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This unique compendium gives an updated presentation of clustering, one of the most challenging tasks in machine learning. Clustering is a part of machine learning that seeks to identify groups into sets of objects such that objects that belong to the same group are as similar as possible, and objects that belong to two distinct groups are as dissimilar as possible. In general, clustering exploration is based on computing similarities (or dissimilarities) between objects but does not provide the reasons for the existence of these groupings. Various notions of dissimilarities are considered among objects ranging from simple dissimilarities, metrics on linear spaces, ultrametrics, and extensions of these measures to sets. Studying these measures requires incursions in a variety of mathematical disciplines ranging from linear algebra and optimization to functional analysis and topology. The book provides a unitary presentation of classical and contemporary algorithms ranging from partitional and hierarchical clustering up to density-based clustering, clustering of categorical data, and spectral clustering.
Most of the mathematical background is provided in appendices, highlighting algebraic and complexity theory, in order to make this volume as self-contained as possible. A substantial number of exercises and supplements makes this a useful reference textbook for researchers and students.
Preface.
Introduction.
Set-Theoretical Preliminaries.
Dissimilarities, Metrics, and Ultrametrics.
Convexity.
Graphs and Hypergraphs.
Partitional Clustering.
Statistical Approaches to Clustering.
Hierarchical Clustering.
Density-based Clustering.
Categorical Data Clustering.
Spectral Clustering.
Correlation and Consensus Clustering.
Clustering Quality.
Clustering Axiomatization.
Biclustering.
Semi-supervised Clustering.
Appendix A Special Functions and Applications.
Appendix B Linear Algebra.
Appendix C Linear Programming.
Appendix D NP Completeness.
Bibliography.
Index