Binary classification via spherical separator by DC programming and DCA

In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set from the set (i.e. a sphere enclosing all points of and no points of ). The problem can...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of global optimization Vol. 56; no. 4; pp. 1393 - 1407
Main Authors:	Le Thi, Hoai An, Le, Hoai Minh, Pham Dinh, Tao, Van Huynh, Ngai
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01.08.2013 Springer Springer Nature B.V Springer Verlag
Subjects:	Algorithms Classification Computational efficiency Computer programming Computer Science Convex analysis Customizing Data mining Direct current Investigations Laboratories Mathematical models Mathematics Mathematics and Statistics Numerical analysis Operations Research/Decision Theory Optimization Programming Real Functions Simulation Studies Support vector machines DC programming 90C90 DCA 90C30 Spherical separation Classification
ISSN:	0925-5001, 1573-2916
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set from the set (i.e. a sphere enclosing all points of and no points of ). The problem can be cast into the DC (Difference of Convex functions) programming framework and solved by DCA (DC Algorithm) as shown in the works of Astorino et al. (J Glob Optim 48(4):657–669, 2010 ). The aim of this paper is to investigate more attractive DCA based algorithms for this problem. We consider a new optimization model and propose two interesting DCA schemes. In the first scheme we have to solve a quadratic program at each iteration, while in the second one all calculations are explicit. Numerical simulations show the efficiency of our customized DCA with respect to the methods developed in Astorino et al.
AbstractList	In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set from the set (i.e. a sphere enclosing all points of and no points of ). The problem can be cast into the DC (Difference of Convex functions) programming framework and solved by DCA (DC Algorithm) as shown in the works of Astorino et al. (J Glob Optim 48(4):657–669, 2010 ). The aim of this paper is to investigate more attractive DCA based algorithms for this problem. We consider a new optimization model and propose two interesting DCA schemes. In the first scheme we have to solve a quadratic program at each iteration, while in the second one all calculations are explicit. Numerical simulations show the efficiency of our customized DCA with respect to the methods developed in Astorino et al. (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Issue Title: Special issue for the 8th international conference on optimization: techniques and applications In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set ... from the set ... (i.e. a sphere enclosing all points of ... and no points of ...). The problem can be cast into the DC (Difference of Convex functions) programming framework and solved by DCA (DC Algorithm) as shown in the works of Astorino et al. (J Glob Optim 48(4):657-669, 2010 ). The aim of this paper is to investigate more attractive DCA based algorithms for this problem. We consider a new optimization model and propose two interesting DCA schemes. In the first scheme we have to solve a quadratic program at each iteration, while in the second one all calculations are explicit. Numerical simulations show the efficiency of our customized DCA with respect to the methods developed in Astorino et al.