IEEE Systems, Man and Cybernetics Magazine - April 2020 - 25

these two candidates are rejected. The VCV2 images in Figure 7(e) and (f) have roughly the same visual structure as
the VAT image I (R )), the principal difference being the
second block in the image for c = 6, which is somewhat
lighter in color, indicating that a very small subset of
points (possibly a singleton) was chosen as the sixth cluster. Based on visual image similarity, the VCV2 algorithm
clearly suggests that c = 5 is the preferred solution.
A few papers have tried to understand the relationship
between the VAT-based VCV indices described previously
and the traditional numeric cluster validity indices. Havens
et al. [49] addressed the relationship between the VAT algorithm and Dunn's cluster validity index [50]. Their experiments on a variety of data sets demonstrate that the
effectiveness of VAT in showing cluster tendency is strongly
related to Dunn's index, which provides a measure of contrast between the dark diagonal blocks in the VAT RDI and
the bright background regions. Similarly, a framework that
couples the possibilistic Rand index and the VAT algorithm
to estimate the number of clusters and identify coincident
clusters found by the PCM algorithm was discussed in [38].
Automating VAT/iVAT for Clustering
Tendency Assessment
The RDI generated by the VAT algorithm provides an excellent tool to (visually) interpret possible cluster structure in
a data set. A human observer can (sometimes) count the

number of dark blocks along the diagonal of a VAT image
to get an estimate for k, the number of clusters for which
to look. For data sets with compact, well-separated clusters, the dark blocks along the diagonal of the VAT image
are clear and easily countable, but as the data become
more and more mixed, the VAT image will degrade considerably. Although humans can usually deduce the suggested
number of clusters from a VAT image in all but the most
incorrigible data sets, different humans may see different
values, especially when the clusters have significant overlap or strange geometries, both of which lead to VAT images with nondistinct diagonal block boundaries.
Due to these shortcomings, visual methods, such as VAT,
have been criticized for being subjective and requiring human
input, which becomes impractical and seems somewhat
archaic in the current climate of automation created by
advances in artificial intelligence. Several groups have tackled this problem and designed methods to automatically
detect the number of clusters without requiring human input
to interpret a VAT/iVAT RDI. These techniques, classified by
the technique used in them to automatically determine k
from the VAT RDI, are discussed next.
Automatic Assessment Based on Image
Processing of the VAT RDI
Keller and Sledge [51] were the first to develop an algorithm
that takes the VAT RDI as an input to determine the degree

20

10

15

20

(a)

(b)

(c)

100
200
300
400
500
600
700
800
900
1,000

10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
90
1, 0
00
0

10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
90
1, 0
00
0

100
200
300
400
500
600
700
800
900
1,000

10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
90
1, 0
00
0

100
200
300
400
500
600
700
800
900
1,000

10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
90
1, 0
00
0

5

0
40
0
50
0
60
0
70
0
80
0
90
1, 0
00
0

0

0

-5
-5

30

0

0

5

100
200
300
400
500
600
700
800
900
1,000

20

10

100
200
300
400
500
600
700
800
900
1,000

10

15

(d)

(e)

(f)

Figure 7. The VAT I (R *) and VCV2 images I (U *) for different values of c for a five-cluster data set: (a) input
data with five clusters; (b) a VAT-ordered image of I (R *); and VCV2 images of (c)  I (U *) for c = 2, (d)  I (U *) for
c = 4, (e)  I (U *) for c = 5, and (f)  I (U *) for c = 6.

	

Ap ri l 2020

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE	

25



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
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 3
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 4
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 5
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 6
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 7
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 8
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 9
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 10
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 11
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 12
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 13
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 14
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 15
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 16
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 17
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 18
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 19
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 20
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 21
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 22
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 23
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 24
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 25
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 26
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 27
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 28
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 29
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 30
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 31
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 32
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 33
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 34
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 35
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 36
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 37
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 38
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 39
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 40
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 41
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 42
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 43
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 44
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 45
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 46
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 47
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 48
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 49
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 50
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 51
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 52
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 53
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 54
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 55
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 56
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 57
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 58
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 59
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 60
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover3
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/smc_202010
https://www.nxtbook.com/nxtbooks/ieee/smc_202007
https://www.nxtbook.com/nxtbooks/ieee/smc_202004
https://www.nxtbook.com/nxtbooks/ieee/smc_202001
https://www.nxtbook.com/nxtbooks/ieee/smc_201910
https://www.nxtbook.com/nxtbooks/ieee/smc_201907
https://www.nxtbook.com/nxtbooks/ieee/smc_201904
https://www.nxtbook.com/nxtbooks/ieee/smc_201901
https://www.nxtbook.com/nxtbooks/ieee/smc_201810
https://www.nxtbook.com/nxtbooks/ieee/smc_201807
https://www.nxtbook.com/nxtbooks/ieee/smc_201804
https://www.nxtbook.com/nxtbooks/ieee/smc_201801
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1017
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0717
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0417
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0117
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1016
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0716
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0416
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0116
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1015
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0715
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0415
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0115
https://www.nxtbookmedia.com