IEEE Systems, Man, and Cybernetics Magazine - January 2018 - 48

By the Book

by Lawrence O. Hall

A Primer on
Cluster Analysis
by James C. Bezdek

A

Primer on Cluster Analysis:
4 Basic Methods That (Usually) Work (Design Publishing, 2017) focuses on four widely used
basic clustering methods suitable
for most unlabeled data. The algorithms are k-means (also called hard
c-means in the text), fuzzy c-means
(FCM), expectation maximization
(EM), and a couple for relational clustering (sequential, agglomerative, hierarchical, and nonoverlapping). There
is also a discussion of how to choose
the right number of clusters for each
approach. This includes interna l
and external validity measures for
the clusters obtained by applying
an algorithm.
The book includes more than the
four basic methods when variants and
competitors are noted during discussions of the methods, and it dives into
clustering approaches for big data. At
the end of the chapters are historical
notes, exercises, and additional examples of other algorithms.
To whom is this book useful? If you
have read this far, it is likely you. It is
especially valuable for someone just
starting to use clustering who wants
background information on major underlying approaches. There are many
nicely illustrated examples of clustering and validation of clusters. It is also
of interest to people who know about
clustering and use/develop algorithms.
Digital Object Identifier 10.1109/MSMC.2017.2769202
Date of publication: 17 January 2018

48

on clustering? Yes, there are good
examples, the algorithms are shown
in detail, and the pitfalls are shown
mathematically but also in clearly
written explanations (e.g., the final
partition of data obtained by a clustering algorithm may not match what
a person perceives as the correct data
partitions). The author carefully exaplins the ways a clustering algorithm
The book has a deep, rigorous mathcan fail you, how you can recognize
ematical treatment of the subject and
that it failed, and what you might
covers work in an area with which
do about it (e.g., switch algorithms,
only few are completely familiar. The
change parameters, or simply provide
historical notes are likely to be inforanother initialization).
mational to most. Finally, if you teach
The first part of the book covers
a course on clustering, this would
what you need to know to understand
serve as a great textbook. It includes
clustering. The first and third chapa deep discussion of
ters carefully point
algorithms and their
out that what we
variations with exer(the human's point
A Primer on
cises, then moves to
of view) consider a
Cluster Analysis:
the modern problem
cluster is not necesof clustering big-dasarily going to match
4 Basic Methods
ta sets. It also shows
what one of our algoThat (Usually)
how to evaluate the
rithms (or the comWork is especially
resulting partition
puter's point of view)
valuable for some(set of clusters).
considers a cluster.
The author of this
Chapter 2 contains
one starting to use
primer, Jim Bezdek,
background on fuzzy
clustering who
is one of the originaset theory, which is
wants background
tors of the FCM clusneeded for a deep
information on
tering algorithm and
understanding of
has done extensive
FCM. Chapter 3 conmajor underlying
work in general clustains the types of
approaches.
tering, including scalpossible data partiable clustering. He
tions (sets of clushas been a pioneer in
ters) with different
work on visual assessment of data for
algorithms and what you will use (e.g.,
clustering (i.e., how many clusters there
feature vectors) to cluster data.
are). Bezdek has a background in mathChapter 4 discusses the problem of
ematics, and this book includes necesassessment of whether clusters exist
sary mathematical details as well as
in data and how many exist. It intropointers to any mathematics required
duces improved visual assessment of
to fully comprehend the subtleties of
cluster tendency, which provides an
an algorithm.
image that can be interpreted to deA reader may ask, can I follow this
termine the likely number of clusters
book if my mathematics skills are not
in the data so you can set c or k. It is
strong and I just want information
a powerful algorithm, and it can be a

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Janu ar y 20 18



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