[PUBLICATION ABSTRACT] In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set A from the set B (i.e. a sphere enclosing all points of A and no points of B. The problem can be cast into the DC (Difference of Convex functions) programming framework and solved by DCA (DC Algorithm) as shown in the works of Astorino et al. (J Glob Optim 48(4):657-669, 2010). The aim of this paper is to investigate more attractive DCA based algorithms for this problem. We consider a new optimization model and propose two interesting DCA schemes. In the first scheme we have to solve a quadratic program at each iteration, while in the second one all calculations are explicit. Numerical simulations show the efficiency of our customized DCA with respect to the methods developed in Astorino et al. In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the feature space, a minimal volume sphere separating the set A from the set B (i.e. a sphere enclosing all points of A and no points of B). The problem can be cast into the DC (Difference of Convex functions) programming framework and solved by DCA (DC Algorithm) as shown in the works of Astorino et al. (J Glob Optim 48(4):657-669, 2010). The aim of this paper is to investigate more attractive DCA based algorithms for this problem. We consider a new optimization model and propose two interesting DCA schemes. In the first scheme we have to solve a quadratic program at each iteration, while in the second one all calculations are explicit. Numerical simulations show the efficiency of our customized DCA with respect to the methods developed in Astorino et al. Keywords Classification * Spherical separation * DC programming * DCA
Audience	Academic
Author	Le, Hoai Minh Pham Dinh, Tao Van Huynh, Ngai Le Thi, Hoai An
Author_xml	– sequence: 1 givenname: Hoai An surname: Le Thi fullname: Le Thi, Hoai An email: lethi@univ-metz.fr organization: Laboratory of Theoretical and Applied Computer Science, LITA EA 3097, UFR MIM, University of Paul Verlaine-Metz – sequence: 2 givenname: Hoai Minh surname: Le fullname: Le, Hoai Minh organization: Laboratory of Theoretical and Applied Computer Science, LITA EA 3097, UFR MIM, University of Paul Verlaine-Metz – sequence: 3 givenname: Tao surname: Pham Dinh fullname: Pham Dinh, Tao organization: Laboratory of Modelling, Optimization & Operations Research, National Institute for Applied Sciences-Rouen – sequence: 4 givenname: Ngai surname: Van Huynh fullname: Van Huynh, Ngai organization: Department of Mathematics, University of Quynhon
BackLink	https://hal.univ-lorraine.fr/hal-01636671$$DView record in HAL
BookMark	eNp9kUFrFDEYhoNUcFv9Ad4GvOhhar5kkkyO66qtsOBFz-FLJtmmzGTWZLbQf2_WUZCCkkPg5XnC9-W9JBdpTp6Q10CvgVL1vgDtdd9SYK3uhW7lM7IBoXjLNMgLsqGaiVZQCi_IZSn3lNKKsQ25-RAT5sfGjVhKDNHhEufUPERsyvHO5xqMTfFHzLjMubGPzcddc8zzIeM0xXRoMA012r4kzwOOxb_6fV-R758_fdvdtvuvN192233rOsaWlktAy0Eza4XslWWasZ47CLYTg8BOKx4kw6BCZzWTqAbwNijPBt87tIJfkXfru3c4mmOOUx3ezBjN7XZvzhkFyaVU8ACVfbuydd4fJ18WM8Xi_Dhi8vOpGKhY19EOzuibJ-j9fMqpbmKgo5Qr3SteqeuVOuDoTUxhXjK6egY_RVcLCbHmW9VxAT0IWgW1Ci7PpWQfjIvLrx-uYhwNUHNuz6zt1dmZObdnZDXhifln2f85bHVKZdPB57-W-Kf0E3uYq7A
CitedBy_id	crossref_primary_10_1007_s11634_013_0141_7 crossref_primary_10_1016_j_orl_2022_11_008 crossref_primary_10_1016_j_apm_2015_01_044 crossref_primary_10_1109_TNNLS_2015_2430935 crossref_primary_10_1080_02331934_2017_1306743 crossref_primary_10_1016_j_ejor_2014_11_031 crossref_primary_10_3390_a12120249 crossref_primary_10_1162_NECO_a_00836 crossref_primary_10_1007_s00521_016_2374_9 crossref_primary_10_1080_02331934_2013_840625 crossref_primary_10_1007_s10957_020_01721_x crossref_primary_10_1007_s10618_014_0369_7 crossref_primary_10_1007_s10107_018_1235_y crossref_primary_10_1007_s11081_017_9359_0 crossref_primary_10_1007_s00500_020_05352_2 crossref_primary_10_1007_s10957_013_0458_6
