TESI DOCTORAL - La Salle

Chapter 5. Multimedia clustering based on cluster ensembles
As far as this latter issue is concerned, it is important to notice that, if the cluster
ensemble generation process proposed in section 5.1 is followed, multimodality induces an
important increase in the cluster ensemble size. Indeed, if a set of f mutually crossed
diversity factors of cardinalities |df1|, |df2|, ..., |dff | are applied on a particular unimodal
data collection, we obtain a cluster ensemble of size:
lunimodal = |df1||df2| ...|dff| (5.4)
However, if the same data collection was multimodal and contained m modalities, the
application of the previously presented multimedia cluster ensemble creation procedure –
using exactly the same diversity factors applied on the unimodal version of the data set–
would yield an ensemble of size:
lmultimodal =(m +1)|df1||df2| ...|dff| (5.5)
That is, multimodality increases the size of cluster ensembles by a factor of (m +1)
—i.e. in the minimally multimodal case, m = 2, the cluster ensembles obtained are three
times larger than those that would be created in a unimodal scenario. For this reason, and
allowing for the conclusions of chapter 3, it seems that hierarchical consensus architectures
are likely to be the most computationally efficient implementation alternative for deriving
consensus clustering solutions upon multimodal cluster ensembles —however, the running
time estimation process proposed in chapter 3 constitutes a valid tool for selecting apriori,
and with a high degree of precision, which is the computationally optimal consensus
architecture for solving a specific consensus clustering problem.
Regardless of the consensus architecture employed, it will output a consensus clustering
solution λc. The next and final step consists in applying the consensus self-refining procedure
proposed in section 4.1, so as to obtain a presumably higher quality refined consensus
clustering solution λ final
c . Quite obviously, in a multimedia clustering scenario, the selfrefining
process will be based on selecting a subset of the components of the multimodal
cluster ensemble E for creating a select cluster ensemble. Otherwise, it follows exactly the
steps presented in table 4.1.
In this work, a three-stage deterministic hierarchical consensus architecture (or DHCA
for short) has been applied for deriving the consensus clustering solution λc upon our
multimodal cluster ensembles. This is due to the fact that we have deemed multimodality
as a diversity factor (denoted as dfM) in itself. Moreover, in contrast to the procedure
followed in the previous chapters, the multimodal cluster ensemble E considered in each
individual experiment conducted in this chapter only contains clusterings created by a
single clustering algorithm, despite, as mentioned earlier, |dfA| = 28 of them have been
employed. In other words, for each data collection, experiments on |dfA| = 28 different
cluster ensembles have been conducted. The components of each one of these ensembles
only differ in the representational (dfR), dimensional (dfD) and multimodal (dfM) diversity
factors, while having been created by means of a single clustering algorithm.
According to the conclusions drawn in section 3.3, the DHCA variant that minimizes the
number of executed consensus processes and the running time of its serial implementation
is the one in which consensus processes are sequentially run on the distinct diversity factors
that make up the cluster ensemble E arranged in decreasing cardinality order.
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