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© 2020

Partitional Clustering via Nonsmooth Optimization

Clustering via Optimization

Book

Part of the Unsupervised and Semi-Supervised Learning book series (UNSESUL)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 3-13
    3. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 15-50
    4. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 51-94
  3. Clustering Algorithms

    1. Front Matter
      Pages 95-95
    2. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 97-133
    3. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 135-163
    4. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 165-183
    5. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 185-200
    6. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 201-223
    7. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 225-241
  4. Implementations and Evaluations of Clustering Algorithms

    1. Front Matter
      Pages 243-243
    2. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 245-268
    3. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 269-279
    4. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 281-314
    5. Adil M. Bagirov, Napsu Karmitsa, Sona Taheri
      Pages 315-317
  5. Back Matter
    Pages 319-336

About this book

Introduction

This book describes optimization models of clustering problems and clustering algorithms based on optimization techniques, including their implementation, evaluation, and applications. The book gives a comprehensive and detailed description of optimization approaches for solving clustering problems; the authors' emphasis on clustering algorithms is based on deterministic methods of optimization. The book also includes results on real-time clustering algorithms based on optimization techniques, addresses implementation issues of these clustering algorithms, and discusses new challenges arising from big data. The book is ideal for anyone teaching or learning clustering algorithms. It provides an accessible introduction to the field and it is well suited for practitioners already familiar with the basics of optimization.

  • Provides a comprehensive description of clustering algorithms based on nonsmooth and global optimization techniques
  • Addresses problems of real-time clustering in large data sets and challenges arising from big data
  • Describes implementation and evaluation of optimization based clustering algorithms

Keywords

Optimization models of clustering problems Clustering with different similarity measures Clustering in very large data sets Real-time clustering algorithms Heuristic clustering algorithms Clustering algorithms based on metaheuristics Nonsmooth optimization based clustering algorithms Global optimization based clustering algorithms Visualization of clustering results Application of clustering algorithms

Authors and affiliations

  1. 1.School of Science, Engineering & Information TechnologyFederation University AustraliaBallaratAustralia
  2. 2.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland
  3. 3.School of Science, Engineering & Information TechnologyFederation University AustraliaBallaratAustralia

About the authors

Adil M. Bagirov is currently an Associate Professor at School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, Australia. He received a master degree in Applied Mathematics from Baku State University, Azerbaijan in 1983, and the Candidate of Sciences degree in Mathematical Cybernetics from the Institute of Cybernetics of Azerbaijan National Academy of Sciences in 1989 and PhD degree in Optimization from Federation University Australia (formerly the University of Ballarat), Ballarat, Australia in 2002. He worked at the Space Research Institute (Baku, Azerbaijan), Baku State University (Baku, Azerbaijan), Joint Institute for Nuclear Research (Moscow, Russia). Dr. Bagirov is with Federation University Australia (Ballarat, Australia) since 1999. He currently holds the Associate Professor position at this university. He has won five Australian Research Council Discovery and Linkage grants to conduct research in nonsmooth and global optimization and their applications. He was awarded the Australian Research Council Postdoctoral Fellowship and the Australian Research Council Research Fellowship. His main research interests are in the area of nonsmooth and global optimization and their applications in data mining, regression analysis and water management. Dr. Bagirov has published a book on nonsmooth optimization, more than 150 journal papers, book chapters and papers in conference proceedings.

Napsu Karmitsa has been a Docent (Associate Professor) of Applied Mathematics at the Department of Mathematics and Statistics at the University of Turku, Finland, since 2011. She obtained her MSc degree in Organic Chemistry in 1998 and PhD degree in Scientific Computing in 2004 both from the University of Jyväskylä, Finland. At the moment, she holds a position of Academy Research Fellow at the University of Turku. Her research is focused on nonsmooth optimization and analysis. Special emphasis is given to nonconvex, global and large-scale cases. She is also studying theory of generalized pseudo and quasiconvexities for nonsmooth functions, developing numerical methods for solving nonsmooth, possible nonconvex and large-scale optimization problems and applying these method for solving data mining problems.

Sona Taheri is currently a Research Fellow at the School of Science, Engineering & Information Technology, Federation University Australia. Dr. Taheri has been at this University since 2009. She received her PhD degree in Mathematics from Federation University Australia (formerly the University of Ballarat) in 2012. Underpinning this is her Master degree in Applied Mathematics and Bachelor of Science in Pure Mathematics through University of Tabriz Iran completed in 2004 and 2001, respectively. Her research interests lie in the areas of optimization, particularly nonsmooth nonconvex optimization, and their applications in data mining, in particular cluster analysis and regression analysis.

Bibliographic information