TESI DOCTORAL - La Salle

C.4. Computationally optimal RHCA, DHCA and flat consensus comparison
Running time comparison
The miniNG data collection is one of those cases where the cardinality of the diversity factors
employed for generating the cluster ensemble, besides the number of objects it contains,
makes flat consensus non-executable (for all but the EAC consensus function) in those
scenarios where the cluster ensemble size is relatively large. In this situation, hierarchical
consensus architectures become a means for making consensus clustering feasible.
As regards the serial implementation of RHCA and DHCA –figure C.50–, the former
tends to be faster than the latter, except when the HGPA and MCLA consensus functions
are employed. This inter-consensus architecture performance is also observed in the parallel
implementation case, presented in figure C.51.
Consensus quality comparison
The analysis of the quality of the consensus clustering solutions output by the flat and
hierarchical consensus architectures can be made based on the φ (NMI) boxplot charts depicted
in figure C.52. A single remark as regards the perforance of the distinct consensus
functions: notice that CSPA, ALSAD and KMSAD based consensus solutions are the best
ones in quality terms. And last, the φ (NMI) values of the consensus clusterings output by
the two hierarchical consensus architectures –the only ones able to operate across all the
diversity scenarios– are pretty similar in most cases.
C.4.9 Segmentation data set
This section presents the comparison between flat consensus and the computationally optimal
consensus architectures in terms of CPU execution time and normalized mutual information
between the ground truth and the consensus clustering solution yielded by each one
of them. On the Segmentation data collection, the cluster ensemble sizes corresponding to
the four diversity scenarios are l =52, 520, 988 and 1456.
Running time comparison
Figure C.53 presents the execution times of the flat consensus architecture and the estimated
computationally optimal serial random and deterministic hierarchical consensus
architectures. In this case, flat consensus is faster than RHCA and DHCA regardless of
the cluster ensemble size (in our range of observation), except when the HGPA and MCLA
consensus functions are employed —in fact, MCLA-based flat consensus is unfeasible in the
two largest diversity scenarios. Moreover, the relative speed comparison between RHCA
and DHCA yields different results depending on the consensus function employed: RHCA
is faster than DHCA if consensus is based on CSPA, EAC, ALSAD or SLSAD, while the
opposite behaviour is observed when the HGPA, MCLA and KMSAD consensus functions
are used.
Pretty similar results are obtained when the running times of the fully parallel implementation
of RHCA and DHCA are analyzed, as figure C.53 reveals. The main difference
with respect to what has been just reported is the logical speed up of HCA, which makes
them be faster than flat consensus in the highest diversity scenario.
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