Pattern Recognition on Oriented Matroids / / Andrey O. Matveev.
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 theo...
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Matveev, Andrey O., author. aut http://id.loc.gov/vocabulary/relators/aut Pattern Recognition on Oriented Matroids / Andrey O. Matveev. Berlin ; Boston : De Gruyter, [2017] ©2017 1 online resource (XII, 219 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- 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 -- 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 -- List of Notation -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Oriented matroids. Data Mining. Graphentheorie. Kombinatorik. Lineares Gleichungssystem. Mustererkennung. MATHEMATICS / Combinatorics. bisacsh Committee methods in pattern recognition, hypercubes, hyperplane arrangements, infeasible systems of linear inequalities, oriented matroids. Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 9783110719543 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 9783110540550 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE ENGLISH 2017 9783110625264 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 9783110548204 ZDB-23-DMA EPUB 9783110530841 print 9783110530711 https://doi.org/10.1515/9783110531145 https://www.degruyter.com/isbn/9783110531145 Cover https://www.degruyter.com/cover/covers/9783110531145.jpg |
language |
English |
format |
eBook |
author |
Matveev, Andrey O., Matveev, Andrey O., |
spellingShingle |
Matveev, Andrey O., Matveev, Andrey O., Pattern Recognition on Oriented Matroids / Frontmatter -- 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 -- 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 -- List of Notation -- Index |
author_facet |
Matveev, Andrey O., Matveev, Andrey O., |
author_variant |
a o m ao aom a o m ao aom |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Matveev, Andrey O., |
title |
Pattern Recognition on Oriented Matroids / |
title_full |
Pattern Recognition on Oriented Matroids / Andrey O. Matveev. |
title_fullStr |
Pattern Recognition on Oriented Matroids / Andrey O. Matveev. |
title_full_unstemmed |
Pattern Recognition on Oriented Matroids / Andrey O. Matveev. |
title_auth |
Pattern Recognition on Oriented Matroids / |
title_alt |
Frontmatter -- 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 -- 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 -- List of Notation -- Index |
title_new |
Pattern Recognition on Oriented Matroids / |
title_sort |
pattern recognition on oriented matroids / |
publisher |
De Gruyter, |
publishDate |
2017 |
physical |
1 online resource (XII, 219 p.) |
contents |
Frontmatter -- 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 -- 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 -- List of Notation -- Index |
isbn |
9783110531145 9783110719543 9783110540550 9783110625264 9783110548204 9783110530841 9783110530711 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA166 |
callnumber-sort |
QA 3166.6 M388 42017 |
url |
https://doi.org/10.1515/9783110531145 https://www.degruyter.com/isbn/9783110531145 https://www.degruyter.com/cover/covers/9783110531145.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
511 - General principles of mathematics |
dewey-full |
511.6 |
dewey-sort |
3511.6 |
dewey-raw |
511.6 |
dewey-search |
511.6 |
doi_str_mv |
10.1515/9783110531145 |
oclc_num |
1004883055 |
work_keys_str_mv |
AT matveevandreyo patternrecognitiononorientedmatroids |
status_str |
n |
ids_txt_mv |
(DE-B1597)477216 (OCoLC)1004883055 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE ENGLISH 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 |
is_hierarchy_title |
Pattern Recognition on Oriented Matroids / |
container_title |
Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 |
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fullrecord |
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