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5.3. Multimodal consensus clustering results
Therefore, it is necessary to determine the cardinality of the three diversity factors so
as to devise the computationally optimal DHCA topology. As described in section 5.1, the
cardinality of the representational diversity factor is either |dfR| =4or|dfR| = 5, depending
on the data set. The inspection of table 5.1 reveals that the dimensional diversity factor
adopts a wide range of cardinalities, but all of them fall in the [5, 19] interval. Last, the newly
introduced modality diversity factor entails not only the m = 2 original data modalities,
but also the multimodal one resulting from the feature-level fusion of the former —thus, its
cardinality is equal to |dfM| = 3. For this reason, the specific DHCA variant implemented is
referred to as DRM (as |dfD| > |dfR| > |dfM|), and consensus will be sequentially conducted
across dimensionalities, representations and modalities at each of its three stages.
For illustration purposes, figure 5.2 depicts a toy DHCA DRM variant applied on a 27dimensional
multidimensional cluster ensemble created on dimension, representation and
modality diversity factors all of cardinality equal to 3. In its first stage, consensus are conducted
across dimensionalities, thus yielding a first set of intermediate consensus clusterings
denoted as λD,j,k, wherej and k index object representations and modalities, respectively.
Subsequently, the second consensus stage executes consensus processes across the distinct
object representations, giving rise to a second set of partial consensus clustering solutions,
denoted as λD,R,k, wherek designates modalities. Assuming that two of these modalities
are truly original modes, and that the third one is a created by feature-level fusion of the
mod 1
former, the clusterings output by the second stage of the DHCA are also denoted as λc ,
mod 2 mod 1+mod 2
λc and λc , respectively. Finally, the execution of a consensus process on
these three intermediate clusterings yields the final consensus clustering solution λc, which
is referred to as intermodal hereafter.
Notice that conducting consensus by means of this DHCA variant instead of a flat
or a random hierarchical consensus architecture is specially interesting from an analytic
viewpoint, as it makes it possible to compare the effect of the consensus process on each
of the three modalities, by simply evaluating the three intermediate consensus clusterings
mod 1 mod 2 mod 1+mod 2
input to the last consensus stage –i.e. λ , λ and λ in figure 5.2.
5.3 Multimodal consensus clustering results
c
In this section, the results of the proposed multimodal consensus clustering experiments
conducted in this work are described. The design of these experiments has followed the
rationale described next.
– What do we want to measure?
c
i) In section 5.3.1, we evaluate the quality of the partial consensus clusterings obtained
on each separate modality and on the one resulting from multimodal
mod 1 mod 2 mod 1+mod 2
feature-level fusion (i.e. λc , λc and λc , respectively) plus the
intermodal clustering λc resulting from applying the consensus process for combining
the three aforementioned consensus clustering solutions. Moreover, we
also analyze how do the unimodal, multimodal and intermodal consensus clusterings
compare to each other plus the components of the cluster ensembles they
are created upon.
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c