The method of dendrograms disclosure for evaluation of cluster analysis results in IoT domain
Authors: Kaminskyy Roman , Shakhovska Nataliya 
Published: August 2020

Background:
Increasing the amount of information generated as a result of smart city activity leads to the
problem of its accumulation and preprocessing. One type of data preprocessing is clustering. The cluster analysis is an
objective method of classification. It provides an appropriate choice of further processing methods as well as the
visualization and interpretation of the collected data, which are multidimensional objects. The most valuable feature of
cluster analysis is the representation of the result by an image of a dendrogram that reflects a particular hierarchy of
relationships between the selected clusters and their objects. The aim of the paper is to develop method of 3D visualization
of hierarchical clustering for streaming and multidimensional data collected from IoT devices and open databases.

Methods:

It is suggested that a more detailed interpretation of the dendrogram is made by implementing the hypothesis
given above. Testing this hypothesis means a procedure of visualizing and interpreting the result of a cluster analysis. The
disclosed dendrogram allows fully usage of association metrics. Since this metric is derived from the calculation of the
values of the proximity matrix in accordance with the chosen object pooling strategy, the use of the disclosed dendrogram
is quite legitimate. In addition, the procedure for opening the dendrogram is specific and unambiguous. This methods is
built on hierarchical clustering algorithm as the simplest and fasters one. The developed algorithm should make it impossible
to cross clusters on a plane. It is also necessary to look for the distance not only between objects, but also between clusters,
represented as complex geometric figures. It will allow explaining the nature of the clusters

Results:

The result of the research and verification of the proposed hypothesis is the diclosure of the dendrogram algorithm
as the extension of classical methods of cluster analysis. This extension is made by studying and disclosing the resulting
image of the dendrogram. The dendrogram visualization thus obtained differs significantly from the classical results. The
opening of the dendrogram according to the developed algorithm allows us 3D visualization of the analysis results, as well
as calculating the area and perimeter of the obtained clusters. Therefore, using analytical geometry methods, it is quite easy
to isolate and calculate the parameters of minimum cluster coverage surfaces and the immediate distances between any
objects of one or different clusters, as well as between the objects of a given cluster. This, in turn, is a significant complement
to cluster analysis.

Conclusion:

The disclosed dendrogram retains proportions in distances between objects. On the basis of these
characteristics, it is possible to determine the close relationship between the clusters themselves by correlating the values of
their quantitative averaged values of the traits. Thus, the opening of the dendrogram allows us to clearly identify the set of clusters, each of which has its own distribution of the range of features values. The quantitative characteristics of clusters
on both dendrograms are quite simple. In addition, the mean values of the features of objects in a given cluster can be
interpreted as generalized characteristics of this cluster, and the cluster itself can be represented as a single integral object.