Mathematical Classification and Clustering

I am very happy to have this opportunity to present the work of Boris Mirkin, a distinguished Russian scholar in the areas of data analysis and decision making methodologies. The monograph is devoted entirely to clustering, a discipline dispersed through many theoretical and application areas, from mathematical statistics and combina torial optimization to biology, sociology and organizational structures. It compiles an immense amount of research done to date, including many original Russian de velopments never presented to the international community before (for instance, cluster-by-cluster versions of the K-Means method in Chapter 4 or uniform par titioning in Chapter 5). The author's approach, approximation clustering, allows him both to systematize a great part of the discipline and to develop many in novative methods in the framework of optimization problems. The optimization methods considered are proved to be meaningful in the contexts of data analysis and clustering. The material presented in this book is quite interesting and stimulating in paradigms, clustering and optimization. On the other hand, it has a substantial application appeal. The book will be useful both to specialists and students in the fields of data analysis and clustering as well as in biology, psychology, economics, marketing research, artificial intelligence, and other scientific disciplines. Panos Pardalos, Series Editor.

Zusammenfassung
The monograph is devoted entirely to clustering, a discipline dispersed through many theoretical and application areas, from mathematical statistics and combina torial optimization to biology, sociology and organizational structures.

Inhalt
Foreword. Preface. 1. Classes and Clusters. 2. Geometry of Data. 3. Clustering Algorithms: A Review. 4. Single Cluster Clustering. 5. Partition: Square Data Table. 6. Partition: Rectangular Table. 7. Hierarchy as a Clustering Structure. Bibliography. Index.