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Classification and Dissimilarity Analysis

  • Book
  • © 1994

Overview

Editors:
  1. Bernard Cutsem

    1. Laboratoire de Modélisation et Calcul, Institut IMAG, Grenoble Cedex 9, France

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Part of the book series: Lecture Notes in Statistics (LNS, volume 93)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Bernard Van Cutsem
    Pages 1-4

  3. The partial order by inclusion of the principal classes of dissimilarity on a finite set, and some of their basic properties

    • Frank Critchley, Bernard Fichet
    Pages 5-65

  4. Similarity functions

    • Serge Joly, Georges Le Calvé
    Pages 67-86

  5. An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. I

    • Frank Critchley, Bernard Van Cutsem
    Pages 87-119

  6. An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. II

    • Frank Critchley, Bernard Van Cutsem
    Pages 121-147

  7. The residuation model for the ordinal construction of dissimilarities and other valued objects

    • Bruno Leclerc
    Pages 149-172

  8. On exchangeability-based equivalence relations induced by strongly Robinson and, in particular, by quadripolar Robinson dissimilarity matrices

    • Frank Critchley
    Pages 173-199

  9. Dimensionality problems in L 1-norm representations

    • Bernard Fichet
    Pages 201-224

  10. Back Matter

    Pages 225-240
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Keywords

About this book

Classifying objects according to their likeness seems to have been a step in the human process of acquiring knowledge, and it is certainly a basic part of many of the sciences. Historically, the scientific process has involved classification and organization particularly in sciences such as botany, geology, astronomy, and linguistics. In a modern context, we may view classification as deriving a hierarchical clustering of objects. Thus, classification is close to factorial analysis methods and to multi-dimensional scaling methods. It provides a mathematical underpinning to the analysis of dissimilarities between objects.

Editors and Affiliations

  • Laboratoire de Modélisation et Calcul, Institut IMAG, Grenoble Cedex 9, France

    Bernard Cutsem

Bibliographic Information

  • Book Title: Classification and Dissimilarity Analysis

  • Editors: Bernard Cutsem

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-2686-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1994

  • Softcover ISBN: 978-0-387-94400-5Published: 07 October 1994

  • eBook ISBN: 978-1-4612-2686-4Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: XIII, 238

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes

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