On the Convergence of Block Majorization-Minimization Algorithms on the Grassmann Manifold
The Majorization-Minimization (MM) framework is widely used to derive efficient algorithms for specific problems that require the optimization of a cost function (which can be convex or not). It is based on a sequential optimization of a surrogate function over closed convex sets. A natural extensio...
Uloženo v:
| Vydáno v: | IEEE signal processing letters Ročník 31; s. 1314 - 1318 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
IEEE
2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 1070-9908, 1558-2361 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | The Majorization-Minimization (MM) framework is widely used to derive efficient algorithms for specific problems that require the optimization of a cost function (which can be convex or not). It is based on a sequential optimization of a surrogate function over closed convex sets. A natural extension of this framework incorporates ideas of Block Coordinate Descent (BCD) algorithms into the MM framework, also known as block MM. The rationale behind the block extension is to partition the optimization variables into several independent blocks, to obtain a surrogate for each block, and to optimize the surrogate of each block cyclically. However, known convergence proofs of the block MM are only valid under the assumption that the constraint sets are closed and convex. Hence, the global convergence of the block MM is not ensured for non-convex sets by classical proofs, which is needed in iterative schemes that naturally emerge in a wide range of subspace-based signal processing applications. For this purpose, the aim of this letter is to review the convergence proof of the block MM and extend it for blocks constrained in the Grassmann manifold. |
|---|---|
| AbstractList | The Majorization-Minimization (MM) framework is widely used to derive efficient algorithms for specific problems that require the optimization of a cost function (which can be convex or not). It is based on a sequential optimization of a surrogate function over closed convex sets. A natural extension of this framework incorporates ideas of Block Coordinate Descent (BCD) algorithms into the MM framework, also known as block MM. The rationale behind the block extension is to partition the optimization variables into several independent blocks, to obtain a surrogate for each block, and to optimize the surrogate of each block cyclically. However, known convergence proofs of the block MM are only valid under the assumption that the constraint sets are closed and convex. Hence, the global convergence of the block MM is not ensured for non-convex sets by classical proofs, which is needed in iterative schemes that naturally emerge in a wide range of subspace-based signal processing applications. For this purpose, the aim of this letter is to review the convergence proof of the block MM and extend it for blocks constrained in the Grassmann manifold. |
| Author | Lopez, Carlos Alejandro Riba, Jaume |