Cites_doi	10.1007/s11634-008-0030-7 10.1007/s10287-007-0051-2 10.1007/s11634-007-0011-2 10.1023/A:1008288411710 10.1137/S1052623494274313 10.1007/s11590-007-0074-1 10.1137/S1052623498342794 10.1016/j.ejor.2005.07.028 10.1137/S1052623402411459 10.1162/08997660360581958 10.1007/s10898-006-9066-4 10.1007/s10479-004-5022-1 10.1016/0022-247X(65)90150-2 10.1007/s10898-010-9558-0 10.1147/rd.266.0759 10.1080/10556780512331318254 10.1145/130385.130401 10.1145/1273496.1273601
ContentType	Journal Article
Copyright	Springer Science+Business Media, LLC. 2012 COPYRIGHT 2022 Springer Springer Science+Business Media New York 2013 Distributed under a Creative Commons Attribution 4.0 International License
Copyright_xml	– notice: Springer Science+Business Media, LLC. 2012 – notice: COPYRIGHT 2022 Springer – notice: Springer Science+Business Media New York 2013 – notice: Distributed under a Creative Commons Attribution 4.0 International License
DBID	AAYXX CITATION 3V. 7SC 7WY 7WZ 7XB 87Z 88I 8AL 8AO 8FD 8FE 8FG 8FK 8FL 8G5 ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JQ2 K60 K6~ K7- L.- L.0 L6V L7M L~C L~D M0C M0N M2O M2P M7S MBDVC P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U 1XC
DOI	10.1007/s10898-012-9859-6
DatabaseName	CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni Edition) Research Library (Alumni Edition) Materials Science & Engineering Database ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Aerospace Database ProQuest Central Essentials Local Electronic Collection Information ProQuest Central Business Premium Collection Technology collection ProQuest One ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student Research Library Prep SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ABI/INFORM Professional Advanced ABI/INFORM Professional Standard ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global (OCUL) Computing Database Research Library Science Database Engineering Database Research Library (Corporate) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Business (UW System Shared) ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic Hyper Article en Ligne (HAL)
DatabaseTitle	CrossRef ProQuest Business Collection (Alumni Edition) Research Library Prep Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest Central China ABI/INFORM Complete ProQuest One Applied & Life Sciences ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest Business Collection ProQuest One Academic UKI Edition ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Pharma Collection ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ABI/INFORM Professional Standard ProQuest Central Korea ProQuest Research Library Advanced Technologies Database with Aerospace ABI/INFORM Complete (Alumni Edition) ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni)
DatabaseTitleList	ProQuest Business Collection (Alumni Edition) Computer and Information Systems Abstracts
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics Sciences (General) Computer Science
EISSN	1573-2916
EndPage	1407
ExternalDocumentID	oai:HAL:hal-01636671v1 3020887591 A743518150 10_1007_s10898_012_9859_6
Genre	Feature
