Nonnegative Matrix Factorization publication-title: Regularization, Optimization, Kernels, and Support Vector Machines – reference: (2016) 1–55. – volume: 12 start-page: 103 year: 1990 end-page: 108 ident: bib0020 article-title: Application of the Karhunen–Loeve procedure for the characterization of human faces publication-title: Pattern Anal. Mach. Intell. IEEE Trans. – volume: 31 start-page: 1100 year: 2009 end-page: 1124 ident: bib0030 article-title: A randomized algorithm for principal component analysis publication-title: SIAM J. Matrix Anal. Appl. – reference: (2016). – reference: N.B. Erichson, K. Manohar, S.L. Brunton, J.N. Kutz, Randomized CP tensor decomposition, Preprint arXiv: – start-page: 586 year: 1991 end-page: 591 ident: bib0033 article-title: Face recognition using eigenfaces publication-title: Proceedings on Computer Vision and Pattern Recognition – volume: 22 start-page: 862 year: 2015 end-page: 866 ident: bib0007 article-title: Fast decomposition of large nonnegative tensors publication-title: IEEE Signal Process. Lett. – reference: N. Gillis, Introduction to nonnegative matrix factorization, arXiv preprint arXiv: – volume: 151 start-page: 3 year: 2015 end-page: 34 ident: bib0038 article-title: Coordinate descent algorithms publication-title: Math. Program. – volume: 5 start-page: 111 year: 1994 end-page: 126 ident: bib0028 article-title: Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values publication-title: Environmetrics – volume: 92 start-page: 708 year: 2009 end-page: 721 ident: bib0006 article-title: Fast local algorithms for large scale nonnegative matrix and tensor factorizations publication-title: IEICE Trans. Fundam. Electr. Commun. Comput. Sci. – volume: 64 start-page: 2269 year: 2016 end-page: 2283 ident: bib0032 article-title: Compressed nonnegative matrix factorization is fast and accurate publication-title: IEEE Trans. Signal Process. – reference: A. Szlam, Y. Kluger, M. Tygert, An implementation of a randomized algorithm for principal component analysis, Preprint arXiv: – volume: 52 start-page: 155 year: 2007 end-page: 173 ident: bib0002 article-title: Algorithms and applications for approximate nonnegative matrix factorization publication-title: Comput. Stat. Data Anal. – volume: 58 start-page: 285 year: 2014 end-page: 319 ident: bib0018 article-title: Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework publication-title: J. Global Optim. – reference: (2014) 1–13. – start-page: 556 year: 2001 end-page: 562 ident: bib0024 article-title: Algorithms for Non-negative Matrix Factorization publication-title: Advances in Neural Information Processing Systems – volume: 23 start-page: 643 year: 2001 end-page: 660 ident: bib0012 article-title: From few to many: illumination cone models for face recognition under variable lighting and pose publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – reference: M. Udell, A. Townsend, Nice latent variable models have log-rank, arXiv preprint arXiv: – reference: (2014). – volume: 12 start-page: 2825 year: 2011 end-page: 2830 ident: bib0029 article-title: Scikit-learn: machine learning in python publication-title: J. Mach. Learn. Res. – volume: 5 start-page: 354 year: 2012 end-page: 379 ident: bib0003 article-title: Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches publication-title: IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. – volume: 3 start-page: 123 year: 2011 end-page: 224 ident: bib0025 article-title: Randomized algorithms for matrices and data publication-title: Found. Trends Mach. Learn. – volume: 14 start-page: 2729 year: 2013 end-page: 2769 ident: bib0036 article-title: Improving cur matrix decomposition and the nyström approximation via adaptive sampling publication-title: J. Mach. Learn. Res. – start-page: 145 year: 2012 end-page: 162 ident: bib0001 article-title: Computing a nonnegative matrix factorization–provably publication-title: Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing – reference: N.B. Erichson, S. Voronin, S.L. Brunton, J.N. Kutz, Randomized matrix decompositions using r, arXiv preprint arXiv: – volume: 39 start-page: 129 year: 2015 end-page: 141 ident: bib0019 article-title: A Fast Hierarchical Alternating Least Squares Algorithm for Orthogonal Nonnegative Matrix Factorization publication-title: Proceedings of the Sixth Asian Conference on Machine Learning – reference: (2015) 1–15. – volume: 24 start-page: 1085 year: 2012 end-page: 1105 ident: bib0015 article-title: Accelerated multiplicative updates and hierarchical als algorithms for nonnegative matrix factorization publication-title: Neural Comput. – reference: P.