Graphs for Pattern Recognition

Infeasible Systems of Linear Inequalities
1. Auflage 2016
ISBN: 978-3-11-048013-9
Verlag: De Gruyter

Buch, Englisch, 148 Seiten, HC runder Rücken kaschiert, Format (B × H): 175 mm x 246 mm, Gewicht: 458 g

This 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

Zielgruppe

Mathematicians, Electrical Engineers, Computer Scientists.

Autoren/Hrsg.

Gainanov, Damir

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Mustererkennung, Biometrik
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Data Mining
• Mathematik | Informatik Mathematik Operations Research Graphentheorie

Über Autor(innen)

Damir Gainanov, Ural Federal University, Russia.