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The Resource Pattern recognition on oriented matroids, Andrey O. Matveev

Pattern recognition on oriented matroids, Andrey O. Matveev

Label
Pattern recognition on oriented matroids
Title
Pattern recognition on oriented matroids
Statement of responsibility
Andrey O. Matveev
Creator
Author
Subject
Genre
Language
eng
Summary
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. ContentsOriented Matroids, the Pattern Recognition Problem, and Tope CommitteesBoolean IntervalsDehn-Sommerville Type RelationsFarey SubsequencesBlocking Sets of Set Families, and Absolute Blocking Constructions in PosetsCommittees of Set Families, and Relative Blocking Constructions in PosetsLayers of Tope CommitteesThree-Tope CommitteesHalfspaces, Convex Sets, and Tope CommitteesTope Committees and Reorientations of Oriented MatroidsTopes and Critical CommitteesCritical Committees and Distance SignalsSymmetric Cycles in the Hypercube Graphs
Member of
Cataloging source
DEGRU
http://library.link/vocab/creatorName
Matveev, Andrey O
Dewey number
510
Illustrations
illustrations
Index
index present
Language note
In English
LC call number
QA166.6
LC item number
.M38 2017
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Oriented matroids
  • MATHEMATICS
  • Oriented matroids
  • Orientiertes Matroid
  • Mustererkennung
Label
Pattern recognition on oriented matroids, Andrey O. Matveev
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 5. Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets
  • 6. Committees of Set Families, and Relative Blocking Constructions in Posets
  • 7. Layers of Tope Committees
  • 8. Three-Tope Committees
  • 9. Halfspaces, Convex Sets, and Tope Committees
  • 10. Tope Committees and Reorientations of Oriented Matroids
  • 11. Topes and Critical Committees
  • 12. Critical Committees and Distance Signals
  • 13. Symmetric Cycles in the Hypercube Graphs
  • Bibliography
  • Frontmatter
  • List of Notation
  • Index
  • Preface
  • Contents
  • Committees for Pattern Recognition: Infeasible Systems of Linear Inequalities, Hyperplane Arrangements, and Realizable Oriented Matroids
  • 1. Oriented Matroids, the Pattern Recognition Problem, and Tope Committees
  • 2. Boolean Intervals
  • 3. Dehn-Sommerville Type Relations
  • 4. Farey Subsequences
Control code
1004883055
Extent
1 online resource (xi, 219 pages)
Form of item
online
Isbn
9783110531152
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
  • 10.1515/9783110531145
  • 9783110531145
  • urn:nbn:de:101:1-201710046974
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
1036841
Specific material designation
remote
System control number
(OCoLC)1004883055
Label
Pattern recognition on oriented matroids, Andrey O. Matveev
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 5. Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets
  • 6. Committees of Set Families, and Relative Blocking Constructions in Posets
  • 7. Layers of Tope Committees
  • 8. Three-Tope Committees
  • 9. Halfspaces, Convex Sets, and Tope Committees
  • 10. Tope Committees and Reorientations of Oriented Matroids
  • 11. Topes and Critical Committees
  • 12. Critical Committees and Distance Signals
  • 13. Symmetric Cycles in the Hypercube Graphs
  • Bibliography
  • Frontmatter
  • List of Notation
  • Index
  • Preface
  • Contents
  • Committees for Pattern Recognition: Infeasible Systems of Linear Inequalities, Hyperplane Arrangements, and Realizable Oriented Matroids
  • 1. Oriented Matroids, the Pattern Recognition Problem, and Tope Committees
  • 2. Boolean Intervals
  • 3. Dehn-Sommerville Type Relations
  • 4. Farey Subsequences
Control code
1004883055
Extent
1 online resource (xi, 219 pages)
Form of item
online
Isbn
9783110531152
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
  • 10.1515/9783110531145
  • 9783110531145
  • urn:nbn:de:101:1-201710046974
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
1036841
Specific material designation
remote
System control number
(OCoLC)1004883055

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