| Author_xml | – sequence: 1 givenname: Carlos Alejandro orcidid: 0000-0002-2216-2786 surname: Lopez fullname: Lopez, Carlos Alejandro email: carlos.alejandro.lopez@upc.edu organization: Signal Processing and Communications Group, Department de Teoria del Senyal i Comunicacions, Universitat Politècnica de Catalunya, Barcelona, Spain – sequence: 2 givenname: Jaume orcidid: 0000-0002-5515-8169 surname: Riba fullname: Riba, Jaume email: jaume.riba@upc.edu organization: Signal Processing and Communications Group, Department de Teoria del Senyal i Comunicacions, Universitat Politècnica de Catalunya, Barcelona, Spain |
| BookMark | eNp9kLFOwzAQQC0EEm1hZ2CIxJxyjhPHHksFBalVkYCFJXIdu3VJ7WKnSPD1uKQDYmC6O929O93ro2PrrELoAsMQY-DX06fHYQZZPiSEU0rhCPVwUbA0IxQfxxxKSDkHdor6IawBgGFW9NDr3CbtSiVjZz-UXyorVeJ0ctM4-ZbMxNp58yVa42w6M9ZsDkUyapax0642IXHdgokXIWyEtZGyRrumPkMnWjRBnR_iAL3c3T6P79PpfPIwHk1TSUjeppzWmBe6VAww1mUGEvNSylpiqXOthFpoSoTOmSpqnVHNuATGGGVkIaGsGRmgq27v1rv3nQpttXY7b-PJikBR4JID0DgF3ZT0LgSvdLX1ZiP8Z4Wh2husosFqb7A6GIwI_YNI0_7833phmv_Ayw40SqlfdwrMonbyDcEcgLs |
| CODEN | ISPLEM |
| CitedBy_id | crossref_primary_10_1109_TSP_2024_3488554 crossref_primary_10_1109_TVT_2025_3550184 |
| Cites_doi | 10.1162/08997660360581958 10.1109/18.978730 10.1137/S0895479895290954 10.1109/CVPR.2017.466 10.1109/IJCNN.2008.4634046 10.1137/19m1243956 10.1109/ALLERTON.2010.5706976 10.1109/TSP.2016.2601299 10.1109/ICASSP39728.2021.9415032 10.1090/S0002-9947-1986-0857446-4 10.1007/s10444-023-10090-8 10.1109/TSP.2007.909335 10.1109/ICACCS54159.2022.9785082 10.1137/120891009 10.1073/pnas.60.1.75 10.1023/a:1017501703105 10.1109/TIP.2007.904387 10.1561/2400000003 10.1109/TSP.2015.2421485 10.1214/08-sts264 10.1109/TSP.2021.3058442 10.1137/18M122457X |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2024 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2024 |
| DBID | 97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/LSP.2024.3396660 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE/IET Electronic Library CrossRef Computer and Information Systems Abstracts Electronics & Communications 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 Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE/IET Electronic Library url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1558-2361 |
| EndPage | 1318 |
| ExternalDocumentID | 10_1109_LSP_2024_3396660 10518081 |
| Genre | orig-research |
| GrantInformation_xml | – fundername: 2023 FI-3 00155 by Generalitat de Catalunya and the European Social Fund – fundername: MAYTE (PID2022-136512OB-C21 financed by MCIN/AEI/10.13039/501100011033 – fundername: ERDF A way of making Europe – fundername: RODIN (PID2019-105717RB-C22/AEI/10.13039/501100011033) grantid: 2021 SGR 01033 |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 85S 97E AAJGR AARMG AASAJ AAWTH AAYJJ ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACIWK AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD F5P HZ~ H~9 ICLAB IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P RIA RIE RNS TAE TN5 VH1 AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c334t-96d195f7e8011f720c197ccdc1cf4feaebf63af48e5df26f89c0888683bc07d83 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001224409900006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1070-9908 |
| IngestDate | Mon Jun 30 10:15:36 EDT 2025 Sat Nov 29 03:38:55 EST 2025 Tue Nov 18 20:42:39 EST 2025 Wed Aug 27 02:05:23 EDT 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c334t-96d195f7e8011f720c197ccdc1cf4feaebf63af48e5df26f89c0888683bc07d83 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-5515-8169 0000-0002-2216-2786 |
