TESI DOCTORAL - La Salle

C.3. Estimation of the computationally optimal DHCA
and in terms of the execution time overheads (in both absolute and relative terms)
between the truly and the allegedly fastest DHCA variants in the case prediction
fails.
– How are the experiments designed? The f! DHCA variants corresponding to
all the possible permutations of the f diversity factors employed in the generation
of the cluster ensemble have been implemented (see table 3.6). As described in appendix
A.4, cluster ensembles have been created by the mutual crossing of f =3
diversity factors: clustering algorithms (dfA), object representations (dfR) and data
dimensionalities (dfD). Thus, in all our experiments, the number of DHCA variants is
f! = 3! = 6, which are identified by an acronym describing the order in which diversity
factors are assigned to stages —for instance, ADR describes the DHCA variant
defined by the ordered list O = {df1 = dfA,df2 = dfD,df3 = dfR}. For a given data
collection, the cardinalities of the representational and dimensional diversity factors
(|dfR| and |dfD|, respectively) are constant, while the cardinality of the algorithmic
diversity factor takes four distinct values |dfA| = {1, 10, 19, 28}, giving rise to the four
diversity scenarios where our proposals are analyzed. Moreover, consensus clustering
has been conducted by means of the seven consensus functions for hard cluster
ensembles described in appendix A.5, which allows evaluating the behaviour of our
proposals under distinct consensus paradigms. In all cases, the real running times
correspond to an average of 10 independent runs of the whole RHCA, in order to
obtain representative real running time values. As described in appendix A.6, all the
experiments have been executed under Matlab 7.0.4 on Pentium 4 3GHz/1 GB RAM
computers.
– How are results presented? Both the real and estimated running times of the
serial and parallel implementations of the DHCA variants are depicted by means of
curves representing their average values.
– Which data sets are employed? For brevity reasons, this section only describes
the results of the experiments conducted on the Zoo data collection. On this data
set, the cardinalities of the representational and dimensional diversity factors are
|dfR| = 5 and |dfD| = 14, respectively. The presentation of the results of these
same experiments on the Iris, Wine, Glass, Ionosphere, WDBC, Balance and MFeat
unimodal data collections is deferred to appendix C.3.
C.3.1 Iris data set
In this section, we present the estimated and real running times of the serial and parallel implementations
of DHCA on the Iris data collection. As aforementioned, this experiment has
been replicated across four diversity scenarios that, in the case of this data set, correspond
to cluster ensembles of size l =9, 90, 171 and 252.
The left and right columns of figure C.15 present the estimated and real running times
of several variants of the serial implementation of the DHCA and flat consensus on this data
set across the four diversity scenarios. There are a couple of issues worth noting: firstly,
SERTDHCA is a pretty accurate estimator of the real execution time of the serial DHCA
implementation, SRTDHCA. Secondly, notice that flat consensus is faster than the most
efficient DHCA variants regardless of the consensus function and the diversity scenario.
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