IEEE Systems, Man and Cybernetics Magazine - October 2020 - 48

in Figure 2(b). On the other hand,
O = " o 1, o 2, f, o N ,, and executes a
an sVAT and siVAT allow us to creVAT on the distance matrix of n
The advantage of VAT
ate images by sampling n = 500
sample. The sample is selected
such that it contains a cluster
points (0.05% of the total data set)
as opposed to other
structure identical to the full set.
from O. In Figure 2(c), the sVAT
visual techniques is
This operation requires one to first
image indicates that there are four
pick a set of kl distinguished
clusters, which are enhanced in
its ability to highlight
the siVAT image [Figure 2(d)].
objects using a maximin sampling
the potential number
[19] to provide a depiction of each
of the clusters. Subsequently, the
A Scalable, Single-Linkage
of clusters in the data
remainder of the sample is proVisual Assessment of Cluster
by suitably reordering
duced by selecting additional data
Tendency for High-Volume
the objects.
near each of the distinguished
Data Sets
objects, leading to maximin and
Although the sVAT is helpful in
random sampling (MMRS).
understanding the cluster strucTo assess the cluster tendency
ture of the big data and determinof large volume data sets, we apply
ing the optimal value of k-the
the VAT algorithm on the MMRS samples. In Figure 2(a),
number of clusters to seek based on the visual evidence-
we see the scatterplot of N = 1, 000, 000 2D points drawn
on their own, they do not partition the data into k clusfrom four Gaussian components and 250,000 points per
ters. To tackle this issue, the scalable, single-linkage
cluster. However, we cannot create a VAT image, as shown
visual assessment of cluster tendency (sVAT-SL) [20]

400
300
200
100
0
-100
-200
-300
-400
-500
-400 -300 -200 -100

0

100

200

300

400

(a)

( )
(b)

(c)

(d)

Figure 2. Images of big data Gaussian clusters. (a) The data scatterplot, (b) VAT, (c) sVAT, and (d) siVAT.

48

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IEEE Systems, Man and Cybernetics Magazine - October 2020

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