The Resource Pattern recognition on oriented matroids, Andrey O. Matveev
Pattern recognition on oriented matroids, Andrey O. Matveev
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The item Pattern recognition on oriented matroids, Andrey O. Matveev represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.This item is available to borrow from 1 library branch.
Resource Information
The item Pattern recognition on oriented matroids, Andrey O. Matveev represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (xi, 219 pages)
- 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
- Isbn
- 9783110531145
- Label
- Pattern recognition on oriented matroids
- Title
- Pattern recognition on oriented matroids
- Statement of responsibility
- Andrey O. Matveev
- Subject
-
- (BISAC Subject Heading)COM018000: COM018000 COMPUTERS / Data Processing / General
- (BISAC Subject Heading)COM021030: COM021030 COMPUTERS / Database Management / Data Mining
- (BISAC Subject Heading)COM051300: COM051300 COMPUTERS / Programming / Algorithms
- (BISAC Subject Heading)MAT036000
- (Produktform)Electronic book text
- (Produktrabattgruppe)PR: rabattbeschränkt/Bibliothekswerke
- (VLB-WN)9620
- (Zielgruppe)Fachpublikum/ Wissenschaft
- Committee methods in pattern recognition, hypercubes, hyperplane arrangements, infeasible systems of linear inequalities, oriented matroids
- Data Mining
- Electronic book
- Graphentheorie
- Kombinatorik
- Lineares Gleichungssystem
- MATHEMATICS -- General
- Mustererkennung
- Mustererkennung
- Oriented matroids
- Oriented matroids
- Orientiertes Matroid
- Electronic books
- (BISAC Subject Heading)COM018000: COM018000 COMPUTERS / Data Processing
- 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
- 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
- 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
- 9783110531145
- 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
- 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
- 9783110531145
- 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
Subject
- (BISAC Subject Heading)COM018000: COM018000 COMPUTERS / Data Processing / General
- (BISAC Subject Heading)COM021030: COM021030 COMPUTERS / Database Management / Data Mining
- (BISAC Subject Heading)COM051300: COM051300 COMPUTERS / Programming / Algorithms
- (BISAC Subject Heading)MAT036000
- (Produktform)Electronic book text
- (Produktrabattgruppe)PR: rabattbeschränkt/Bibliothekswerke
- (VLB-WN)9620
- (Zielgruppe)Fachpublikum/ Wissenschaft
- Committee methods in pattern recognition, hypercubes, hyperplane arrangements, infeasible systems of linear inequalities, oriented matroids
- Data Mining
- Electronic book
- Graphentheorie
- Kombinatorik
- Lineares Gleichungssystem
- MATHEMATICS -- General
- Mustererkennung
- Mustererkennung
- Oriented matroids
- Oriented matroids
- Orientiertes Matroid
- Electronic books
- (BISAC Subject Heading)COM018000: COM018000 COMPUTERS / Data Processing
Genre
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.mst.edu/portal/Pattern-recognition-on-oriented-matroids-Andrey/teZbPP7en9w/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.mst.edu/portal/Pattern-recognition-on-oriented-matroids-Andrey/teZbPP7en9w/">Pattern recognition on oriented matroids, Andrey O. Matveev</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.mst.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.mst.edu/">Missouri University of Science & Technology Library</a></span></span></span></span></div>
