Graphs For Pattern Recognition: Infeasible Systems Of Linear Inequalities
by Damir Gainanov /
2016 / English / PDF
1.3 MB Download
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.
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.
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.
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:
Contents:
Preface
Preface
Pattern recognition, infeasible systems of linear inequalities,
and graphs
Pattern recognition, infeasible systems of linear inequalities,
and graphs
Infeasible monotone systems of constraints
Infeasible monotone systems of constraints
Complexes, (hyper)graphs, and inequality systems
Complexes, (hyper)graphs, and inequality systems
Polytopes, positive bases, and inequality systems
Polytopes, positive bases, and inequality systems
Monotone Boolean functions, complexes, graphs, and inequality
systems
Monotone Boolean functions, complexes, graphs, and inequality
systems
Inequality systems, committees, (hyper)graphs, and alternative
covers
Inequality systems, committees, (hyper)graphs, and alternative
covers
Bibliography
Bibliography
List of notation
List of notation
Index
Index