GroupedDBID	-52 -57 -5G -BR -EM -Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 28- 29K 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 7WY 88I 8AO 8FE 8FG 8FL 8G5 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYOK AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYQZM AZFZN AZQEC B-. BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP D-I DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GUQSH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IAO IHE IJ- IKXTQ ITC ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV KOW L6V LAK LLZTM M0C M0N M2O M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P62 P9M PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SBE SCLPG SDD SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YLTOR Z45 Z5O Z7R Z7X Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8T Z8U Z8W Z92 ZMTXR ZWQNP ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 7XB 8AL 8FD 8FK JQ2 L.- L.0 L7M L~C L~D MBDVC PKEHL PQEST PQUKI PRINS Q9U PUEGO 1XC
ID	FETCH-LOGICAL-c422t-361ab3192bb5687b292283c1fb45d5a4973f62af7f4b926a7d1ebf7e2de8cab53
IEDL.DBID	RSV
ISICitedReferencesCount	21
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000321921500009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0925-5001
IngestDate	Sat Nov 29 15:08:51 EST 2025 Thu Sep 04 16:50:53 EDT 2025 Tue Nov 04 23:05:47 EST 2025 Sat Nov 29 10:13:43 EST 2025 Sat Nov 29 01:59:30 EST 2025 Tue Nov 18 22:24:12 EST 2025 Fri Feb 21 02:42:30 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	4
Keywords	DC programming 90C90 DCA 90C30 Spherical separation Classification
Language	English
License	http://www.springer.com/tdm Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c422t-361ab3192bb5687b292283c1fb45d5a4973f62af7f4b926a7d1ebf7e2de8cab53
Notes	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ORCID	0000-0001-7337-1505 0000-0002-2239-2100
PQID	1400379873
PQPubID	29930
PageCount	15
ParticipantIDs	hal_primary_oai_HAL_hal_01636671v1 proquest_miscellaneous_1671440411 proquest_journals_1400379873 gale_infotracacademiconefile_A743518150 crossref_citationtrail_10_1007_s10898_012_9859_6 crossref_primary_10_1007_s10898_012_9859_6 springer_journals_10_1007_s10898_012_9859_6
PublicationCentury	2000
PublicationDate	2013-08-01
PublicationDateYYYYMMDD	2013-08-01
PublicationDate_xml	– month: 08 year: 2013 text: 2013-08-01 day: 01
PublicationDecade	2010
PublicationPlace	Boston
PublicationPlace_xml	– name: Boston – name: Dordrecht
PublicationSubtitle	An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering
PublicationTitle	Journal of global optimization
PublicationTitleAbbrev	J Glob Optim
PublicationYear	2013
Publisher	Springer US Springer Springer Nature B.V Springer Verlag
Publisher_xml	– name: Springer US – name: Springer – name: Springer Nature B.V – name: Springer Verlag
References	Barnes (CR6) 1982; 26 Le Thi, Belghiti, Pham (CR15) 2007; 37 Le Thi, Le, Van Nguyen, Pham (CR16) 2008; 2 Le Thi, Le, Pham (CR13) 2007; 1 Rosen (CR22) 1965; 10 CR19 CR18 CR12 Wu, Liu (CR24) 2009; 19 Audet, Hansen, Karam, Ng, Perron (CR4) 2008; 2 Astorino, Fuduli, Gaudioso (CR3) 2010; 48 Mangasarian (CR17) 1997; 22 Le Thi, Pham (CR10) 2003; 14 CR5 CR7 Le Thi, Pham (CR11) 2005; 133 Astorino, Gaudioso (CR2) 2009; 6 Pham, Le Thi (CR20) 1997; 22 Astorino, Gaudioso (CR1) 2005; 20 CR23 Yuille, Rangarajan (CR25) 2003; 15 Le Thi, Le, Pham (CR14) 2007; 183 Pham, Le Thi (CR21) 1998; 8 Fuduli, Gaudioso, Giallombardo (CR8) 2004; 14 Le Thi, Pham (CR9) 1997; 11 Y. Wu (9859_CR24) 2009; 19 9859_CR12 A. Astorino (9859_CR1) 2005; 20 H.A. Le Thi (9859_CR10) 2003; 14 9859_CR19 9859_CR18 H.A. Le Thi (9859_CR15) 2007; 37 D.T. Pham (9859_CR20) 1997; 22 A. Astorino (9859_CR3) 2010; 48 O.L. Mangasarian (9859_CR17) 1997; 22 E.R. Barnes (9859_CR6) 1982; 26 H.A. Le Thi (9859_CR11) 2005; 133 H.A. Le Thi (9859_CR13) 2007; 1 J.B. Rosen (9859_CR22) 1965; 10 D.T. Pham (9859_CR21) 1998; 8 9859_CR5 H.A. Le Thi (9859_CR14) 2007; 183 9859_CR23 9859_CR7 A. Astorino (9859_CR2) 2009; 6 H.A. Le Thi (9859_CR9) 1997; 11 A. Fuduli (9859_CR8) 2004; 14 A.L. Yuille (9859_CR25) 2003; 15 C. Audet (9859_CR4) 2008; 2 H.A. Le Thi (9859_CR16) 2008; 2
