Graphs for Pattern Recognition : Infeasible Systems of Linear Inequalities / Damir Gainanov.

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 -- Index

Open Access unrestricted online access star

https://purl.org/coar/access_right/c_abf2

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

Mode of access: Internet via World Wide Web.

This eBook is made available Open Access under a CC BY-NC-ND 4.0 license:

https://creativecommons.org/licenses/by-nc-nd/4.0

https://www.degruyter.com/dg/page/open-access-policy

In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Feb 2021)