03833nam 2200613 450 991013479560332120200520144314.03-11-048030-13-11-048106-510.1515/9783110481068(CKB)3850000000001073(EBL)4718418(OCoLC)962793042(DE-B1597)466925(OCoLC)951141809(OCoLC)963114749(DE-B1597)9783110481068(Au-PeEL)EBL4718418(CaPaEBR)ebr11283245(CaONFJC)MIL964181(OCoLC)961059086(ScCtBLL)a80371dd-766f-4802-9ff9-c024f7263329(oapen)https://directory.doabooks.org/handle/20.500.12854/48863(CaSebORM)9783110480306(MiAaPQ)EBC4718418(EXLCZ)99385000000000107320161028h20162016 uy 0gerurcn#nnn|||||txtrdacontentcrdamediacrrdacarrierGraphs for pattern recognition infeasible systems of linear inequalities /Damir GainanovDe Gruyter2016Berlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2016.©20161 online resource (x, 147 pages)3-11-048013-1 Includes bibliographical references and index.Frontmatter -- Preface -- Contents -- 1. Pattern recognition, infeasible systems of linear inequalities, and graphs -- 2. Complexes, (hyper)graphs, and inequality systems -- 3. Polytopes, positive bases, and inequality systems -- 4. Monotone Boolean functions, complexes, graphs, and inequality systems -- 5. Inequality systems, committees, (hyper)graphs, and alternative covers -- Bibliography -- List of notation -- IndexThis monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition.Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important special subclass of infeasible systems of constraints with a monotonicity property - systems whose multi-indices of feasible subsystems form abstract simplicial complexes (independence systems), which are fundamental objects of combinatorial topology.The methods of data mining and machine learning discussed in this monograph form the foundation of technologies like big data and deep learning, which play a growing role in many areas of human-technology interaction and help to find solutions, better solutions and excellent solutions. Contents:PrefacePattern recognition, infeasible systems of linear inequalities, and graphsInfeasible monotone systems of constraintsComplexes, (hyper)graphs, and inequality systemsPolytopes, positive bases, and inequality systemsMonotone Boolean functions, complexes, graphs, and inequality systemsInequality systems, committees, (hyper)graphs, and alternative coversBibliographyList of notationIndexInequalities (Mathematics)Graph theoryInequalities (Mathematics)Graph theory.516/.1Gainanov Damir(Damir N.),871838MiAaPQMiAaPQMiAaPQBOOK9910134795603321Graphs for pattern recognition1946278UNINA01566nam0 22003491i 450 UON0028732220231205103906.696978-01-953129-3-520070129d2007 |0itac50 baengUS|||| |||||Ancient Greek scholarshipa guide to finding, reading, and understanding scholia, commentaries, lexica, and grammatical treatises, from their beginnings to the Byzantine periodEleanor Dickey New YorkOxfordOxford University Press2007xvii, 345 p.24 cm001UON002928672001 American philological association. Classical resources series editor Justina GregoryFILOLOGIA GRECAUONC027924FIGreciaCiviltàUONC028526FILETTERATURA GRECA Critica del testoUONC063595FISCOLIAUONC063594FITrasmissione dei testiUONC053754FIGBOxfordUONL000029USNew YorkUONL000050480.9Lingue Elleniche. Greco Classico. Storia20DICKEYEleanorUONV145395446540Oxford University PressUONV245947650ITSOL20250704RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00287322SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI Q 1 061 SI MC 31083 5 Ancient Greek scholarship97164UNIOR