Data Analysis and Applications 1: Clustering and Regression, Modeling-estimating, Forecasting and Data Mining [Hardcover]

This series of books collects a diverse array of work that provides the reader with theoretical and applied information on data analysis methods, models, and techniques, along with appropriate applications.

Volume 1 begins with an introductory chapter by Gilbert Saporta, a leading expert in the field, who summarizes the developments in data analysis over the last 50 years. The book is then divided into three parts: Part 1 presents clustering and regression cases; Part 2 examines grouping and decomposition, GARCH and threshold models, structural equations, and SME modeling; and Part 3 presents symbolic data analysis, time series and multiple choice models, modeling in demography, and data mining.

Preface xi

Introduction xv
Gilbert SAPORTA

Part 1 Clustering and Regression 1

Chapter 1 Cluster Validation by Measurement of Clustering Characteristics Relevant to the User 3
Christian HENNIG

1.1 Introduction 3

1.2 General notation 5

1.3 Aspects of cluster validity 6

1.3.1 Small within-cluster dissimilarities 6

1.3.2 Between-cluster separation 7

1.3.3 Representation of objects by centroids 7

1.3.4 Representation of dissimilarity structure by clustering 8

1.3.5 Small within-cluster gaps 9

1.3.6 Density modes and valleys 9

1.3.7 Uniform within-cluster density 12

1.3.8 Entropy 12

1.3.9 Parsimony 13

1.3.10 Similarity to homogeneous distributional shapes 13

1.3.11 Stability 13

1.3.12 Further Aspects 14

1.4 Aggregation of indexes 14

1.5 Random