Reverse Clustering: Formulation, Interpretation and Case Studies

Description

This book presents a new perspective on and a new approach to a wide spectrum of situations, related to data analysis, actually, a kind of a new paradigm. Namely, for a given data set and its partition, whose origins may be of any kind, the authors try to reconstruct this partition on the basis of the data set given, using very broadly conceived clustering procedure. The main advantages of this new paradigm concern the substantive aspects of the particular cases considered, mainly in view of the variety of interpretations, which can be assumed in the framework of the paradigm. Due to the novel problem formulation and the flexibility in the interpretations of this problem and its components, the domains, which are encompassed (or at least affected) by the potential use of the paradigm, include cluster analysis, classification, outlier detection, feature selection, and even factor analysis as well as geometry of the data set. The book is useful for all those who look for new, nonconventional approaches to their data analysis problems. Preface Introduction Contents List of Figures List of Tables 1 The Concept of Reverse Clustering 1.1 The Concept 1.2 The Notation 1.3 The Elements of Vector Z: The Dimensions of the Search Space 1.4 The Criterion: Maximising the Similarity Between Partitions PA and PB 1.5 The Search Procedure References 2 Reverse Clustering—The Essence and The Interpretations 2.1 The Background and the Broad Context 2.2 Some More Specific Related Work 2.3 The Interpretations References 3 Case Studies: An Introduction 3.1 A Short Characterisation of the Cases Studied 3.2 The Interpretations of the Cases Treated References 4 The Road Traffic Data 4.1 The Setting 4.2 The Experiments 4.3 Conclusions References 5 The Chemicals in the Natural Environment 5.1 The Data and the Background 5.2 The Procedure: Determining the Partition PA 5.3 The Procedure: Reverse Clustering 5.4 Discussion and Conclusions References 6 Administrative Units, Part I 6.1 The Background: Polish Administrative Division and the Province of Masovia 6.2 The Data 6.3 The Analysis Regarding the Administrative Categorization of Municipalities 6.4 A Verification 6.5 The Analysis Regarding the Functional Categorization of Municipalities 6.6 Conclusions and Discussion References 7 Administrative Units, Part II 7.1 The Background 7.2 The Computational Experiments 7.3 Discussion and Conclusions References 8 Academic Examples 8.1 Introduction 8.2 Fisher’s Iris Data 8.3 Artificial Data Sets 8.4 Conclusions References 9 Summary and Conclusions 9.1 Interpretation and Use of Results 9.2 Some Final Observations Reference