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
