TESI DOCTORAL - La Salle

C.4. Computationally optimal RHCA, DHCA and flat consensus comparison
C.4.5 WDBC data set
In this section, we present the running times and consensus clustering solution qualities
of the hierarchical and flat consensus architectures corresponding to the WDBC data collection.
In this case, each diversity scenario corresponds to a cluster ensemble of size
l = 113, 1130, 2147 and 3164, respectively.
Running time comparison
Figure C.41 presents the running time of flat consensus and of the serial implementation
of the fastest random and hierarchical consensus architectures across the four diversity
scenarios. In this case, the relationship between the execution times of these consensus architectures
is a little different from what has been observed in the previous data collections.
In particular, flat consensus is more a competitive alternative, being faster or almost as fast
as RHCA in all diversity scenarios when consensus is based on the CSPA, EAC, ALSAD
and SLSAD clustering combiners. In contrast, DHCA is notably slower than RHCA in most
cases. This is due to the large cardinality of the dimensional diversity factor (|dfD|=28 on
this data set) that makes the DHCA stage where consensus is conducted on this diversity
factor much more computationally costly compared to the intermediate consensus processes
of RHCA.
In figure C.42, the execution times of the computationally optimal parallel RHCA and
DHCA variants and flat consensus are presented. Two trends are observed in these boxplots:
firstly, hierarchical architectures are faster than flat consensus, especially in diversity
scenarios where large cluster ensembles are employed. And secondly, parallel DHCA are in
general slower than their RHCA counterparts, for the same reason stated before.
Consensus quality comparison
Figure C.43 presents the φ (NMI) of the consensus clustering solutions yielded by the RHCA,
DHCA and flat consensus architectures across the four diversity scenarios on the WDBC
data collection. Firstly, notice that the EAC and SLSAD consensus functions give rise to
very low quality consensus clusterings regardless of the consensus architecture employed.
In contrast, flat consensus yields reasonably good consensus clusterings when it is derived
by means of HGPA, although hierarchical consensus architectures based on this consensus
function output poor consensus clustering solutions. Meanwhile, the remaining clustering
combiners yield pretty good consensus —notice that slightly better results are obtained
when it is derived by means of RHCA and flat consensus architectures.
C.4.6 Balance data set
This section presents the execution times of the estimated computationally optimal serial
and parallel implementations of RHCA and DHCA and flat consensus in the four
diversity scenarios for the Balance data set, which give rise to cluster ensembles of sizes
l =7, 70, 133 and 196 each. Moreover, the quality of the consensus clustering solutions
output by each consensus architecture are evaluated in terms of the normalized mutual
information (φ (NMI) ) with respect to the ground truth.
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