宮本定明（著）／階層的クラスタリングの理論 Theory of Agglomerative Hierarchical Clustering (Behaviormetrics: Quantitative Approaches to Human Behavior)

Miyamoto, Sadaaki

Springer Verlag, Singapore（2022/03発売）

• 製本 Hardcover:ハードカバー版／ページ数 109 p.
• 言語 ENG
• 商品コード 9789811904196
• DDC分類 519

Full Description

This book discusses recent theoretical developments in agglomerative hierarchical clustering. The general understanding of agglomerative hierarchical clustering is that its theory was completed long ago and there is no room for further methodological studies, at least in its fundamental structure. This book has been planned counter to that view: it will show that there are possibilities for further theoretical studies and they will be not only for methodological interests but also for usefulness in real applications. When compared with traditional textbooks, the present book has several notable features. First, standard linkage methods and agglomerative procedure are described by a general algorithm in which dendrogram output is expressed by a recursive subprogram. That subprogram describes an abstract tree structure, which is used for a two-stage linkage method for a greater number of objects. A fundamental theorem for single linkage using a fuzzy graph is proved, which uncovers several theoretical features of single linkage. Other theoretical properties such as dendrogram reversals are discussed. New methods using positive-definite kernels are considered, and some properties of the Ward method using kernels are studied. Overall, theoretical features are discussed, but the results are useful as well for application-oriented users of agglomerative clustering.



 

Contents

Introduction.- Linkage Methods and Algorithms.- Theory of the Single Linkage Method.- Positive-Definite Kernels in Agglomerative Hierarchical Clustering.- Some Other Topics in Agglomerative Hierarchical Clustering.- Miscellanea.