Ebook: Classification and Dissimilarity Analysis

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.

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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.

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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.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-4
The partial order by inclusion of the principal classes of dissimilarity on a finite set, and some of their basic properties....Pages 5-65
Similarity functions....Pages 67-86
An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. I....Pages 87-119
An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. II....Pages 121-147
The residuation model for the ordinal construction of dissimilarities and other valued objects....Pages 149-172
On exchangeability-based equivalence relations induced by strongly Robinson and, in particular, by quadripolar Robinson dissimilarity matrices....Pages 173-199
Dimensionality problems in L 1-norm representations....Pages 201-224
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.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-4
The partial order by inclusion of the principal classes of dissimilarity on a finite set, and some of their basic properties....Pages 5-65
Similarity functions....Pages 67-86
An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. I....Pages 87-119
An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. II....Pages 121-147
The residuation model for the ordinal construction of dissimilarities and other valued objects....Pages 149-172
On exchangeability-based equivalence relations induced by strongly Robinson and, in particular, by quadripolar Robinson dissimilarity matrices....Pages 173-199
Dimensionality problems in L 1-norm representations....Pages 201-224
Back Matter....Pages 225-240
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