TESI DOCTORAL - La Salle

Chapter 3. Hierarchical consensus architectures
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat 0 0 0 0 0 0.2 0
RHCA 0.4 0 0 0 1.2 0.1 0
DHCA 0 0 0 0 0 0.3 0
Table 3.14: Percentage of experiments in which the consensus clustering solution is better
than the best cluster ensemble component.
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat – – – – – 0.07 –
RHCA 0.85 – – – 0.8 0.07 –
DHCA – – – – – 1.1 –
Table 3.15: Relative percentage φ (NMI) gain between the consensus clustering solution and
the best cluster ensemble component.
large cluster ensembles if their complexity increases quadratically with the number of components
in the ensemble.
To our knowledge, most previous proposals oriented towards this aim deal with subsampling
strategies as a means for reducing the computational complexity of consensus
processes. That is, if the clustering combination task becomes more costly as the number of
the objects in the data set and/or the number of the cluster ensemble components grow, a
natural solution consists in applying the consensus clustering process on a reduced version
of the data collection (Lange and Buhmann, 2005; Greene and Cunningham, 2006; Gionis,
Mannila, and Tsaparas, 2007) and/or the cluster ensemble (Greene and Cunningham, 2006),
which is created by means of some sufficient subsampling procedure. Once the consensus
process is completed on the reduced data set (or cluster ensemble), it is extended to those
entities (objects or cluster ensemble components) that have been left out of the mentioned
subset. Whereas reducing the size of the data collection and/or the cluster ensemble subject
to the consensus clustering process entails an automatic saving of time complexity, one
should take into account the cost associated to the subsampling and extension processes,
which is often linear with the size of the data collection (Lange and Buhmann, 2005; Greene
and Cunningham, 2006; Gionis, Mannila, and Tsaparas, 2007).
In contrast, our hierarchical consensus architecture proposals are based on reducing the
time complexity of consensus processes without discarding any of the objects in the data
set nor any of the cluster ensemble components. By means of a divide and conquer type
of approach (Dasgupta, Papadimitriou, and Vazirani, 2006), we break a single consensus
clustering problem into multiple smaller problems, which gives rise to hierarchical consensus
architectures that allow to achieve important computational time savings, specially in high
diversity scenarios —i.e. the ones we might find ourselves in if the strategy of using multiple
mutually crossed diversity factors for creating large cluster ensembles is followed.
As far as we know, the use of divide and conquer approaches to the consensus clustering
problem has only been reported in (He et al., 2005) as a means for clustering data sets
that contain both numeric and categorical attributes. This proposal consists of dividing
the original data collection into two purely numeric and categorical subsets, conducting
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