References_xml	– ident: CR18 – volume: 2 start-page: 259 issue: 3 year: 2008 end-page: 278 ident: CR16 article-title: A DC programming approach for feature selection in support vector machines learning publication-title: J. Adv. Data Anal. Classif. doi: 10.1007/s11634-008-0030-7 – ident: CR12 – volume: 6 start-page: 357 issue: 3 year: 2009 end-page: 372 ident: CR2 article-title: A fixed-centre spherical separation algorithm with kernel transformations for classification problems publication-title: Comput. Manag. Sci. doi: 10.1007/s10287-007-0051-2 – volume: 1 start-page: 85 issue: 2 year: 2007 end-page: 104 ident: CR13 article-title: Fuzzy clustering based on nonconvex optimisation approaches using difference of convex (DC) functions algorithms publication-title: Adv. Data Anal. Classif. doi: 10.1007/s11634-007-0011-2 – volume: 11 start-page: 253 issue: 3 year: 1997 end-page: 285 ident: CR9 article-title: Solving a class of linearly constrained indefinite quadratic problems by DC algorithms publication-title: J. Glob. Optim. doi: 10.1023/A:1008288411710 – volume: 8 start-page: 476 year: 1998 end-page: 505 ident: CR21 article-title: DC optimization algorithms for solving the trust region subproblem publication-title: SIAM J.Optim. doi: 10.1137/S1052623494274313 – volume: 2 start-page: 483 issue: 4 year: 2008 end-page: 495 ident: CR4 article-title: Exact L2-norm plane separation publication-title: Optim. Lett. doi: 10.1007/s11590-007-0074-1 – volume: 22 start-page: 289 issue: 1 year: 1997 end-page: 355 ident: CR20 article-title: Convex analysis approach to DC programming: theory, algorithms and applications publication-title: Acta Math. Vietnam. – volume: 14 start-page: 77 issue: 1 year: 2003 end-page: 114 ident: CR10 article-title: Large scale global molecular optimization from exact distance matrices by a DC optimization approach publication-title: SIAM J. Optim. doi: 10.1137/S1052623498342794 – ident: CR23 – volume: 19 start-page: 801 year: 2009 end-page: 817 ident: CR24 article-title: Variable selection in quantile regression publication-title: Stat. Sin. – ident: CR19 – volume: 183 start-page: 1067 year: 2007 end-page: 1085 ident: CR14 article-title: Optimization based DC programming and DCA for Hierarchical clustering publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2005.07.028 – volume: 14 start-page: 743 year: 2004 end-page: 756 ident: CR8 article-title: Minimizing nonconvex nonsmooth functions via cutting planes and proximity control publication-title: SIAM J. Optim. doi: 10.1137/S1052623402411459 – volume: 15 start-page: 915 issue: 4 year: 2003 end-page: 936 ident: CR25 article-title: The concave-convex procedure publication-title: Neural Comput. doi: 10.1162/08997660360581958 – volume: 37 start-page: 593 year: 2007 end-page: 608 ident: CR15 article-title: A new efficient algorithm based on DC programming and DCA for clustering publication-title: J. Glob. Optim. doi: 10.1007/s10898-006-9066-4 – volume: 133 start-page: 23 year: 2005 end-page: 46 ident: CR11 article-title: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems publication-title: Ann. Oper. Res. doi: 10.1007/s10479-004-5022-1 – volume: 10 start-page: 123 year: 1965 end-page: 134 ident: CR22 article-title: Pattern separation by convex programming publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(65)90150-2 – volume: 48 start-page: 657 issue: 4 year: 2010 end-page: 669 