IEEE Systems, Man and Cybernetics Magazine - October 2020 - 50

rows of X are x and y coordinates corresponding to the
data points of the first cluster; the subsequent 1,000 rows
correspond to the second cluster, and so forth. The different
columns of Figure 3 show a subset of X coming from the
first cluster, the first two clusters, and the remaining clusters, respectively.
To emphasize the difference in the time complexities of
VAT/iVAT and inc-VAT/inc-iVAT, we shuffled the rows of X
such that the data points of the same cluster are apart.
This was initiated with two data points and then by adding
a data point at each time step. At each time step, we measured the time required by each algorithm (VAT, iVAT, incVAT, and inc-iVAT) to compute the reordered dissimilarity
matrices. From Figure 4(a) we see that, as n increases,
VAT + iVAT requires more time to update when compared
to inc-VAT + inc-iVAT. Likewise, to reveal the time complexity between dec-VAT/dec-iVAT and VAT/iVAT, we performed the experiment on the aforementioned 2D data
(X ). Because we were comparing the decremental nature
of the algorithms, we initiated the process with n = 5, 000
data points and eliminated a single arbitrarily selected
data point at each time step. From Figure 4(b) we see that,
as n decreases, dec-VAT + dec-iVAT requires much less
time than VAT + iVAT 6O ^ n 2 h@ .

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Figure 4. The time required for a combination of

VAT, iVAT, inc-VAT, inc-iVAT, dec-VAT, and dec-iVAT
algorithms for the 5,000-point 2D data set. (a) VAT
+ iVAT versus inc-VAT + inc-iVAT and (b) VAT + iVAT
versus dec-VAT + dec-iVAT.
50

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE O ctober 2020

Clustering Large Volumes of
High-Dimensional Data
The majority of clustering algorithms are designed to handle data sets with either 1) a very large sample size or 2) a
very high number of dimensions. However, they are usually
impractical when the data set (generated especially from
IoT devices) is large (both in sample size and dimensions).
From the "Extensions of VAT for Handling Big Data" section, we see that both the sVAT-SL and clusiVAT algorithms
have the ability to handle data cardinality with sampling
schemes; however, they cannot deal with high-dimensional
data. To address this critical issue, Fast clustering by combining ENsemble of random projects with Scalable version
of iVAT (FensiVAT) [25] is proposed. FensiVAT is a fast,
ensemble-based scalable iVAT algorithm. It integrates a
new, random projection-based distance matrix with MMRS
sampling and iVAT to cluster large volumes of high-dimensional data. FensiVAT is also several orders of magnitudes
faster than alternative clustering techniques, such as clusiVAT, without sacrificing accuracy.
Real-World Applications of VAT
families to the IoT
Monitoring the Great Barrier Reef of Australia
The Great Barrier Reef (GBR) of Australia comprises 3,200
coral reefs spanning more than 280, 000 km 2 [26]. The GBR
is both economically and ecologically sensitive, however,
and the burning of fossil fuels has led to the absorption of
carbon dioxide in oceans, resulting in acidification of the
ocean. This process prevents corals from secreting calcium
carbonate exoskeletons, diminishing the reef-building
mechanism and its associated organisms. Human-induced
activities are increasing the stress on coral reefs, leading to
coral bleaching, wherein the symbiotic relationship
between the coral and algae breaks down during rapid
changes in sea-water temperature (hot or cold) [26].
The Great Barrier Reef Ocean Observing System project aims to provide observational data to determine the
long-term effects of the Coral Sea on the ecosystems and
the impact on the GBR. To monitor the reef's ecosystem,
we collected temperature profiles and weather data from
Heron Island in the GBR. The iVAT algorithm detected the
passage of Tropical Cyclone Hamish in March 2009 (see
Figure 5) [27]. We considered one month of data (21 February-22 March 2009, from 9:00 a.m. to 3:00 p.m., using 10
min of sampling frequency) as a case study. Figure 6 shows
the Cyclone Hamish event as two anomalous clusters.
Urban Forest Monitoring in the City of Melbourne
IoT infrastructure for the creation of smart cities consists
of Internet-connected sensors, devices, and citizens. This
IoT infrastructure generates an enormous amount of data in
the form of city-scale physical measurements and public
opinions, constituting big data. Smart cities aim to efficiently use this wealth of data to manage and solve the problems

IEEE Systems, Man and Cybernetics Magazine - October 2020

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