IEEE Systems, Man and Cybernetics Magazine - April 2020 - 37

applications, such as electrocardiography (ECG), the
effects of drugs, amino acids, and so on. Lourenco and
Fred [111] applied VAT-based clustering to analyze ECG
recordings performed during the execution of a cognitive
task using the computer, such as a concentration task
where two grids with 800 digits were presented, and participants were given the goal of identifying every pair of
digits that added 10; the activity was designed for an average completion time of 10 min. This task was meant to
induce stress in participants, and clustering of the ECG
signals helped researchers understand the typical patterns
of the temporal evolution of the ECG-extracted features.
In the field of pharmacology, Stallaert et al. [112] studied the drugs targeting a single G-protein-coupled receptor, which is involved in many diseases and is also the
target of approximately 34% of all modern medicinal
drugs. These drugs can differentially modulate distinct
subsets of the receptor signaling repertoire, but they create a challenge for drug discovery at these important therapeutic targets.
Recognizing that impedance responses provide an integrative assessment of ligand activity, Stallaert et  al. [112]
screened a collection of b2- adrenergic ligands to determine if differences in the signaling repertoire engaged by
compounds would lead to distinct impedance signatures.
To this end, they visualized the pairwise differences
among ligand signatures using the VAT algorithm; this suggested that the ligands fall into five distinct clusters, which
were later confirmed by hierarchical clustering. To help
pharmaceutical companies analyze their ever-increasing
corporate database of compounds for internal diversity or
the diversity that they add to the current compounds, Rivera-Borroto et al. [113] used VAT and Dunn's index as a measure of cluster separability to assess the classification
accuracy of various clustering algorithms tested on eight
pharmacological data sets.
Amino acids are the basic building blocks of proteins,
which are critical to life, and they have many important functions in living cells. The AAindex is a database of numerical
indices representing various physicochemical and biochemical properties of amino acids and pairs of amino acids. Saha
et al. [114] presented a novel method of partitioning the bioinformatics data using consensus fuzzy clustering and visualized the clustering solution using VAT reordering. The
discovered clusters describe some of the properties of amino
acids, such as the isoelectric point, polarity, molecular
weight, average accessible surface area, mutability, hydration
potential, refractivity, optical activity, and flexibility. These
cluster structures were then used to resolve the problem of
unknown amino acid indices by assigning them to clusters
that have defined biological meaning.
Recent advances in high-throughput lipid profiling by
liquid chromatography/electrospray ionization/tandem
mass spectrometry have made it possible to quantify hundreds of individual molecular lipid species (e.g., fatty acyls,
glycerolipids, glycerophospholipids, sphingolipids) in a
	

single experimental run for hundreds of samples. This can
help identify lipid biomarkers significantly associated with
disease risk, progression, and treatment response. Clinically, these lipid biomarkers can be used to construct classification models for disease screening or diagnosis.
However, the inclusion of a large number of highly correlated biomarkers within a model may reduce classification performance, unnecessarily inflate associated costs
of a diagnosis or a screening, and reduce the feasibility of
clinical translation. Kingwell et al. [115] proposed an unsupervised feature-reduction approach by estimating the
degree of correlation in a lipid data set using the VAT-generated MST, which helps reduce feature redundancy in lipidomic biomarkers by limiting the number of highly
correlated lipids while retaining informative features to
achieve good classification performance for various clinical outcomes.
Gene-Expression Data
Microarrays are one of the latest breakthroughs in experimental molecular biology, and they allow monitoring of the
expression levels of tens of thousands of genes in parallel.
This field produces huge amounts of valuable data [116],
but the analysis and handling of such data are major bottlenecks in the utilization of microarray analysis. Keller
et al. [117] were the first to use VAT on gene ontology (GO)
data. They built similarity relations on pairs of terms that
are used in the GO as linguistic descriptors of genes and
gene products. The VAT algorithm was then used to discover the tendencies of groups of gene products to cluster
them together.
Along similar lines, Kim et  al. [118] proposed a VATbased method they call user-interacted cluster. The method presents the RDI as basic information for user
interaction because it helps an operator visually grasp the
clustering tendency of a given data set. Havens et al. [119]
proposed a methodology to couple the results of a microarray experiment with the GO annotations of each gene to
produce aggregate relational data. The two relational
matrices, one derived from a fuzzy GO similarity measure
and the other derived from the microarray data using a statistical similarity measure, are then combined and used as
an input to the non-Euclidean relational fuzzy c-means
clustering algorithm [120]. Then, a validity measure called
correlation cluster validity (CCV) is used to validate the
resulting clusters in the relational data.
Figure 17 illustrates the methodology proposed in [119],
which was applied to a selected set of Arabidopsis (a leafy
plant) genes in the presence of insect feeding and wounding stress. This framework was extended for very large
gene-expression data sets (e.g., a human genome data set
consisting of approximately 30,000 genes, which would
produce a 30,000 # 30,000 distance matrix) by Popescu
et al. [121]. The authors extend the CCV algorithm to a new
validity measure: extension to correlation cluster validity,
which consists of two steps: sampling of the large matrix,
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IEEE Systems, Man and Cybernetics Magazine - April 2020

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