IEEE Systems, Man and Cybernetics Magazine - April 2020 - 35

Havens et al. [95], [96] proposed an alternate coVAT reordering scheme called coVAT2, which does not run VAT on the
D r , c matrix as is done by coVAT. Instead, it generates a reordering of the row and column indices of D by applying VAT
to D r and D c , respectively. Based on this row and column
reordering, the row and columns of D are reordered to showcase possible coclusters in D. The pseudocode for coVAT2 is
given in algorithm S24 in "Pseudocode for Various Algorithms
Belonging to the Visual Assessment of Tendency Family." The
coVAT2 algorithm is not limited to just relational data, and it
can also be applied to feature data, such as gene microarray
data. Another important advantage of coVAT2 is that it does
not use VAT to reorder D r , c , so, unlike coVAT, it can be
applied to dissimilarity data that have negative values as well.
Honda et  al. [97] proposed using a spectral-orderingbased approach on the full distance matrix D r , c for visual
cocluster structure assessment. They observed that, by considering the sparse nature of the enlarged matrix D r , c , the
eigenproblem of the full square relational matrix is reduced
to a smaller problem with less computational cost. This
approach is different from the heuristic approach used by
the coVAT algorithm [94] and provides an analytical solution
through the minimization of an objective function.
Coclustering Big Data
Similar to VAT, the coVAT and coVAT2 algorithms suffer
from high computational complexity and memory requirements as the data size increases. To address this issue,
Park et  al. [98] pursued the use of the sVAT sampling
scheme to extend coVAT to very large data and named the
new algorithm scalable coVAT (scoVAT ). The key step in
scoVAT is to work out a method for sampling the big D M # N
distance matrix when it exceeds the capacity limits of
coVAT. To do so, Park et al. [98] used sVAT on the m row
objects and n column objects of D M # N to generate a representative sample D m # n, where m % M and n % N.
The coVAT algorithm is then applied to the small D m # n
distance matrix to infer coclusters in the big data. The
pseudocode for scoVAT is given in algorithm S25 in "Pseudocode for Various Algorithms Belonging to the Visual Assessment of Tendency Family." This procedure is easily extended
to scoiVAT by replacing VAT with iVAT in algorithm S25.
Applications of the VAT Family to
Different Domains
Due to its applicability to EDA, parameter-light nature, and
visual output, the VAT family of algorithms has been
extensively used in a variety of applications to understand
newly collected data sets; based on this initial analysis,
different future tasks are designed for more advanced data
analysis. The application areas for VAT are diverse and
cover a range of topics, such as audiovisual data processing, biomedical applications, smart city, social media data
analysis, WSNs, and so on. Next, we describe some of the
works that have utilized the VAT family of algorithms in
various application domains.
	

Application to Multimedia Data
Speech Data Processing
A series of papers by Prasad, Nennuri, Reddy, and Basha
[99]-[101] used VAT, iVAT, and SpecVAT with the GMM and
cosine distance matrix for the application of speaker classification. They developed new techniques, GMMVAT and
cosine-based VAT (cVAT), for clustering speech utterances
by the same speaker. In GMMVAT, the GMM mean vectors
are derived for a set of speech segments (or utterances),
whereas in cVAT, the cosine distance function is used to calculate the distance matrix before applying VAT to it. The
experimental evaluations performed on a variety of data sets
show that GMMVAT/cVAT gives a better assessment of cluster tendency for speech data. Another VAT-based technique
for speaker clustering was proposed in [102], which derives
the explicit speaker clustering results directly from VAT
instead of using either k-means or MST-based clustering.
Image Processing
Chen [103] proposed a new nonparametric mechanism based
on unsupervised learning (VAT) for feature assessment and

6

Column
Cluster

Column
Cluster

4
2
0
-2
-4

Co-Cluster

Row
Cluster Co-Cluster

-6
-8 -6 -4 -2

(b)

0
(a)

(c)

2

4

6

8

(d)

(e)
Figure 15. An example illustrating coVAT with

(a) 20 row (5) and 40 column (d) objects as points
in the plane: (b) k = 3 in Or , (c) k = 4 in Oc , (d) k = 5
in Orjc , and (e) k = 2 (mixed) in Orjc . (Source: Bezdek
et al. [94].)

Ap ri l 2020

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IEEE Systems, Man and Cybernetics Magazine - April 2020

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