Reverse Clustering : Formulation, Interpretation and Case Studies

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 6 Introduction 8 Contents 11 List of Figures 13 List of Tables 15 1 The Concept of Reverse Clustering 18 1.1 The Concept 18 1.2 The Notation 21 1.3 The Elements of Vector Z: The Dimensions of the Search Space 22 1.4 The Criterion: Maximising the Similarity Between Partitions PA and PB 28 1.5 The Search Procedure 29 References 30 2 Reverse Clustering—The Essence and The Interpretations 32 2.1 The Background and the Broad Context 32 2.2 Some More Specific Related Work 37 2.3 The Interpretations 42 References 48 3 Case Studies: An Introduction 53 3.1 A Short Characterisation of the Cases Studied 53 3.2 The Interpretations of the Cases Treated 56 References 57 4 The Road Traffic Data 59 4.1 The Setting 59 4.2 The Experiments 61 4.3 Conclusions 67 References 68 5 The Chemicals in the Natural Environment 69 5.1 The Data and the Background 69 5.2 The Procedure: Determining the Partition PA 72 5.3 The Procedure: Reverse Clustering 74 5.4 Discussion and Conclusions 77 References 78 6 Administrative Units, Part I 79 6.1 The Background: Polish Administrative Division and the Province of Masovia 79 6.2 The Data 80 6.3 The Analysis Regarding the Administrative Categorization of Municipalities 83 6.4 A Verification 87 6.5 The Analysis Regarding the Functional Categorization of Municipalities 88 6.6 Conclusions and Discussion 92 References 94 7 Administrative Units, Part II 95 7.1 The Background 95 7.2 The Computational Experiments 96 7.3 Discussion and Conclusions 103 References 104 8 Academic Examples 105 8.1 Introduction 105 8.2 Fisher’s Iris Data 105 8.3 Artificial Data Sets 107 8.4 Conclusions 110 References 110 9 Summary and Conclusions 111 9.1 Interpretation and Use of Results 111 9.2 Some Final Observations 114 Reference 117