-G. Martinsson, Randomized methods for matrix computations and analysis of high dimensional data, Preprint arXiv: – volume: 17 start-page: 1 year: 2016 end-page: 49 ident: bib0037 article-title: Towards more efficient spsd matrix approximation and cur matrix decomposition publication-title: J. Mach. Learn. Res. – reference: (2017) 1–29. – volume: 46 start-page: 543 year: 2017 end-page: 589 ident: bib0005 article-title: Optimal cur matrix decompositions publication-title: SIAM J. Comput. – volume: 86 start-page: 2278 year: 1998 end-page: 2324 ident: bib0022 article-title: Gradient-based learning applied to document recognition publication-title: Proc. IEEE – start-page: 1286 year: 2012 end-page: 1290 ident: bib0040 article-title: Bilateral random projections publication-title: Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on – reference: A.N. Langville, C.D. Meyer, R. Albright, J. Cox, D. Duling, Algorithms, initializations, and convergence for the nonnegative matrix factorization, arXiv preprint arXiv: – volume: 401 start-page: 788 year: 1999 end-page: 791 ident: bib0023 article-title: Learning the parts of objects by non-negative matrix factorization publication-title: Nature – volume: 106 start-page: 697 year: 2009 end-page: 702 ident: bib0026 article-title: Cur matrix decompositions for improved data analysis publication-title: Proc. Natl. Acad. Sci. – reference: S. Voronin, P.-G. Martinsson, Rsvdpack: subroutines for computing partial singular value decompositions via randomized sampling on single core, multi core, and GPU architectures, Preprint arXiv: – volume: 59 start-page: 80 year: 2016 end-page: 90 ident: bib0008 article-title: Randnla: randomized numerical linear algebra publication-title: Commun. ACM – volume: 53 start-page: 217 year: 2011 end-page: 288 ident: bib0017 article-title: Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions publication-title: SIAM Rev. – start-page: 917 year: 2013 end-page: 926 ident: bib0039 article-title: Divide-and-conquer anchoring for near-separable nonnegative matrix factorization and completion in high dimensions publication-title: Data Mining (ICDM), 2013 IEEE 13th International Conference on – reference: (2017). – volume: 5 start-page: 111 issue: 2 year: 1994 ident: 10.1016/j.patrec.2018.01.007_bib0028 article-title: Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values publication-title: Environmetrics doi: 10.1002/env.3170050203 – volume: 1 start-page: 211 issue: 3 year: 1936 ident: 10.1016/j.patrec.2018.01.007_bib0009 article-title: The approximation of one matrix by another of lower rank publication-title: Psychometrika doi: 10.1007/BF02288367 – volume: 14 start-page: 2729 issue: 1 year: 2013 ident: 10.1016/j.patrec.2018.01.007_bib0036 article-title: Improving cur matrix decomposition and the nyström approximation via adaptive sampling publication-title: J. Mach. Learn. Res. – volume: 46 start-page: 543 issue: 2 year: 2017 ident: 10.1016/j.patrec.2018.01.007_bib0005 article-title: Optimal cur matrix decompositions publication-title: SIAM J. Comput. doi: 10.1137/140977898 – volume: 17 start-page: 1 issue: 210 year: 2016 ident: 10.1016/j.patrec.2018.01.007_bib0037 article-title: Towards more efficient spsd matrix approximation and cur matrix decomposition publication-title: J. Mach. Learn. Res. – ident: 10.1016/j.patrec.2018.01.007_bib0035 – volume: 151 start-page: 3 issue: 1 year: 2015 ident: 10.1016/j.patrec.2018.01.007_bib0038 article-title: Coordinate descent algorithms publication-title: Math. Program. doi: 10.1007/s10107-015-0892-3 – ident: 10.1016/j.patrec.2018.01.007_bib0014 – start-page: 145 year: 2012 ident: 10.1016/j.patrec.2018.01.007_bib0001 article-title: Computing a nonnegative matrix factorization–provably – volume: 3 start-page: 123 issue: 2 year: 2011 ident: 10.1016/j.patrec.2018.01.007_bib0025 article-title: Randomized algorithms for matrices and data publication-title: Found. Trends Mach. Learn. – volume: 12 start-page: 2825 year: 2011 ident: 10.1016/j.patrec.2018.01.007_bib0029 article-title: Scikit-learn: machine learning in python publication-title: J. Mach. Learn. Res. – volume: 5 start-page: 354 issue: 2 year: 2012 ident: 10.1016/j.patrec.2018.01.007_bib0003 article-title: Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches publication-title: IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. doi: 10.1109/JSTARS.2012.2194696 – start-page: 1286 year: 2012 ident: 10.1016/j.patrec.2018.01.007_bib0040 article-title: Bilateral random projections – start-page: 257 year: 2014 ident: 10.1016/j.patrec.2018.01.007_bib0013 article-title: The Why and How of Nonnegative Matrix Factorization – volume: 106 start-page: 697 issue: 3 year: 2009 ident: 10.1016/j.patrec.2018.01.007_bib0026 article-title: Cur matrix decompositions for improved data analysis publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.0803205106 – volume: 64 start-page: 2269 issue: 9 year: 2016 ident: 10.1016/j.patrec.2018.01.007_bib0032 article-title: Compressed nonnegative matrix factorization is fast and accurate publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2016.2516971 – volume: 401 start-page: 788 issue: 6755 year: 1999 ident: 10.1016/j.patrec.2018.01.007_bib0023 article-title: Learning the parts of objects by non-negative matrix factorization publication-title: Nature doi: 10.1038/44565 – start-page: 917 year: 2013 ident: 10.1016/j.patrec.2018.01.007_bib0039 article-title: Divide-and-conquer anchoring for near-separable nonnegative matrix factorization and completion in high dimensions – volume: 59 start-page: 80 issue: 6 year: 2016 ident: 10.1016/j.patrec.2018.01.007_bib0008 article-title: Randnla: randomized numerical linear algebra publication-title: Commun. ACM doi: 10.1145/2842602 – ident: 10.1016/j.patrec.2018.01.007_bib0027 – start-page: 586 year: 1991 ident: 10.1016/j.patrec.2018.01.007_bib0033 article-title: Face recognition using eigenfaces – volume: 92 start-page: 708 issue: 3 year: 2009 ident: 10.1016/j.patrec.2018.01.007_bib0006 article-title: Fast local algorithms for large scale nonnegative matrix and tensor factorizations publication-title: IEICE Trans. Fundam. Electr. Commun. Comput. Sci. doi: 10.1587/transfun.E92.A.708 – volume: 53 start-page: 217 issue: 2 year: 2011 ident: 10.1016/j.patrec.2018.01.007_bib0017 article-title: Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions publication-title: SIAM Rev. doi: 10.1137/090771806 – volume: 12 start-page: 103 issue: 1 year: 1990 ident: 10.1016/j.patrec.2018.01.007_bib0020 article-title: Application of the Karhunen–Loeve procedure for the characterization of human faces publication-title: Pattern Anal. Mach. Intell. IEEE Trans. doi: 10.1109/34.41390 – ident: 10.1016/j.patrec.2018.01.007_bib0021 – start-page: 556 year: 2001 ident: 10.1016/j.patrec.2018.01.007_bib0024 article-title: Algorithms for Non-negative Matrix Factorization – volume: 86 start-page: 2278 issue: 11 year: 1998 ident: 10.1016/j.patrec.2018.01.007_bib0022 article-title: Gradient-based learning applied to document recognition publication-title: Proc. IEEE doi: 10.1109/5.726791 – ident: 10.1016/j.patrec.2018.01.007_bib0011 – ident: 10.1016/j.patrec.2018.01.007_bib0010 doi: 10.1088/2632-2153/ab8240 – volume: 43 start-page: 687 issue: 2 year: 2014 ident: 10.1016/j.patrec.2018.01.007_bib0004 article-title: Near-optimal column-based matrix reconstruction publication-title: SIAM J. Comput. doi: 10.1137/12086755X – ident: 10.1016/j.patrec.2018.01.007_bib0034 – volume: 37 start-page: 1139 issue: 3 year: 2015 ident: 10.1016/j.patrec.2018.01.007_bib0016 article-title: Subspace iteration randomization and singular value problems publication-title: SIAM J. Sci. Comput. doi: 10.1137/130938700 – volume: 52 