Theory of Agglomerative Hierarchical Clustering

This book discusses recent theoretical developments in agglomerative hierarchical clustering, which suggests that there are possibilities for further studies that can be useful for real applications. It describes standard linkage methods and agglomerative procedures using a general algorithm, proves a fundamental theorem for single linkage using a fuzzy graph, and discusses other theoretical properties such as dendrogram reversals. New methods using positive-definite kernels are considered, and the results are useful for application-oriented users of agglomerative clustering.

Format: Hardback
Length: 109 pages
Publication date: 22 March 2022
Publisher: Springer Verlag, Singapore

This comprehensive book delves into the latest theoretical advancements in agglomerative hierarchical clustering, challenging the notion that the theory has reached its full potential and that further methodological studies are unnecessary. Counter to this prevailing perspective, this book showcases the exciting possibilities for theoretical exploration, not only for methodological interests but also for practical applications.

One of the notable features of this book is its approach to standard linkage methods and agglomerative procedures. It presents a general algorithm that encompasses both, allowing for the expression of dendrogram output through a recursive subprogram. This subprogram describes an abstract tree structure, which serves as the foundation for a two-stage linkage method for handling a larger number of objects. Furthermore, a fundamental theorem for single linkage using a fuzzy graph is established, unveiling several theoretical aspects of single linkage. The book also delves into other theoretical properties, such as dendrogram reversals, providing valuable insights into the field.

In addition to theoretical discussions, the book explores new methods utilizing positive-definite kernels, offering potential solutions for complex clustering scenarios. Furthermore, it examines the properties of the Ward method using kernels, shedding light on its effectiveness and limitations. While the focus of the book is on theoretical developments, the results presented are equally valuable for application-oriented users of agglomerative clustering.

Overall, this book serves as a valuable resource for researchers, practitioners, and students interested in the field of agglomerative hierarchical clustering. It provides a comprehensive overview of the latest theoretical advancements, while also offering practical insights and applications that can be utilized in various real-world scenarios.

Weight: 354g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811904196
Edition number: 1st ed. 2022