Graphs for Pattern Recognition: Infeasible Systems of Linear Inequalities

Damir Gainanov

Open Access Published by De Gruyter 2016

Graphs for Pattern Recognition

Infeasible Systems of Linear Inequalities

Damir Gainanov

https://doi.org/10.1515/9783110481068

Overview
Contents

About this book

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:
Preface
Pattern recognition, infeasible systems of linear inequalities, and graphs
Infeasible monotone systems of constraints
Complexes, (hyper)graphs, and inequality systems
Polytopes, positive bases, and inequality systems
Monotone Boolean functions, complexes, graphs, and inequality systems
Inequality systems, committees, (hyper)graphs, and alternative covers
Bibliography
List of notation
Index

Author / Editor information

Damir Gainanov, Ural Federal University, Russia.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Open Access Download PDF	V
Contents Publicly Available Download PDF	IX
1. Pattern recognition, infeasible systems of linear inequalities, and graphs Open Access Download PDF	1
2. Complexes, (hyper)graphs, and inequality systems Open Access Download PDF	20
3. Polytopes, positive bases, and inequality systems Open Access Download PDF	58
4. Monotone Boolean functions, complexes, graphs, and inequality systems Open Access Download PDF	93
5. Inequality systems, committees, (hyper)graphs, and alternative covers Open Access Download PDF	115
Bibliography Open Access Download PDF	133
List of notation Open Access Download PDF	141
Index Open Access Download PDF	144

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Mathematicians, Electrical Engineers, Computer Scientists.
Pages
- Front matter: 10
- Main content: 148
Keywords: Mustererkennung; Kombinatorik; Graphentheorie; Lineares Gleichungssystem; Data Mining

eBook

Published: October 10, 2016
ISBN: 9783110481068

Hardcover

Published: October 10, 2016
ISBN: 9783110480139