TESI DOCTORAL - La Salle

3.4. Flat vs. hierarchical consensus
3.4 Flat vs. hierarchical consensus
In sections 3.2 and 3.3, two specific implementations of hierarchical consensus architectures
have been proposed, alongside a methodology for determining aprioriwhich is the fastest
(random or deterministic) HCA variant, and deciding whether it is computationally advantageous
with respect to classic flat consensus. In this section, we present a direct twofold
comparison between flat consensus and those DHCA and RHCA variants deemed as the
most computationally efficient by the proposed running time estimation methodologies.
Firstly, we compare them in terms of computational complexity. In fact, such comparison
could be made upon the results presented in sections 3.2 and 3.3, but we think that a
comparison considering only the allegedly best performing variants may simplify the process
of drawing meaningful conclusions. And secondly, these least time consuming hierarhical
consensus architecture variants will be compared with flat consensus in terms of the quality
of the consensus clustering solutions they yield. By doing so, we intend to present a comprehensive
picture of our hierarchical consensus architecture proposals in terms of the two
main factors that condition robust clustering by consensus: time complexity and quality.
3.4.1 Running time comparison
This section compares the real execution times of the allegedly fastest DHCA and RHCA
variants and flat consensus. The experiments conducted follow the design outlined next.
Experimental design
– What do we want to measure? The time complexity of the allegedly fastest
DHCA and RHCA variants and flat consensus.
– How do we measure it? We measure the CPU time required for the execution of
the aforementioned consensus architectures.
– How are the experiments designed? Such comparison entails the running times
of ten independent runs of each one of the compared consensus architectures. So
as to evaluate their computational efficiency under distinct experimental conditions,
the consensus processes involved have been conducted by means of the seven consensus
functions for hard cluster ensembles employed in this work —see appendix A.5.
Moreover, experiments have been replicated on the four diversity scenarios described
in appendix A.4 —recall that they differ in the algorithmic diversity factor, as a set of
|dfA| = {1, 10, 19, 28} randomly chosen clustering algorithms are employed for creating
the cluster ensemble in each diversity scenario.
– How are results presented? In formal terms, the measured execution times are
presented by means of boxplot charts, so as to provide the reader with a notion
of the degree of dispersion and asymmetry of the running times of each consensus
architecture. When comparing boxplots, notice that non-overlapping boxes notches
indicate that the medians of the compared running times differ at the 5% significance
level, which allows a quick inference of the statistical significance of the results.
– Which data sets are employed? A detailed description of the results of this
comparison on the Zoo data collection is presented in the following paragraphs. Recall
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