start-page: 155 issue: 1 year: 2007 ident: 10.1016/j.patrec.2018.01.007_bib0002 article-title: Algorithms and applications for approximate nonnegative matrix factorization publication-title: Comput. Stat. Data Anal. doi: 10.1016/j.csda.2006.11.006 – volume: 23 start-page: 643 issue: 6 year: 2001 ident: 10.1016/j.patrec.2018.01.007_bib0012 article-title: From few to many: illumination cone models for face recognition under variable lighting and pose publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.927464 – ident: 10.1016/j.patrec.2018.01.007_bib0031 – volume: 24 start-page: 1085 issue: 4 year: 2012 ident: 10.1016/j.patrec.2018.01.007_bib0015 article-title: Accelerated multiplicative updates and hierarchical als algorithms for nonnegative matrix factorization publication-title: Neural Comput. doi: 10.1162/NECO_a_00256 – volume: 22 start-page: 862 issue: 7 year: 2015 ident: 10.1016/j.patrec.2018.01.007_bib0007 article-title: Fast decomposition of large nonnegative tensors publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2014.2374838 – volume: 58 start-page: 285 issue: 2 year: 2014 ident: 10.1016/j.patrec.2018.01.007_bib0018 article-title: Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework publication-title: J. Global Optim. doi: 10.1007/s10898-013-0035-4 – volume: 39 start-page: 129 year: 2015 ident: 10.1016/j.patrec.2018.01.007_bib0019 article-title: A Fast Hierarchical Alternating Least Squares Algorithm for Orthogonal Nonnegative Matrix Factorization – volume: 31 start-page: 1100 issue: 3 year: 2009 ident: 10.1016/j.patrec.2018.01.007_bib0030 article-title: A randomized algorithm for principal component analysis publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/080736417 |
| SSID | ssj0006398 |
| Score | 2.4638472 |
| Snippet | •A novel randomized hierarchical alternating least squares algorithm for NMF.•The randomized algorithm scales up to big data.•The algorithm outperforms... Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of ‘big data’ has severely challenged our ability to compute... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1 |
| SubjectTerms | Algorithms Big Data Data management Data mining Data processing Decomposition Dimension reduction Factorization Matrix NMF Numerical analysis Probability Randomization Randomized algorithm Randomized algorithms |
| Title | Randomized nonnegative matrix factorization |
| URI | https://dx.doi.org/10.1016/j.patrec.2018.01.007 https://www.proquest.com/docview/2066664679 |
| Volume | 104 |
| WOSCitedRecordID | wos000425990600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-7344 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0006398 issn: 0167-8655 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEF5BywEOPAqIQkE-IC6RkXf92PUxoFRQSqhQKuW2Wu9uGkeJG5oURfx6Zl92yqtw4OJYjh_JzOfZ2dmZbxB6SbBIy9Rw7AtJ4ozIJC6rSsc5pYqojBmU2GYTdDhk43F54qNKK9tOgDYN22zK5X9VNRwDZZvS2X9Qd3tTOAD7oHTYgtph-1eK_ywadb6ov5l1fZPFcuaovReGi3_j--v44sttz_TEEm2a4hafUQSwmNtan87rBps5DRVavTe6mYlF3YLro25UXbns5D78z6Yz-PV0DlBzkdbz5bRuwfTh0raT7R2ZpOmpB6qPQWDWJWG5wFgojgn2qMtIsjFLsMWm_tUNOc7OMgqOfeqoH1tDnGRbphT_0sC7WMPstVkp0IaCEjNLu-pa517l0x5-4oenx8d8NBiPXi2_xKbVmFmS931XbqJdQvMSjONu__1gfNQO4OC0sUAJb353qLi0aYE_P_h3Hs0PY7t1WEb30V0_04j6DiEP0A3d7KF7oYtH5IW4h-5sUVI-RL0OPtEWfCIHn-gKfB6h08PB6O272DfUiGXKknWsKlJhDRPcXKQTlTMmMUlolYALr3MMnwXMFmBOyrIJoeB7YlJVSkqVlwUTicjTx2gHHq2foIiB8dZEFCqVMCmgRTkpGMukgLtneUayfZQGoXDp2eZN05M5D2mFM-5EyY0oeYI5iHIfxe1VS8e2cs35NMibe4_ReYIc8HLNlQdBPdy_vCtuWhsUBbgO5dM_f_0M3e5egwO0s7641M_RLfl1Xa8uXng8fQcLDZRQ |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Randomized+nonnegative+matrix+factorization&rft.jtitle=Pattern+recognition+letters&rft.au=Erichson%2C+N+Benjamin&rft.au=Mendible%2C+Ariana&rft.au=Wihlborn%2C+Sophie&rft.au=Kutz%2C+J+Nathan&rft.date=2018-03-01&rft.pub=Elsevier+Science+Ltd&rft.issn=0167-8655&rft.eissn=1872-7344&rft.volume=104&rft.spage=1&rft_id=info:doi/10.1016%2Fj.patrec.2018.01.007&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-8655&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-8655&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-8655&client=summon |