| OpenAccessLink | http://hdl.handle.net/2117/416725 |
| PQID | 3055179006 |
| PQPubID | 75747 |
| PageCount | 5 |
| ParticipantIDs | proquest_journals_3055179006 crossref_citationtrail_10_1109_LSP_2024_3396660 crossref_primary_10_1109_LSP_2024_3396660 ieee_primary_10518081 |
| PublicationCentury | 2000 |
| PublicationDate | 20240000 2024-00-00 20240101 |
| PublicationDateYYYYMMDD | 2024-01-01 |
| PublicationDate_xml | – year: 2024 text: 20240000 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE signal processing letters |
| PublicationTitleAbbrev | LSP |
| PublicationYear | 2024 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 Zhu (ref24) 2018; 31 Lau (ref26) 2020 ref12 ref15 ref14 ref30 ref33 ref10 ref32 ref2 ref1 Ahn (ref17) 2021 ref16 ref19 ref18 Yuan (ref22) 2013; 14 Zhou (ref5) 2012; 56 Zhang (ref31) 2018 Vishnoi (ref28) 2018 ref25 ref20 Liu (ref29) 2017; 30 ref27 ref8 ref7 ref9 Qu (ref23) 2019; 32 ref4 ref3 ref6 Landgraf (ref21) 2020; 180 Jolliffe (ref11) 1986 |
| References_xml | – ident: ref6 doi: 10.1162/08997660360581958 – ident: ref18 doi: 10.1109/18.978730 – volume: 30 volume-title: Proc. Adv. Neural Inf. Process. Syst. year: 2017 ident: ref29 article-title: Accelerated first-order methods for geodesically convex optimization on riemannian manifolds – volume: 14 start-page: 899 issue: 28 volume-title: J. Mach. Learn. Res. year: 2013 ident: ref22 article-title: Truncated power method for sparse eigenvalue problems – volume-title: Proc. 8th Int. Conf. Learn. Representations year: 2020 ident: ref26 article-title: Short-and-sparse deconvolution - a. geometric approach – ident: ref10 doi: 10.1137/S0895479895290954 – ident: ref25 doi: 10.1109/CVPR.2017.466 – ident: ref16 doi: 10.1109/IJCNN.2008.4634046 – ident: ref8 doi: 10.1137/19m1243956 – volume: 32 volume-title: Proc. Adv. Neural Inf. Process. Syst. year: 2019 ident: ref23 article-title: A nonconvex approach for exact and efficient multichannel sparse blind deconvolution – ident: ref13 doi: 10.1109/ALLERTON.2010.5706976 – volume: 56 start-page: 3909 issue: 12 volume-title: Comput. Statist. Data Anal. year: 2012 ident: ref5 article-title: EM vs MM: A case study – ident: ref3 doi: 10.1109/TSP.2016.2601299 – ident: ref14 doi: 10.1109/ICASSP39728.2021.9415032 – ident: ref20 doi: 10.1090/S0002-9947-1986-0857446-4 – ident: ref30 doi: 10.1007/s10444-023-10090-8 – year: 2018 ident: ref31 article-title: Grassmannian learning: Embedding geometry awareness in shallow and deep learning – ident: ref15 doi: 10.1109/TSP.2007.909335 – ident: ref1 doi: 10.1109/ICACCS54159.2022.9785082 – ident: ref9 doi: 10.1137/120891009 – year: 2021 ident: ref17 article-title: Riemannian perspective on matrix factorization – volume: 31 volume-title: Proc. Adv. Neural Inf. Process. Syst. year: 2018 ident: ref24 article-title: Dual principal component pursuit: Improved analysis and efficient algorithms – ident: ref32 doi: 10.1073/pnas.60.1.75 – start-page: 115 year: 1986 ident: ref11 publication-title: Principal Compon. Anal. and Factor Anal. – year: 2018 ident: ref28 article-title: Geodesic convex optimization: Differentiation on manifolds, geodesics, and convexity – ident: ref33 doi: 10.1023/a:1017501703105 – ident: ref2 doi: 10.1109/TIP.2007.904387 – volume: 180 volume-title: J. Multivariate Anal. year: 2020 ident: ref21 article-title: Dimensionality reduction for binary data through the projection of natural parameters – ident: ref7 doi: 10.1561/2400000003 – ident: ref12 doi: 10.1109/TSP.2015.2421485 – ident: ref4 doi: 10.1214/08-sts264 – ident: ref19 doi: 10.1109/TSP.2021.3058442 – ident: ref27 doi: 10.1137/18M122457X |
