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

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

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.

The refereed proceedings of the First Iberial Conference on Pattern Recognition and Image Analysis, IbPria 2003, held in Puerto de Andratx, Mallorca, Spain in June 2003. The 130 revised papers presented were carefully reviewed and selected from 185 full papers submitted. All current aspects of ongoing research in computer vision, image processing, pattern recognition, and speech recognition are addressed.

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

"While recognizing a "progressive ethos" - a mixture of idealistic vision and pragmatic reforms that characterized the period - Chambers elaborates the role of civic volunteerism as well as the state in achieving directed social change. He also emphasizes the importance of radical and conservative forces in shaping the so-called "Progressive Era.""--BOOK JACKET.

This book constitutes the refereed proceedings of the 10th International Workshop on Structural and Syntactic Pattern Recognition, SSPR 2004 and the 5th International Workshop on Statistical Techniques in Pattern Recognition, SPR 2004, held jointly in Lisbon, Portugal, in August 2004. The 59 revised full papers and 64 revised poster papers presented together with 4 invited papers were carefully reviewed and selected from 219 submissions. The papers are organized in topical sections on graphs; visual recognition and detection; contours, lines, and paths; matching and superposition; transduction and translation; image and video analysis; syntactics, languages, and strings; human shape and action; sequences and graphs; pattern matching and classification; document image analysis; shape analysis; multiple classifier systems; density estimation; clustering; feature selection; classification; and representation.

This original research monograph concerns various aspects of how (based on the decompositions of vertices of hypercube graphs with respect to their symmetric cycles) the vertex sets of related discrete hypercubes, as well as the power sets of the corresponding ground sets, emerge from rank 2 oriented matroids, from underlying rank 2 systems of linear inequalities, and thus literally from arrangements of straight lines crossing a common point on a piece of paper. It reveals some beautiful and earlier-hidden fragments in the true foundations of discrete mathematics. The central observation made and discussed in the book from various viewpoints consists in that 2t subsets of a finite t-element set Et, which form in a natural way a cyclic structure (well, just t subsets that are the vertices of a path in the cycle suffice), allow us to construct any of 2t subsets of the set Et by means of a more than elementary voting procedure expressed in basic linear algebraic terms. The monograph will be of interest to researchers, students, and readers in the fields of discrete mathematics, theoretical computer science, Boolean function theory, enumerative combinatorics and combinatorics on words, combinatorial optimization, coding theory, and discrete and computational geometry.

First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.