Elementary Cluster Analysis: Four Basic Methods that (Usually) Work

by James C. Bezdek

Overview

The availability of packaged clustering programs means that anyone with data can easily do cluster analysis on it. But many users of this technology don't fully appreciate its many hidden dangers. In today's world of "grab and go algorithms," part of my motivation for writing this book is to provide users with a set of cautionary tales about cluster analysis, for it is very much an art as well as a science, and it is easy to stumble if you don't understand its pitfalls. Indeed, it is easy to trip over them even if you do! The parenthetical word usually in the title is very important, because all clustering algorithms can and do fail from time to time.

Modern cluster analysis has become so technically intricate that it is often hard for the beginner or the non-specialist to appreciate and understand its many hidden dangers. Here's how Yogi Berra put it, and he was right:

In theory there's no difference between theory and practice. In practice, there is ~Yogi Berra

This book is a step backwards, to four classical methods for clustering in small, static data sets that have all withstood the tests of time. The youngest of the four methods is now almost 50 years old:

• Gaussian Mixture Decomposition (GMD, 1898)
• SAHN Clustering (principally single linkage (SL, 1909))
• Hard c-means (HCM, 1956, also widely known as (aka) "k-means")
• Fuzzy c-means (FCM, 1973, reduces to HCM in a certain limit)

The dates are the first known writing (to me, anyway) about these four models. I am (with apologies to Marvel Comics) very comfortable in calling HCM, FCM, GMD and SL the Fantastic Four.

Cluster analysis is a vast topic. The overall picture in clustering is quite overwhelming, so any attempt to swim at the deep end of the pool in even a very specialized subfield requires a lot of training. But we all start out at the shallow end (or at least that's where we should start!), and this book is aimed squarely at teaching toddlers not to be afraid of the water. There is no section of this book that, if explored in real depth, cannot be expanded into its own volume. So, if your needs are for an in-depth treatment of all the latest developments in any topic in this volume, the best I can do - what I will try to do anyway - is lead you to the pool, and show you where to jump in.

Product Details

ISBN-13:	9788770042727
Publisher:	River Publishers
Publication date:	10/21/2024
Pages:	516
Product dimensions:	8.00(w) x 10.00(h) x (d)

About the Author

James C. Bezdek, PhD is a visiting senior fellow at University of Melbourne, Australia. He received his BS in Civil Engineering from the University of Nevada (Reno) in 1969; and his PhD in Applied Mathematics from Cornell University in 1973. He is past president of NAFIPS (North American Fuzzy Information Processing Society), IFSA (International Fuzzy Systems Association) and the IEEE CIS (Computational Intelligence Society when it was the Neural Networks Council); founding editor of the International Journal Approximate Reasoning and the IEEE Transactions on Fuzzy Systems; Life fellow of the IEEE and IFSA; recipient of the IEEE 3rd Millennium, IEEE CIS Fuzzy Systems Pioneer, and IEEE technical field award Rosenblatt medals; and the IPMU Kempe de Feret award.

Table of Contents

Preface
1. Clusters: The Human Point of View (HPOV)
2. Uncertainty: Fuzzy sets and models
3. Clusters: the Computer Point of View (CPOV)
4. The Three Canonical Problems
5. Feature Analysis
6. The c-means (aka k-means) Models
7. Probabilistic Clustering - GMD/EM
8. Relational Clustering - The SAHN Models
9. Properties of the Fantastic Four: External Cluster Validity
10. Alternating Optimization
11. Clustering in Big Static Data
12. Structural Assessment in Streaming Data Lists of Acronyms, Abbreviations, Algorithms, Definitions, Examples, Figures, Tables, Theorems, Video Links
Subject Index