Sparse Covariance Matrix Estimation by DCA-Based Algorithms
This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle....
Gespeichert in:
| Veröffentlicht in: | Neural computation Jg. 29; H. 11; S. 3040 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
United States
01.11.2017
|
| ISSN: | 1530-888X, 1530-888X |
| Online-Zugang: | Weitere Angaben |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods. |
|---|---|
| AbstractList | This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods. This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods. |
| Author | Phan, Duy Nhat Dinh, Tao Pham Le Thi, Hoai An |
| Author_xml | – sequence: 1 givenname: Duy Nhat surname: Phan fullname: Phan, Duy Nhat email: duy-nhat.phan@univ-loraine.fr organization: Laboratory of Theoretical and Applied Computer Science EA 3097, University of Lorraine, Ile du Saulcy, 57045 Metz, France duy-nhat.phan@univ-loraine.fr – sequence: 2 givenname: Hoai An surname: Le Thi fullname: Le Thi, Hoai An email: hoai-an.le-thi@univ-lorraine.fr organization: Laboratory of Theoretical and Applied Computer Science EA 3097, University of Lorraine, Ile du Saulcy, 57045 Metz, France hoai-an.le-thi@univ-lorraine.fr – sequence: 3 givenname: Tao Pham surname: Dinh fullname: Dinh, Tao Pham email: pham@insa-rouen.fr organization: Laboratory of Mathematics, INSA-Rouen, University of Normandie, 76801 Saint-Etienne-du-Rouvray cedex, France pham@insa-rouen.fr |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/28957024$$D View this record in MEDLINE/PubMed |
| BookMark | eNpNj0tLxDAUhYOMOA_duZYu3VRv0qSmuKp1fMCICxXclZtHtdI2NWnF-fcWHMHV-RaHc_iWZNa5zhJyTOGM0pSdd1a7EkugQNkeWVCRQCylfJ394zlZhvABACkFcUDmTGbiAhhfkMunHn2wUeG-0NfYaRs94ODr72gdhrrFoXZdpLbRdZHHVxisifLmzfl6eG_DIdmvsAn2aJcr8nKzfi7u4s3j7X2Rb2LNOR9ibdLpNlFCM2mU5UykkFFVKbRcooIKhUmNRCkkg4QrzLTRMhFiIkaVZity-rvbe_c52jCUbR20bRrsrBtDSTMuGKMZJFP1ZFcdVWtN2fvJwW_LP2H2A8KGWTY |
| CitedBy_id | crossref_primary_10_1007_s10898_023_01272_1 crossref_primary_10_1162_neco_a_01266 crossref_primary_10_1016_j_neunet_2020_08_024 crossref_primary_10_1109_TSP_2024_3361082 crossref_primary_10_1016_j_neucom_2021_09_039 crossref_primary_10_1109_LSP_2024_3495576 crossref_primary_10_1007_s10107_018_1235_y crossref_primary_10_1016_j_cam_2020_113353 crossref_primary_10_1109_TSP_2023_3311523 crossref_primary_10_1371_journal_pone_0315740 crossref_primary_10_1016_j_amc_2020_125904 |
| ContentType | Journal Article |
| DBID | NPM 7X8 |
| DOI | 10.1162/neco_a_01012 |
| DatabaseName | PubMed MEDLINE - Academic |
| DatabaseTitle | PubMed MEDLINE - Academic |
| DatabaseTitleList | MEDLINE - Academic PubMed |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: 7X8 name: MEDLINE - Academic url: https://search.proquest.com/medline sourceTypes: Aggregation Database |
| DeliveryMethod | no_fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1530-888X |
| ExternalDocumentID | 28957024 |
| Genre | Journal Article |
