IEEE Systems, Man and Cybernetics Magazine - April 2020 - 6

Sequential
Cluster
Estimation
A Generalized
Model for Finding
Large Numbers
of Clusters in Data

C

lustering is an unsupervised learning method
that partitions a set of objects into groups
(clusters) of similar objects, where similarity
is often computed from numerical object feature vectors (also called data points). An
early (and still very popular) clustering algorithm, called
k-means [1], finds clusters by minimizing the sum of the
squared distances between data points and associated
cluster centers. The k-means algorithm (like many other
so-called hard clustering algorithms) assigns each object
to one and only one of the considered clusters. In practice,
however, cluster assignments may often be ambiguous.
Objects may partially belong to several clusters or fit to
none of these clusters. Such kinds of ambiguity can be
mathematically handled by what is termed fuzzy set theory [2]. A fuzzy variant of k-means called fuzzy c-means
(FCM) has emerged to become one of the most popular
Digital Object Identifier 10.1109/MSMC.2020.2965319
Date of current version: 20 April 2020

6

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2020

fuzzy clustering methods, with hundreds of thousands of
scientific publications. For a survey, see [3]-[5]. Fuzzy clustering is often used to generate membership functions for
fuzzy rule-based systems [6], [7]. Alternating cluster estimation (ACE) [8] is an extension of FCM for arbitrary
membership function shapes. This article introduces
sequential cluster estimation (SCE), a variant of ACE that
finds clusters sequentially and outperforms nonsequential
clustering for data with many clusters.
ACE
In cluster partitions generated by FCM, the memberships
of each object in all clusters will sum up to one. Even outliers will be partially assigned to the clusters and hence
strongly affect the clustering results. This effect is avoided
by what is termed possibilistic c-means (PCM) [9]. In contrast to FCM, PCM yields convex membership functions,
more specifically Cauchy functions, for which outliers will
receive close to zero membership values, making the clustering algorithm more robust against outliers. Both FCM
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IEEE Systems, Man and Cybernetics Magazine - April 2020

Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - April 2020

Contents
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover1
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover2
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Contents
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 2
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IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover3
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