| SSID | ssj0008185 |
| Score | 2.4198878 |
| Snippet | The Majorization-Minimization (MM) framework is widely used to derive efficient algorithms for specific problems that require the optimization of a cost... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1314 |
| SubjectTerms | Algorithms Constraints Convergence Convexity Cost function geodesically convex optimization Grassmann manifold Independent variables majorization-minimization Manifolds Manifolds (mathematics) Minimization Non-convex optimization Optimization Principal component analysis Riemannian optimization Signal processing Signal processing algorithms |
| Title | On the Convergence of Block Majorization-Minimization Algorithms on the Grassmann Manifold |
| URI | https://ieeexplore.ieee.org/document/10518081 https://www.proquest.com/docview/3055179006 |
| Volume | 31 |
| WOSCitedRecordID | wos001224409900006&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: PRVIEE databaseName: IEEE/IET Electronic Library customDbUrl: eissn: 1558-2361 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008185 issn: 1070-9908 databaseCode: RIE dateStart: 19940101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlR1NT8IwtFHiQQ9-YkTR9ODFw2Cj3dYekYgeAEnUhHhZtq7VKXRmDH-_bVeQxGjibcv6uuW9vc--DwAuidLZgse-E3IdrWKBq1iKxo5IKU59yhERplB4EI5GZDKhY1usbmphOOcm-Yy39KU5y09zttChMsXhvqcnRWyCzTAMqmKtldjVmqdKMFSvoy5Znkm6tD14GCtPsINbCCnr3nSj_NZBZqjKD0ls1Et_758ftg92rR0JuxXhD8AGl4dgZ6274BF4vpdQmXewpxPLTY0lh7mA10p9vcNh_JYXtgbTGWYym9kb2J2-qCfl62wO82qD20JZ2LNYSgUlM5FP0zp46t889u4cO0rBYQjh0qFB6lFfhFwpJE-EHZd5NGQsZR4TWNGKJyJAscCE-6noBIJQpsQPCQhKmBumBB2DmswlPwGQxR0vxtjXxgZmzE90ECnBJFaOFKLca4D2ErkRs33G9biLaWT8DZdGihyRJkdkydEAVyuIj6rHxh9r6xr9a-sqzDdAc0nAyHLhPNLdzHQHMjc4_QXsDGzr3auYShPUymLBz8EW-yyzeXFhfrAvZKnNfA |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlR1NT4Mw9MWvRD34bZxO7cGLBxRogfaoxqmRzSXOZPFCoLQ63cBs099vWzpdYjTxBqGPkvd4n30fAEdU6Wwp0sCJhI5W8dBVLMVSR-aM5AETmEpTKBxHrRbtdlnbFqubWhghhEk-Eyf60pzl5yV_16EyxeGBpydFzMK8Hp1ly7W-BK_WPVWKodqQuXRyKumy0_i-rXxBn5xgrOx704_yWwuZsSo_ZLFRMI3Vf37aGqxYSxKdVaRfhxlRbMDyVH_BTXi8K5Ay8NCFTi03VZYClRKdKwX2iprpSzm0VZhOs1f0BvYGnfWf1JPx82CEyuoFV0NlYw_SolBQRU-W_XwLHhqXnYtrxw5TcDjGZOywMPdYICOhVJInI9_lHos4z7nHJVHUEpkMcSoJFUEu_VBSxpUAoiHFGXejnOJtmCvKQuwA4qnvpYQE2twgnAeZDiNlhKbKlcJMeDU4nSA34bbTuB540U-Mx-GyRJEj0eRILDlqcPwF8VZ12fhj7ZZG_9S6CvM1qE8ImFg-HCW6n5nuQeaGu7-AHcLidacZJ_FN63YPlvROVYSlDnPj4bvYhwX-Me6NhgfmZ_sERC7QxQ |
| 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=On+the+Convergence+of+Block+Majorization-Minimization+Algorithms+on+the+Grassmann+Manifold&rft.jtitle=IEEE+signal+processing+letters&rft.au=Lopez%2C+Carlos+Alejandro&rft.au=Riba%2C+Jaume&rft.date=2024&rft.pub=IEEE&rft.issn=1070-9908&rft.volume=31&rft.spage=1314&rft.epage=1318&rft_id=info:doi/10.1109%2FLSP.2024.3396660&rft.externalDocID=10518081 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1070-9908&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1070-9908&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1070-9908&client=summon |