ident: CR3 article-title: DC models for spherical separation publication-title: J. Glob. Optim. doi: 10.1007/s10898-010-9558-0 – ident: CR5 – ident: CR7 – volume: 26 start-page: 759 year: 1982 end-page: 764 ident: CR6 article-title: An algorithm for separating patterns by ellipsoids publication-title: IBM. J. Res. Dev. doi: 10.1147/rd.266.0759 – volume: 20 start-page: 267 year: 2005 end-page: 276 ident: CR1 article-title: Ellipsoidal separation for classification problems publication-title: Optim. Methods Softw. doi: 10.1080/10556780512331318254 – volume: 22 start-page: 199 year: 1997 end-page: 205 ident: CR17 article-title: Solution of general linear complementarity problems via nondifferentiable concave minimization publication-title: Acta Math. Vietnam. – ident: 9859_CR5 doi: 10.1145/130385.130401 – volume: 37 start-page: 593 year: 2007 ident: 9859_CR15 publication-title: J. Glob. Optim. doi: 10.1007/s10898-006-9066-4 – volume: 14 start-page: 743 year: 2004 ident: 9859_CR8 publication-title: SIAM J. Optim. doi: 10.1137/S1052623402411459 – volume: 19 start-page: 801 year: 2009 ident: 9859_CR24 publication-title: Stat. Sin. – volume: 2 start-page: 483 issue: 4 year: 2008 ident: 9859_CR4 publication-title: Optim. Lett. doi: 10.1007/s11590-007-0074-1 – volume: 133 start-page: 23 year: 2005 ident: 9859_CR11 publication-title: Ann. Oper. Res. doi: 10.1007/s10479-004-5022-1 – ident: 9859_CR19 – volume: 20 start-page: 267 year: 2005 ident: 9859_CR1 publication-title: Optim. Methods Softw. doi: 10.1080/10556780512331318254 – volume: 15 start-page: 915 issue: 4 year: 2003 ident: 9859_CR25 publication-title: Neural Comput. doi: 10.1162/08997660360581958 – volume: 22 start-page: 199 year: 1997 ident: 9859_CR17 publication-title: Acta Math. Vietnam. – volume: 8 start-page: 476 year: 1998 ident: 9859_CR21 publication-title: SIAM J.Optim. doi: 10.1137/S1052623494274313 – volume: 11 start-page: 253 issue: 3 year: 1997 ident: 9859_CR9 publication-title: J. Glob. Optim. doi: 10.1023/A:1008288411710 – volume: 26 start-page: 759 year: 1982 ident: 9859_CR6 publication-title: IBM. J. Res. Dev. doi: 10.1147/rd.266.0759 – volume: 22 start-page: 289 issue: 1 year: 1997 ident: 9859_CR20 publication-title: Acta Math. Vietnam. – volume: 1 start-page: 85 issue: 2 year: 2007 ident: 9859_CR13 publication-title: Adv. Data Anal. Classif. doi: 10.1007/s11634-007-0011-2 – volume: 2 start-page: 259 issue: 3 year: 2008 ident: 9859_CR16 publication-title: J. Adv. Data Anal. Classif. doi: 10.1007/s11634-008-0030-7 – volume: 10 start-page: 123 year: 1965 ident: 9859_CR22 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(65)90150-2 – ident: 9859_CR18 – ident: 9859_CR23 doi: 10.1145/1273496.1273601 – volume: 14 start-page: 77 issue: 1 year: 2003 ident: 9859_CR10 publication-title: SIAM J. Optim. doi: 10.1137/S1052623498342794 – volume: 48 start-page: 657 issue: 4 year: 2010 ident: 9859_CR3 publication-title: J. Glob. Optim. doi: 10.1007/s10898-010-9558-0 – ident: 9859_CR7 – volume: 183 start-page: 1067 year: 2007 ident: 9859_CR14 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2005.07.028 – ident: 9859_CR12 – volume: 6 start-page: 357 issue: 3 year: 2009 ident: 9859_CR2 publication-title: Comput. Manag. Sci. doi: 10.1007/s10287-007-0051-2
SSID	ssj0009852
Score	2.124317
Snippet	In this paper, we consider a binary supervised classification problem, called spherical separation, that consists of finding, in the input space or in the... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Issue Title: Special issue for the 8th international conference on optimization:...
