LEADER 03831nam 2200613 450 001 996328048203316 005 20200520144314.0 010 $a3-11-048030-1 010 $a3-11-048106-5 024 7 $a10.1515/9783110481068 035 $a(CKB)3850000000001073 035 $a(EBL)4718418 035 $a(OCoLC)962793042 035 $a(DE-B1597)466925 035 $a(OCoLC)951141809 035 $a(OCoLC)963114749 035 $a(DE-B1597)9783110481068 035 $a(Au-PeEL)EBL4718418 035 $a(CaPaEBR)ebr11283245 035 $a(CaONFJC)MIL964181 035 $a(OCoLC)961059086 035 $a(ScCtBLL)a80371dd-766f-4802-9ff9-c024f7263329 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/48863 035 $a(CaSebORM)9783110480306 035 $a(MiAaPQ)EBC4718418 035 $a(EXLCZ)993850000000001073 100 $a20161028h20162016 uy 0 101 0 $ager 135 $aurcn#nnn||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGraphs for pattern recognition $einfeasible systems of linear inequalities /$fDamir Gainanov 210 $cDe Gruyter$d2016 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2016. 210 4$dİ2016 215 $a1 online resource (x, 147 pages) 311 $a3-11-048013-1 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPreface -- $tContents -- $t1. Pattern recognition, infeasible systems of linear inequalities, and graphs -- $t2. Complexes, (hyper)graphs, and inequality systems -- $t3. Polytopes, positive bases, and inequality systems -- $t4. Monotone Boolean functions, complexes, graphs, and inequality systems -- $t5. Inequality systems, committees, (hyper)graphs, and alternative covers -- $tBibliography -- $tList of notation -- $tIndex 330 $aThis 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 notationIndex 606 $aInequalities (Mathematics) 606 $aGraph theory 615 0$aInequalities (Mathematics) 615 0$aGraph theory. 676 $a516/.1 700 $aGainanov$b Damir$g(Damir N.),$0871838 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996328048203316 996 $aGraphs for pattern recognition$91946278 997 $aUNISA