xiv Preface presentation.We bring together many results that are scattered through the literature of several fields.The most unique feature of this book is its thorough,understand- able treatment of cluster validity,or the objective validation of the results of cluster analysis,from the application viewpoint. This book resulted from class notes that the authors have used in a graduate course on clustering and scaling algorithms in the Department of Computer Science at Michigan State University.We owe a debt of gratitude to the many graduate students who have helped develop this book.Special thanks are due to Karl Pettis, Tom Bailey,Neal Wyse,Steve Smith,Gautam Biswas,George Cross,James Coggins,Phil Nagan,Rick Hoffman,Xiaobo Li,Pat Flynn,and C.C.Chen. The prerequisite for this course is probability theory,matrix algebra,computer programming,and data structures.In addition to homework problems and an exam, the students in this course work on a project which can range from the analysis of a real data set to comparative analysis of various algorithms.This course is particularly useful for students who wish to pursue research in pattern recognition, image processing,and artificial intelligence.Interested readers may contact the authors for homework problems for this course. We have a long-standing interest in cluster analysis,especially in the problems of cluster validity and cluster tendency.Our research in this area has been funded by the National Science Foundation.We are grateful to NSF for this support. We also wish to acknowledge the support and the facilities provided by the Depart- ment of Computer Science,Michigan State University,which were essential for the completion of this book. A.K.JAIN R.C.DUBES