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Books > Computing & IT > Applications of computing > Databases > Data mining
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Pattern Recognition on Oriented Matroids (Hardcover)
Loot Price: R3,635
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Pattern Recognition on Oriented Matroids (Hardcover)
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Pattern Recognition on Oriented Matroids covers a range of
innovative problems in combinatorics, poset and graph theories,
optimization, and number theory that constitute a far-reaching
extension of the arsenal of committee methods in pattern
recognition. The groundwork for the modern committee theory was
laid in the mid-1960s, when it was shown that the familiar notion
of solution to a feasible system of linear inequalities has
ingenious analogues which can serve as collective solutions to
infeasible systems. A hierarchy of dialects in the language of
mathematics, for instance, open cones in the context of linear
inequality systems, regions of hyperplane arrangements, and maximal
covectors (or topes) of oriented matroids, provides an excellent
opportunity to take a fresh look at the infeasible system of
homogeneous strict linear inequalities - the standard working model
for the contradictory two-class pattern recognition problem in its
geometric setting. The universal language of oriented matroid
theory considerably simplifies a structural and enumerative
analysis of applied aspects of the infeasibility phenomenon. The
present book is devoted to several selected topics in the emerging
theory of pattern recognition on oriented matroids: the questions
of existence and applicability of matroidal generalizations of
committee decision rules and related graph-theoretic constructions
to oriented matroids with very weak restrictions on their
structural properties; a study (in which, in particular,
interesting subsequences of the Farey sequence appear naturally) of
the hierarchy of the corresponding tope committees; a description
of the three-tope committees that are the most attractive
approximation to the notion of solution to an infeasible system of
linear constraints; an application of convexity in oriented
matroids as well as blocker constructions in combinatorial
optimization and in poset theory to enumerative problems on tope
committees; an attempt to clarify how elementary changes
(one-element reorientations) in an oriented matroid affect the
family of its tope committees; a discrete Fourier analysis of the
important family of critical tope committees through rank and
distance relations in the tope poset and the tope graph; the
characterization of a key combinatorial role played by the
symmetric cycles in hypercube graphs. Contents Oriented Matroids,
the Pattern Recognition Problem, and Tope Committees Boolean
Intervals Dehn-Sommerville Type Relations Farey Subsequences
Blocking Sets of Set Families, and Absolute Blocking Constructions
in Posets Committees of Set Families, and Relative Blocking
Constructions in Posets Layers of Tope Committees Three-Tope
Committees Halfspaces, Convex Sets, and Tope Committees Tope
Committees and Reorientations of Oriented Matroids Topes and
Critical Committees Critical Committees and Distance Signals
Symmetric Cycles in the Hypercube Graphs
General
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