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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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Graphs for Pattern Recognition - Infeasible Systems of Linear Inequalities (Hardcover, Digital original)
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Graphs for Pattern Recognition - Infeasible Systems of Linear Inequalities (Hardcover, Digital original)
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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
General
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