TESI DOCTORAL - La Salle

3.3. Deterministic hierarchical consensus architectures
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.
Diversity scenario |df A| =1
Figure 3.10 presents the estimated and real running times of the serial and parallel DHCA
implementations in the lowest diversity scenario corresponding to the use of |dfA| = 1
randomly chosen clustering algorithm for creating a cluster ensemble of size l = 57. The
DHCA variants are identified in the horizontal axis of each chart. Meanwhile, the values
of SERTDHCA and PERTDHCA correspond to an arbitrarily chosen estimation experiment
based on a single consensus run (i.e. c =1).
On one hand, figures 3.10(a) and 3.10(b) present the estimated and real running times
of the serial DHCA implementation (SERTDHCA and SRTDHCA). Notice that SERTDHCA
is a fairly good estimator of the real execution time of the DHCA variants. Moreover, it
successfully predicts the fastest consensus architecture —which is what we are ultimately
interested in. Notice that DRA is the DHCA variant minimizing SRTDHCA, which corresponds
to the decreasing ordering of the diversity factors in terms of their cardinality.
On the other hand, figures 3.10(c) and 3.10(d) depict the estimated and real running
times corresponding to the fully parallel implementation of DHCA (PERTDHCA and
PRTDHCA, respectively). There are two issues worth noting in this case: firstly, notice that
the real execution time of the distinct DHCA variants shows a notably lower dispersion than
in the serial case, which somehow corroborates our conjecture regarding the unimportance
of the diversity factors ordering in parallel DHCA variants. And secondly, it is clear that
PERTDHCA does not perform as accurately as regards the determination of the fastest con-
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