Pattern Recognition on Oriented Matroids

Author: Andrey O. Matveev

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110531143

Category: Mathematics

Page: 231

View: 4122

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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
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Pattern Recognition

Introduction, Features, Classifiers and Principles

Author: Jürgen Beyerer,Matthias Richter,Matthias Nagel

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 311053794X

Category: Computers

Page: 311

View: 4070

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The book offers a thorough introduction to Pattern Recognition aimed at master and advanced bachelor students of engineering and the natural sciences. Besides classification - the heart of Pattern Recognition - special emphasis is put on features, their typology, their properties and their systematic construction. Additionally, general principles that govern Pattern Recognition are illustrated and explained in a comprehensible way. Rather than presenting a complete overview over the rapidly evolving field, the book is to clarifies the concepts so that the reader can easily understand the underlying ideas and the rationale behind the methods. For this purpose, the mathematical treatment of Pattern Recognition is pushed so far that the mechanisms of action become clear and visible, but not farther. Therefore, not all derivations are driven into the last mathematical detail, as a mathematician would expect it. Ideas of proofs are presented instead of complete proofs. From the authors’ point of view, this concept allows to teach the essential ideas of Pattern Recognition with sufficient depth within a relatively lean book. Mathematical methods explained thoroughly Extremely practical approach with many examples Based on over ten years lecture at Karlsruhe Institute of Technology For students but also for practitioners
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Progress in Pattern Recognition, Speech and Image Analysis

8th Iberoamerican Congress on Pattern Recognition, CIARP 2003, Havana, Cuba, November 26-29, 2003, Proceedings

Author: Alberto Sanfeliu,José Ruiz-Shulcloper

Publisher: Springer Science & Business Media

ISBN: 354020590X

Category: Computers

Page: 693

View: 3600

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This book constitutes the refereed proceedings of the 8th Iberoamerican Congress on Pattern Recognition, CIARP 2003, held in Havana, Cuba, in November 2003. The 82 revised full papers presented together with two invited papers were carefully reviewed and selected from 140 submissions. All current issues in pattern recognition, image processing, and computer vision are addressed as well as applications in domains like robotics, health, entertainment, space exploration, telecommunications, speech processing, data analysis, document recognition, etc.
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Classification, Data Analysis, and Data Highways

Proceedings of the 21st Annual Conference of the Gesellschaft für Klassifikation e.V., University of Potsdam, March 12–14, 1997

Author: Ingo Balderjahn,Rudolf Mathar,Martin Schader

Publisher: Springer Science & Business Media

ISBN: 3642720870

Category: Business & Economics

Page: 414

View: 2494

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This volume presents 43 articles dealing with models and methods of data analysis and classification, statistics and stochastics, information systems and WWW- and Internet-related topics as well as many applications. These articles are selected from more than 100 papers presented at the 21st Annual Conference of the Gesellschaft für Klassifikation. Based on the submitted and revised papers six sections have been arranged: - Classification and Data Analysis - Mathematical and Statistical Methods - World Wide Web and the Internet - Speech and Pattern Recognition - Marketing.
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Discrete and Computational Geometry

The Goodman-Pollack Festschrift

Author: Boris Aronov,Saugata Basu,Janos Pach,Micha Sharir

Publisher: Springer Science & Business Media

ISBN: 9783540003717

Category: Mathematics

Page: 853

View: 1574

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An impressive collection of original research papers in discrete and computational geometry, contributed by many leading researchers in these fields, as a tribute to Jacob E. Goodman and Richard Pollack, two of the ‘founding fathers’ of the area, on the occasion of their 2/3 x 100 birthdays. The topics covered by the 41 papers provide professionals and graduate students with a comprehensive presentation of the state of the art in most aspects of discrete and computational geometry, including geometric algorithms, study of arrangements, geometric graph theory, quantitative and algorithmic real algebraic geometry, with important connections to algebraic geometry, convexity, polyhedral combinatorics, the theory of packing, covering, and tiling. The book serves as an invaluable source of reference in this discipline.
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Farey Sequences

Duality and Maps Between Subsequences

Author: Andrey O. Matveev

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110546655

Category: Mathematics

Page: 182

View: 9559

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As a first comprehensive overview on Farey sequences and subsequences, this monograph is intended as a reference for anyone looking for specific material or formulas related to the subject. Duality of subsequences and maps between them are discussed and explicit proofs are shown in detail. From the Content Basic structural and enumerative properties of Farey sequences, Collective decision making, Committee methods in pattern recognition, Farey duality, Farey sequence, Fundamental Farey subsequences, Monotone bijections between Farey subsequences
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Handbook of Discrete and Computational Geometry, Second Edition

Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 9781420035315

Category: Mathematics

Page: 1560

View: 4481

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While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies
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