| GroupedDBID | --- -~X .4S .DC 0R~ 123 36B 4.4 41~ 53G 6IK AAJGR AALMD AAYOK ABAZT ABDBF ABDNZ ABEFU ABIVO ABJNI ACGFO ACUHS ACYGS ADIYS ADMLS AEGXH AEILP AENEX AIAGR ALMA_UNASSIGNED_HOLDINGS ARCSS AVWKF AZFZN BEFXN BFFAM BGNUA BKEBE BPEOZ CAG COF CS3 DU5 EAP EAS EBC EBD EBS ECS EDO EJD EMB EMK EMOBN EPL EPS EST ESX F5P FEDTE FNEHJ HVGLF HZ~ H~9 I-F IPLJI JAVBF MCG MINIK MKJ NPM O9- OCL P2P PK0 PQQKQ RMI SV3 TUS WG8 WH7 XJE ZWS 7X8 ABVLG AMVHM |
| ID | FETCH-LOGICAL-c444t-cd66103b5c28dbe4256091bfbae48ab0fa5d6d8a8582034ba9cdc8355ba921bc2 |
| IEDL.DBID | 7X8 |
| ISICitedReferencesCount | 14 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000413292600007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1530-888X |
| IngestDate | Fri Sep 05 14:21:38 EDT 2025 Thu Apr 03 07:05:38 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 11 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c444t-cd66103b5c28dbe4256091bfbae48ab0fa5d6d8a8582034ba9cdc8355ba921bc2 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| PMID | 28957024 |
| PQID | 1945221903 |
| PQPubID | 23479 |
| ParticipantIDs | proquest_miscellaneous_1945221903 pubmed_primary_28957024 |
| PublicationCentury | 2000 |
| PublicationDate | 2017-11-00 20171101 |
| PublicationDateYYYYMMDD | 2017-11-01 |
| PublicationDate_xml | – month: 11 year: 2017 text: 2017-11-00 |
| PublicationDecade | 2010 |
| PublicationPlace | United States |
| PublicationPlace_xml | – name: United States |
| PublicationTitle | Neural computation |
| PublicationTitleAlternate | Neural Comput |
| PublicationYear | 2017 |
| SSID | ssj0006105 |
| Score | 2.3051002 |
| Snippet | This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The... |
| SourceID | proquest pubmed |
| SourceType | Aggregation Database Index Database |
| StartPage | 3040 |
| Title | Sparse Covariance Matrix Estimation by DCA-Based Algorithms |
| URI | https://www.ncbi.nlm.nih.gov/pubmed/28957024 https://www.proquest.com/docview/1945221903 |
| Volume | 29 |
| WOSCitedRecordID | wos000413292600007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB7UevBifVtfrOB1aR67eeBBam3xYEtBhdzCPhIVNImmFv33zuZBT4LgJewlJMzO7Hzf7DwALmQV0PcZFanFKbNTRUNPC1PAHCCYY75SVXf9O386DaIonDUBt7JJq2zPxOqg1rkyMfI-km2ECui-3KvinZqpUeZ2tRmhsQodF6GMSenyo2W3cK9OYUSjtigyvahNfPecfobkLhax6bDm_A4uKycz7v7397Zgs4GXZFDrwzasJNkOdNvRDaSx5F24vC-Q0SZkmC-QLJudJxPTrP-LjNDm63JGIr_JzXBAr9HRaTJ4fcLvzZ_fyj14HI8ehre0maNAFWNsTpVGJ2y5kisn0DJhBuWEtkylSFggpJUKrj0diIAjHHCZFKHSCpEZx5VjS-Xsw1qWZ8khEEQHXCorFALtOLUsyblIlXYd6SJT4XYPzlvxxKin5vJBZEn-WcZLAfXgoJZxXNQNNWIkfdxHsHD0h7ePYcMxnrUqBzyBTopWmpzCulrMX8qPs0oB8DmdTX4A28O6Sg |
| linkProvider | ProQuest |
| 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=Sparse+Covariance+Matrix+Estimation+by+DCA-Based+Algorithms&rft.jtitle=Neural+computation&rft.au=Phan%2C+Duy+Nhat&rft.au=Le+Thi%2C+Hoai+An&rft.au=Dinh%2C+Tao+Pham&rft.date=2017-11-01&rft.issn=1530-888X&rft.eissn=1530-888X&rft.volume=29&rft.issue=11&rft.spage=3040&rft_id=info:doi/10.1162%2Fneco_a_01012&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1530-888X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1530-888X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1530-888X&client=summon |