Theory of Agglomerative Hierarchical Clustering (eBook)

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.

 

Dr. Miyamoto was born in Osaka, Japan, in 1950. He received the B.S., M.S., and the Dr. Eng. degrees in Applied Mathematics and Physics Engineering from Kyoto University, Japan, in 1973, 1975, and 1978, respectively. He was Assistant Professor from 1980 to 1987 and Associate Professor from 1987 to 1990 in the University of Tsukuba. He was Professor with the Faculty of Engineering, the University of Tokushima, where he was working from 1990 to 1994. After working as Professor at the University of Tsukuba from 1994, he retired on March 31, 2016, and became Professor Emeritus from April 1, 2016.

His research interests include methodology for fuzzy systems and uncertainty modeling. In particular, he has been working on data clustering algorithms and related classification methods, multisets, rough sets, and algorithms for data mining. He is Member of the Japan Society of Fuzzy Theory and Systems, and Japanese Classification Society. He has served a number of international conferences as Chair, Co-chair, and Committee Member. He received excellent paper awards from the Japan Society of Fuzzy Theory and Systems in 1994 and 1999. He has published three books of which two are in English and the other in Japanese. He also has published one edited book and over 300 research papers. His papers/books have been cited more than 2,000 times. He became a fellow of International Fuzzy Systems Association in 2007. He was also elected to be a fellow of Japanese Classification Society in 2017.

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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.