SourceID	hal proquest gale crossref springer
SourceType	Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	1393
SubjectTerms	Algorithms Classification Computational efficiency Computer programming Computer Science Convex analysis Customizing Data mining Direct current Investigations Laboratories Mathematical models Mathematics Mathematics and Statistics Numerical analysis Operations Research/Decision Theory Optimization Programming Real Functions Simulation Studies Support vector machines
SummonAdditionalLinks	– databaseName: ABI/INFORM Collection dbid: 7WY link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwELZo4QAHoAVEoCCDkHhUFrHjR3xCS6H0UFUcQJSTZTuOqATZstmuxL9nJuvsLkj0wiUHx55Y-jzjiWf8DSHPlI-y9qZkxnPBpE6SBd7CQ0dtqzrI0Awkrsfm5KQ-PbUf84Fbn9MqR5s4GOpmGvGM_DX8CJSVgT_k6s35T4ZVozC6mktobJGrsFErrGBgvnxdk-7WQ8Wd0grFFNjjMaq5vDpX4-UymCD0skz_sS9l67z1DZMjNzzPv4Klwx50eOt_Z3-b3MzeJ50sl8sOuZK6XXJjg5Nwl-xkbe_pi0xJ_fIO-fB2uLZLI_ramFw04EkXZ572yEuASNM-DTzi0xkNv-i7A5pTv36AWOq7Bpomd8nnw_efDo5YLsHAohRizirNfQAtFSEoXZsgLNLlRN4GqRrlpTVVq4VvTSuDFdqbhqfQmiSaVEcfVHWPbHfTLt0nNHLTeFsG8IGkjK3x0SZbxQg-h-Te1AUpRwBczPzkWCbju1szKyNmDjBziJnTBXm1GnK-JOe4rPNzRNWh4oLc6PP9A5gdUmC5CfhSCvwdVRbkKQC_kogE3EeTY4dt4CBXWhu-4AXZG5F2We17t4a5IE9Wr0FhMQrjuzS9gD4wHEkZOYjYH9fThoh_zf_B5R98SK6LoVIHLuo9sj2fXaRH5FpczM_62eNBL34DZ3UPpg priority: 102 providerName: ProQuest
Title	Binary classification via spherical separator by DC programming and DCA
URI	https://link.springer.com/article/10.1007/s10898-012-9859-6 https://www.proquest.com/docview/1400379873 https://www.proquest.com/docview/1671440411 https://hal.univ-lorraine.fr/hal-01636671
Volume	56
WOSCitedRecordID	wos000321921500009&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: PRVPQU databaseName: ABI/INFORM Global customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: M0C dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: K7- dateStart: 19970101 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: M7S dateStart: 19970101 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest ABI/INFORM Collection customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: 7WY dateStart: 19970101 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest advanced technologies & aerospace journals customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: P5Z dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: BENPR dateStart: 19970101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Proquest Research Library customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: M2O dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/pqrl providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1573-2916 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: M2P dateStart: 19970101 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLink customDbUrl: eissn: 1573-2916 