TESI DOCTORAL - La Salle

A.6. Computational resources
hierarchical clustering algorithm on it. The main difference between our implementation
and the original one lies in the fact that we cut the resulting dendrogram at the
desired number of clusters k, whereas Fred proposes performing the cut at the highest
lifetime level, so that the very consensus function finds the natural number of clusters
in the data set. Its computational complexity is O n 2 l (Fred and Jain, 2005).
– ALSAD (Average-Link on Similarity As Data): this is one of the three consensus
functions presented in (Kuncheva, Hadjitodorov, and Todorova, 2006) based on considering
object similarity measures as object features. Despite the authors do not give
a specific name to this family of consensus functions, we have named them xxSAD
so as to indicate that similarities are deemed as data, replacing xx by the acronym
of the particular clustering algorithm used for obtaining the consensus clustering solution.
In this case, the pairwise object co-association matrix is partitioned using the
average-link (AL) hierarchical clustering algorithm, cutting the resulting dendrogram
at the desired number of clusters. Its computational complexity is O n 2 l for creating
the object similarity matrix plus O n 2 for partitioning it with the hierarchical AL
clustering algorithm (Xu and Wunsch II, 2005).
– KMSAD (K-Means on Similarity As Data): this consensus function belongs to the
same family as the previous one. This time, the object co-association matrix is clustered
using the classic k-means (KM) partitional algorithm. Its computational complexity
is O n 2 l for creating the object similarity matrix plus O (tkm) for partitioning
it with the k-means clustering algorithm (Xu and Wunsch II, 2005) —where t is the
number of iterations of k-means.
– SLSAD (Single-Link on Similarity As Data): following the same approach as the AL-
SAD and KMSAD consensus functions, the pairwise object co-association matrix is
partitioned by means of the single-link (SL) hierarchical clustering algorithm in this
case. As in the ALSAD consensus function, the consensus clustering solution is obtained
by cutting the dendrogram at the desired number of clusters. Its computational
costisthesameasALSAD.
– VMA (Voting Merging Algorithm): this consensus function is based on sequentially
solving the cluster correspondence problem on pairs of cluster ensemble components,
and, at each iteration, applying a weighted version of the sum rule confidence voting
method. This algorithm scales linearly in the number of objects in the data set and
the number of cluster ensemble components, i.e. its complexity is O (nl) (Dimitriadou,
Weingessel, and Hornik, 2002).
A.6 Computational resources
All the experiments conducted in this thesis have been executed under Matlab 7.0.4 on
Dual Pentium 4 3GHz/1 GB RAM computers. The reason for choosing Matlab as the
programming language for codifying our proposals is threefold: besides the fact we are
familiar with it, the existence of multiple built-in functions simplifies the implementation of
many of the processes involved in our proposals (Principal Component Analysis and Random
Projection feature extraction, for instance). Moreover, the availability of the full Matlab
source code of several components of our proposals (e.g. hypergraph consensus functions
230