TESI DOCTORAL - La Salle

Appendix F
Experiments on soft consensus
clustering
This appendix presents the results of the consensus clustering experiments on soft cluster
ensembles. The main purpose of these experiments is to compare the four voting based consensus
functions put forward in chapter 6 –namely BordaConsensus (BC), CondorcetConsensus
(CC), ProductConsensus (PC) and SumConsensus (SC)– with five state-of-the-art
clustering combiners: the soft versions of the hypergraph based hard consensus functions
CSPA, HGPA and MCLA (Strehl and Ghosh, 2002), and the evidence accumulation approach
(EAC) (Fred and Jain, 2005) (see section 6.2), plus the voting-merging soft consensus
function (VMA) of (Dimitriadou, Weingessel, and Hornik, 2002).
Such comparison entails two aspects: the quality of the consensus clustering solutions
obtained (measured in terms of normalized mutual information –φ (NMI) – with respect to
the ground truth of each data set), and the time complexity of each consensus function
(measured in terms of the CPU time required for their execution —see appendix A.6 for a
description of the computational resources employed in this work).
From a formal viewpoint, the results of these experiments are presented by means of a
φ (NMI) vs. CPU time diagram, onto which the performance of each consensus function is
described by means of a scatterplot covering the mean ± 2-standard deviation region of the
corresponding magnitude (i.e. φ (NMI) and CPU time). Moreover, the statistical significance
of the results is evaluated by means of Student’s t-tests that compare all the consensus
functions on a pairwise basis, thus analyzing whether the hypothetical superiority of any of
them is sustained on firm statistical grounds, using the traditional 95% confidence interval
as a reference for distinguishing between significant and non significant differences.
These soft consensus clustering experiments have been conducted on the twelve unimodal
data collections employed in this work (see appendix A.2.1 for a description). The results
corresponding to the Zoo data collection are presented in chapter 6, and the following
paragraphs describe the results obtained on the eleven remaining data sets.
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