TESI DOCTORAL - La Salle

D.2. Experiments on selection-based self-refining
φ (NMI)
φ (NMI)
1
0.5
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E λc
λ c 2
λ c 5
λ c 10
HGPA
E λc
λ c 2
λ c 5
λ c 10
λ c 15
λ c 20
λ c 30
MCLA
(a) RHCA
λ c 40
λ c 50
λ c 60
λ c 75
λ c 90
λ c 15
λ c 20
λ c 30
λ c 40
λ c 50
λ c 60
λ c 75
λ c 90
φ (NMI)
φ (NMI)
1
0.5
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1
0.5
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E λc
λ c 2
λ c 5
λ c 10
HGPA
E λc
λ c 2
λ c 5
λ c 10
λ c 15
λ c 20
λ c 30
MCLA
(b) DHCA
λ c 40
λ c 50
λ c 60
λ c 75
λ c 90
λ c 15
λ c 20
λ c 30
λ c 40
λ c 50
λ c 60
λ c 75
λ c 90
Figure D.11: φ (NMI) boxplots of the cluster ensemble E, the original consensus clustering
λc and the self-refined consensus clustering solutions λc p i output by the flat, RHCA, and
DHCA consensus architectures on the PenDigits data collection across all the consensus
functions employed. The green dashed vertical line identifies the clustering solution selected
by the supraconsensus function in each experiment.
D.2 Experiments on selection-based self-refining
This section presents the results of the clustering self-refining procedure based on the selection
of a cluster ensemble component λref by means of an average normalized mutual
information (φ (ANMI) ) criterion —see section 4.3.
The results are presented in a very similar fashion to that of the previous section,
that is, by means of boxplot charts displaying the φ (NMI) of the cluster ensemble E, the
selected cluster ensemble component λref and the self-refined consensus solutions λcpi ,
with pi = {2, 5, 10, 15, 20, 30, 40, 50, 60, 75, 90}. Moreover, the clustering solution designated
to be the optimal according to the supraconsensus function is highlighted by a vertical
green dashed line, which provides a simple and fast means for evaluating its performance
qualitatively.
D.2.1 Iris data set
Figure D.12 presents the results of the selection-based self-refining procedure applied on
the Iris data set. It can be observed that the selected cluster ensemble component λref is
of notable quality —i.e. well above the median partition in the cluster ensemble E. Notice
how the self-refining process brings about relevant φ (NMI) gains depending on the consensus
function employed. This is the case of the CSPA, MCLA, ALSAD, KMSAD and SLSAD
consensus functions. However, the supraconsensus function selects λref as the optimal
partition, thus ignoring the improvements introduced by the self-refining process on the
aforementioned cases. This again highlights the need for good performing supraconsensus
functions.
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