The clustering is an ill-posed problem and it has been proven that there is no algorithm
that would satisfy all the assumptions about good clustering. This is why numerous
clustering algorithms exist, based on various theories and approaches, one of
them being the well-known Kohonen’s self-organizing map (SOM). Unfortunately,
after training the SOM there is no explicitly obtained information about clusters in
the underlying data, so another technique for grouping SOM units has to be applied
afterwards. In the thesis, a contribution towards a two-level clustering of the SOM
is presented, employing principles of Gravitational Law. The proposed algorithm for
gravitational clustering of the SOM (gSOM) is capable of discovering complex cluster
shapes, not only limited to the spherical ones, and is able to automatically determine
the number of clusters. Experimental comparison with other clustering techniques is
conducted on synthetic and real-world data. We show that gSOM achieves promising
results especially on gene-expression data.
As there is no clustering algorithm that can solve all the problems, it turns out as
very beneficial to analyse the data using multiple partitions of them – an ensemble of
partitions. Cluster-ensemble methods have emerged recently as an effective approach
to stabilize and boost the performance of the single-clustering algorithms. Basically,
data clustering with an ensemble involves two steps: generation of the ensemble with
single-clustering methods and the combination of the obtained solutions to produce a
final consensus partition of the data. To alleviate the consensus step the weighted cluster
ensemble was proposed that tries to assess the relevance of ensemble members. One
way to achieve this is to employ internal cluster validity indices to perform partition
relevance analysis (PRA). Our contribution here is two-fold: first, we propose a novel
cluster validity index DNs that extends the Dunn’s index and is based on the shortest
paths between the data points considering the Gabriel graph on the data; second, we propose an enhancement to the weighted cluster ensemble approach by introducing the
reduction step after the assessment of the ensemble partitions is done. The developed
partition relevance analysis with the reduction step (PRAr) yields promising results
when plugged in the three consensus functions, based on the evidence accumulation
principle.
In the thesis we address all the major stages of data clustering: data generation, data
analysis using single-clustering algorithms, cluster validity using internal end external
indices, and finally the cluster ensemble approach with the focus on the weighted variants.
All the contributions are compared to the state-of-art methods using datasets
from various problem domains. Results are positive and encourage the inclusion of
the proposed algorithms in the machine-learning practitioner’s toolbox.
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