TESI DOCTORAL - La Salle

Appendix A. Experimental setup
Data set name |dfA| =1 |dfA| =10 |dfA| =19 |dfA| =28
CAL500 102 1020 1938 2856
IsoLetters 111 1110 2109 3108
InternetAds 183 1830 3477 5124
Corel 123 1230 2337 3444
Table A.5: Cluster ensemble sizes l corresponding to distinct algorithmic diversity configurations
for the multimodal data sets.
A.5 Consensus functions
In this section, we briefly describe the consensus functions employed in the experimental
section of this thesis, placing special emphasis on specific implementation details when
necessary. Moreover, we present the time complexity of each consensus function for a given
cluster ensemble size (l), number of objects in the data set (n) and clusters (k).
The first seven consensus functions are employed on experiments considering both hard
and soft cluster ensembles (i.e. chapters from 3 to 6). On its part, the last one (VMA) is
only applied on soft cluster ensembles, that is, in chapter 6.
The Matlab source code of the first three consensus functions is available for download
at http://www.strehl.com, whereas the remaining ones were implemented ad hoc for this
work. For a more theoretical description of these consensus functions, see section 2.2.
– CSPA (Cluster-based Similarity Partitioning Algorithm): this consensus function
shares a lot of the rationale of the Evidence Accumulation consensus function (see
below), as it is based on deriving a pairwise object similarity measure from the cluster
ensemble and applying a similarity-based clustering algorithm on it—the METIS
graph partitioning algorithm (Karypis and Kumar, 1998) in this case. Its computational
complexity is O n 2 kl (Strehl and Ghosh, 2002).
– HGPA (HyperGraph Partitioning Algorithm): this clustering combiner exploits a hypergraph
representation of the cluster ensemble, re-partitioning the data by finding
a hyperedge separator that cuts a minimal number of hyperedges, yielding k unconnected
components of approximately the same size—which makes HGPA not an
appropriate consensus function when clusters are highly imbalanced. The hypergraph
partition is conducted by means of the HMETIS package (Karypis et al., 1997). Its
time complexity is O (mkl) (Strehl and Ghosh, 2002).
– MCLA (Meta-CLustering Algorithm): as in HGPA, each cluster corresponds to a hyperedge
of the hypergraph representing the cluster ensemble. Subsequently, related
hyperedges are detected by grouping them using the METIS graph-based clustering algorithm
(Karypis and Kumar, 1998). Next, related hyperedges are collapsed and each
object is assigned to the collapsed hyperedge in which it participates most strongly.
Its computational complexity is O mk 2 l 2 (Strehl and Ghosh, 2002).
– EAC (Evidence Accumulation): this is a pretty direct implementation of the consensus
function presented in (Fred and Jain, 2002a). It consists in the computation of the
pairwise object co-association matrix and the subsequent application of the single-link
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