TESI DOCTORAL - La Salle

A.4. Cluster ensembles
Data set name |dfA| =1 |dfA| =10 |dfA| =19 |dfA| =28
Zoo 57 570 1083 1596
Iris 9 90 171 252
Wine 45 450 855 1260
Glass 29 290 551 812
Ionosphere 97 970 1843 2716
WDBC 113 1130 2147 3164
Balance 7 70 133 196
Mfeat 6 60 114 168
miniNG 73 730 1387 2044
Segmentation 52 520 988 1456
BBC 57 570 1083 1596
PenDigits 57 570 1083 1596
Table A.4: Cluster ensemble sizes l corresponding to distinct algorithmic diversity configurations
for the unimodal data sets.
employ several mutually crossed diversity factors (the twenty-eight clustering algorithms of
the CLUTO clustering package presented in section A.1 are run on the data representations
with varying dimensionalities described in section A.3) so as to generate the individual
components of our cluster ensembles.
However, several cluster ensemble instances have been generated by limiting the cardinality
of the algorithmic diversity factor |dfA| (i.e. the number of clustering algorithms
considered in creating the cluster ensemble components) to a discrete set of values: |dfA| =
{1, 10, 19, 28}. This strategy is adopted with the objective of experimentally evaluating our
proposals both in terms of i) their sensitivity to the cluster ensemble diversity (as the larger
|dfA|, the more diverse the cluster ensemble), and ii) their computational scalability as regards
the cluster ensemble size l (since this factor is proportional to |dfA|). Notice that the
cluster ensembles with |dfA| = {1, 10, 19} are randomly sampled subsets of the maximally
diverse cluster ensemble (the one corresponding to |dfA| =28).
Tables A.4 and A.5 present the sizes of the cluster ensembles corresponding to the
distinct diversity scenarios (i.e. cardinalities of the algorithmic diversity factor dfA) onthe
unimodal and multimodal data collections employed in this work.
Firstly, table A.4 presents the cluster ensemble sizes corresponding to the unimodal
data sets. As expected, the cluster ensemble size l grows linearly with the value of |dfA|.
Depending on the cardinalities of the representational and dimensional diversity factors of
each data collection, fairly distinct cluster ensembles sizes are obtained (from the modest
values of the Iris data set to the highly populated cluster ensembles of the WDBC collection).
Last, table A.5 presents the cluster ensembles corresponding to the four multimodal data
collections employed in this work for each diversity scenario. It is important to highlight
the fact that the values of l presented in this table encompass the two unimodal and the
multimodal data representations of the objects contained in these data sets.
The reader is referred to appendix B for an analysis of the quality and diversity of the
components of these cluster ensembles.
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