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3db9MwED_RjQd4YKyACIzKICS-FClx_BE_dmVjElupGB8bL5HtJGIStKjpKvHfc5c5XUGABC8n2bEvlu_OPsu-3wE8ltaL3Ook1jblsVCViF1aI1FemSx3wpUtiOuhHo_zkxMzCXHcTffavbuSbFfqtWC3nMLBkKXJpYlVDzYlgc3QEf34wyXSbt6m2UkMl7HERbi7yvwdi582o7Ak9z7Ti8g1d_OXG9J249nf-q8h34Qbwc9kwwvF2IYr1bQPW10OBxZMug_X1wAJsXS0QnFt-rAdWjXsaUCnfnYLXu22EbzMk9tN74xa0bLlmWUNQRSQ0FlTtZDiszlz39nLEQuvwL7iT5idllg1vA3v9_fejQ7ikI0h9oLzRZyp1Do0WO6cVLl23BByjk9rJ2QprUBJ1IrbWtfCGa6sLtPK1briZZV762R2Bzams2l1F5hPdWlN4tAdEsLX2npTmcx7dD9EanUeQdKJpfABqpwyZnwpLkGWaWYLnNmCZrZQETxfdfl2gdPxt8ZPSNYF2TDy9TaEIuDoCA2rGKJbJdH1kUkEj1AdVhwJi_tgeFhQHfrKmVI6XaYR7HTaUoQVoMEjFUH7mFxnETxcfUbbpQsZO61m59gGuxM-Y4osXnQatMbiT-O_90-t78M13ubwIE3cgY3F_Lx6AFf9cnHWzAfQ0x9PB7C5uzeevMXSax0jPUpGRPmblk6I6mOkE_lp0JrbDzgNGCw
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VggQcgBYqAgUMAvFRRSSOYycHhJaWstUuKw5F6s3YjiMqQbZstov6p_iNzGST3QWJ3nrgkoPjTBz7eTwTe94APE2NE5lRUahMzEMhvQhtXOJFOpknmRW2aEhch2o0yo6O8k9r8KuLhaFjlZ1ObBR1MXb0j_w1OgJRotBDTt6e_AgpaxTtrnYpNOawGPizn-iy1W8O9nB8n3G-__5wtx-2WQVCJzifhomMjUXgcWtTmSnLc2KAcXFpRVqkRuQqKSU3pSqFzbk0qoi9LZXnhc-csZQlAlX-ZZFkkmbUQIVLkt-syfAT5TwNU9T_3S7qPFQvo2A27BCslYfyj3WwXQ0ufaXDmCuW7l-bs82at3_zf-utW3Cjta5Zbz4dNmDNV5twfYVzcRM2Wm1Wsxct5fbL2_DhXROWzBz5EnR4qsErmx0bVhPvAiGZ1b7hSR9PmD1je7usPdr2HcUyUxVY1LsDny_k87ZgvRpX_i4wF6vC5JFFG08IVyrjcp8nzqFNJWKjsgCibsC1a_nXKQ3IN71kjiaMaMSIJoxoGcCrxSMnc_KR8yo_JxRpUkwo15k2vgJbRxRfuoe2Yor2XBoF8ASBtpBIBOP93lBTGToAiZQqnsUBbHfI0q1aq_USVgE8XtxGhUS7TKby41Osg48T6WSMInY6_K6I-Ff7753_wkdwtX_4caiHB6PBfbjGm6wkNKG2YX06OfUP4IqbTY_rycNmTjL4ctGw_g00omz7
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Rb9MwED6NDiF4ADZAFAYYBAI2RUscx04eEOrWlU2rqgqBtDdjO46YBO1ouqL9NX4dd2nSFiT2tgde8pA4l8T-fL6L774DeJkYJ1KjwkCZiAdCehHYqMCDdDKLUytsXpG49tVgkJ6cZMM1-NXkwlBYZaMTK0Wdjx39I99FRyCMFXrI8W5Rh0UMu733Zz8CqiBFO61NOY05RI79xU9038p3R10c61ec9w4-7R8GdYWBwAnOp0EsI2MRhNzaRKbK8ozYYFxUWJHkiRGZigvJTaEKYTMujcojbwvlee5TZyxVjED1v65idHpasL53MBh-XFL-plW9nzDjSZDgatDsqc4T91JKbcPuwVZZIP9YFeu14dpXCs1csXv_2qqtVsDenf-57-7C7druZp35RNmANT_ahFsrbIybsFHruZK9qcm4396DD3tVwjJz5GVQWFWFZDY7NawkRgbCOCt9xaA-njB7wbr7rA56-45imRnleKpzHz5fyec9gNZoPPIPgblI5SYLLVp_QrhCGZf5LHYOrS0RGZW2IWwGX7uamZ0KhHzTS05pwotGvGjCi5Zt2F7ccjanJbms8WtClCaVhXKdqTMv8O2I_Et30IpM0NJLwja8QNAtJBL1-GGnr-kcugaxlCqaRW3YalCma4VX6iXE2vB8cRlVFe0_mZEfn2MbvJ3oKCMUsdNgeUXEv97_0eUPfAY3EM26fzQ4fgw3eVWuhObWFrSmk3P_BK672fS0nDytJyiDL1eN6982andN
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=Binary+classification+via+spherical+separator+by+DC+programming+and+DCA&rft.jtitle=Journal+of+global+optimization&rft.au=Le+Thi%2C+Hoai+An&rft.au=Le%2C+Hoai+Minh&rft.au=Pham+Dinh%2C+Tao&rft.au=Van+Huynh%2C+Ngai&rft.date=2013-08-01&rft.pub=Springer+US&rft.issn=0925-5001&rft.eissn=1573-2916&rft.volume=56&rft.issue=4&rft.spage=1393&rft.epage=1407&rft_id=info:doi/10.1007%2Fs10898-012-9859-6&rft.externalDocID=10_1007_s10898_012_9859_6
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0925-5001&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0925-5001&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0925-5001&client=summon