IEEE Systems, Man and Cybernetics Magazine - April 2020 - 43

nondominated-solutions set. They can identify only one set
of decision vectors out of the multimodal solutions and terminate at any one global optimum out of the multiple global
optima present in the multiobjective multimodal problems.
Finding all multimodal solutions would allow the decision
maker greater flexibility when choosing between solutions.
For example, in chemical process optimization, the decision
maker would want to know about different temperature settings for which the process can deliver the same results.
Kudikala et al. [167] presented an extended version of
the Pareto estimation method, which can be used to
increase the number of multimodal solutions. The method
uses VAT to identify and separate different clusters in the
space of decision variables, which correspond to the multimodal Pareto optimal solutions. Then, Pareto estimation is
employed for these individual clusters, which increases
the density of available multimodal solutions in multiobjective problems.

◆◆ "A Study on Parallel Versus Sequential Relational Fuzzy

Predicting Ground Vibrations in Mines
Ground vibrations, measured in terms of peak particle velocity (PPV) is one of the hazard effects induced by blasting
operations in open-pit mines, which can affect surrounding
structures, particularly the stability of benches and slopes in
open-pit mines, and their impact on underground water, railway, highway, and so on can be puzzling for neighboring
communities. Therefore, controlling, predicting, and mitigating the effects of blast-induced PPV is desirable.
Nguyen et al. [168] developed a new clustering-based
computational model for predicting blast-induced PPV. To
assess whether the data set is suitable for the use of clustering algorithms, the VAT algorithm was applied, and once the
data were deemed suitable for clustering, a novel hybrid artificial-intelligence model based on the hierarchical k-means
(HKM) clustering algorithm and an artificial neural network
(ANN)-namely, an HKM-ANN model-was developed for
predicting blast-caused PPV in open-pit mines.

Conclusion
This survey article attempts to capture and summarize
work related to the theory and applications of the VAT/
iVAT family of models and algorithms. Inevitably, we
will have missed some articles that belong here, but it
is impossible to know about every work related to this
type of cluster heat map and its widespread applications. Readers may wonder whether subjective analysis
of the visual representation of numerical data, such as
that offered by cluster heat maps, is really useful.
Perhaps a fitting conclusion to this contribution is a
statement about the utility of data visualization made by
Sir Ronald Fisher [183] almost 100 years ago: "The preliminary examination of most data are facilitated by the use
of diagrams. Diagrams prove nothing, but bring outstanding features readily to the eye; they are therefore no substitute for critical tests as may be applied to the data, but
are valuable in suggesting such tests, and in explaining
conclusions founded upon them." This is the rationale for
using methods such as VAT/iVAT and, more generally,
other types of cluster heat maps that abound in the scientific literature. They are there to help us understand the
structure in the data that we cannot see ourselves.

Master's and Ph.D. Theses Inspired
by the VAT Family of Algorithms
The VAT family of algorithms has been a part of the
research of various master's and Ph.D. students, which, in
turn, has also contributed to many of the algorithms and
applications described in this article. Following is the
(chronological) list of dissertations that have used or contributed to the VAT family of algorithms:
◆◆ "Extracting Textual Information From Images and Videos for Automatic Content-Based Annotation and
Retrieval," 2007 [169]
◆◆ "Visual Data Analysis in Air Traffic Management," 2007
[170]
◆◆ "Information Visualization Techniques for Metabolic
Engineering," 2007 [171]
◆◆ "A System for Change Detection and Human Recognition in Voxel Space Using Stereo Vision," 2010 [172]
◆◆ "Clustering in Relational Data and Ontologies," 2010 [173]

Clustering Methods," 2011 [174]
◆◆ "Sparse and Discriminative Clustering for Complex
Data," 2012 [175]
◆◆ "Visualization of Transformation of Graphs Based on
Similarity Functions," 2013 [176]
◆◆ "Support Vector Machine-based Fuzzy Systems for
Quantitative Prediction of Peptide Binding Affinity,"
2015 [177]
◆◆ "Experimental Study of Random Projections Below the
JL Limit," 2015 [178]
◆◆ "Clustering von Recurrence Plots," 2015 [179]
◆◆ "Big Data Clustering for Smart City Applications,"
2016 [180]
◆◆ "Enabling Automatic Creation of Virtual Services for
Service Virtualisation," 2016 [181]
◆◆ "Big Data Cluster Analysis and Its Applications,"
2018 [182].

About the Authors
Dheeraj Kumar (dheeraj.kumar@ece.iitr.ac.in) is with the
Department of Electronics and Communication Engineering, Indian Institute of Technology Roorkee.
James C. Bezdek (jcbezdek@gmail.com) is with the
School of Computing and Information Systems, the University of Melbourne, Australia. He is a Life Fellow of the IEEE.
References
[1] "VAT family of algorithms," GitHub, San Francisco. Accessed on: Oct. 30, 2019.
[Online]. Available: https://github.com/genuine-dheeraj/VAT_family_of_algorithms
[2] A. K. Jain, "Data clustering: 50 years beyond k-means," Pattern Recog. Lett., vol. 31,
no. 8, pp. 651-666, 2010. doi: 10.1016/j.patrec.2009.09.011.

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