A Data Recovery Approach, Second Edition
By Boris Mirkin
Chapman and Hall/CRC – 2012 – 374 pages
Chapman and Hall/CRC – 2012 – 374 pages
Often considered more of an art than a science, books on clustering have been dominated by learning through example with techniques chosen almost through trial and error. Even the two most popular, and most related, clustering methods—K-Means for partitioning and Ward's method for hierarchical clustering—have lacked the theoretical underpinning required to establish a firm relationship between the two methods and relevant interpretation aids. Other approaches, such as spectral clustering or consensus clustering, are considered absolutely unrelated to each other or to the two above mentioned methods.
Clustering: A Data Recovery Approach, Second Edition presents a unified modeling approach for the most popular clustering methods: the K-Means and hierarchical techniques, especially for divisive clustering. It significantly expands coverage of the mathematics of data recovery, and includes a new chapter covering more recent popular network clustering approaches—spectral, modularity and uniform, additive, and consensus—treated within the same data recovery approach. Another added chapter covers cluster validation and interpretation, including recent developments for ontology-driven interpretation of clusters. Altogether, the insertions added a hundred pages to the book, even in spite of the fact that fragments unrelated to the main topics were removed.
Illustrated using a set of small real-world datasets and more than a hundred examples, the book is oriented towards students, practitioners, and theoreticians of cluster analysis. Covering topics that are beyond the scope of most texts, the author’s explanations of data recovery methods, theory-based advice, pre- and post-processing issues and his clear, practical instructions for real-world data mining make this book ideally suited for teaching, self-study, and professional reference.
"This book represents the second edition, aiming to consolidate, strengthen, and extend the presentation of K-means partitioning and Ward hierarchical clustering by adding new material such as five equivalent formulations for K-means, usage of split base vectors in hierarchical clustering, an effective version of least-squares divisive clustering, consensus clustering, etc. In addition, the book presents state-of-the-art material on validation and interpretation of clusters. The book is intended for teaching, self-study, and professional use."
—Marina Gorunescu, Zentralblatt MATH 1297
"The second edition is a refinement of Mirkin’s well-received first edition. … an excellent starting point for those interested in the algorithmic underpinning and theory of cluster analysis…"
—Journal of the American Statistical Association, June 2014
Praise for the First Edition:
"The particular decomposition studied in this book is the decomposition of the total sum of squares matrix into, between, and within cluster components, and the book develops this decomposition, and its associated diagnostics, further than I have seen them developed for cluster analysis before. Overall, the book presents an unusual … approach to cluster analysis, from the perspective of someone who is clearly an enthusiast for the insights these tools can bring to understanding data."
—D.J. Hand, Short Book Reviews of the ISI
What Is Clustering
Case Study Problems
What Is Data
Feature Space and Data Scatter
Pre-Processing and Standardizing Mixed Data
K-Means Clustering and Related Approaches
Choice of K and Initialization of K-Means
Intelligent K-Means: Iterated Anomalous Pattern
Minkowski Metric K-Means and Feature Weighting
Extensions of K-Means Clustering
Least-Squares Hierarchical Clustering
Hierarchical Cluster Structures
Agglomeration: Ward Algorithm
Least-Squares Divisive Clustering
Extensions of Ward Clustering
Similarity Clustering: Uniform, Modularity, Additive, Spectral, Consensus and Single Linkage
Summary Similarity Clustering
Normalized Cut and Spectral Clustering
Single Linkage, Minimum Spanning Tree and Connected Components
Validation and Interpretation
General: Internal and External Validity
Testing Internal Validity
Interpretation Aids in the Data Recovery Perspective
Conceptual Description of Clusters
Mapping Clusters to Knowledge
Least-Squares Data Recovery Clustering Models
Statistics Modelling as Data Recovery
K-Means as a Data Recovery Method
Data Recovery Models for Hierarchical Clustering
Data Recovery Models for Similarity Clustering
Consensus and Ensemble Clustering
Boris Mirkin is a professor of computer science at the University of London, UK.