Classification and Dissimilarity Analysis [Paperback]

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.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.1 Introduction.- 1.1 Classification in the history of Science.- 1.2 Dissimilarity analysis.- 1.3 Organisation of this publication.- 1.4 References.- 2 The partial order by inclusion of the principal classes of dissimilarity on a finite set, and some of their basic properties.- 2.1 Introduction.- 2.1.1 What is dissimilarity analysis?.- 2.1.2 Whats in this chapter?.- 2.2 Preliminaries.- 2.2.1 The vector space D generated by the dissimilarities.- 2.2.2 Some elementary dissimilarities.- 2.2.3 Some general types of dissimilarities.- 2.2.4 Stability under increasing transformations.- 2.2.5 The quotient space of an even dissimilarity.- 2.2.6 Embeddability in a metric space.- 2.2.7 The set of all semi-distances.- 2.2.8 Stability under repliclCÚ