Classification and Dissimilarity Analysis

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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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.

• Analysis of dissimilarity
• Classification
• Cluster analysis
• calculus
• differential equation
• exponential function

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

  Bernard Cutsem

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