TESI DOCTORAL - La Salle

E.1. CAL500 data set
φ (NMI)
CSPA agglo−cos−upgma
1
0.8
0.6
0.4
0.2
0
E λc
λ 2 c
λ 5 c
λ 10
c
λ 15
c
λ 20
c
(a) CSPA
φ (NMI)
λ 30
c
λ 40
c
λ 50
c
λ 75
c
φ (NMI)
1
0.8
0.6
0.4
0.2
0
EAC agglo−cos−upgma
E λc
λ 2 c
λ 5 c
ALSAD agglo−cos−upgma
1
0.8
0.6
0.4
0.2
0
E λc
λ 2 c
λ 5 c
λ 10
c
λ 15
c
λ 20
c
λ 30
c
(e) ALSAD
λ 40
c
λ 10
c
λ 15
c
λ 20
c
(b) EAC
λ 50
c
λ 75
c
φ (NMI)
λ 30
c
λ 40
c
λ 50
c
λ 75
c
φ (NMI)
HGPA agglo−cos−upgma
1
0.8
0.6
0.4
0.2
0
E λc
λ 2 c
λ 5 c
KMSAD agglo−cos−upgma
1
0.8
0.6
0.4
0.2
0
E λc
λ 2 c
λ 5 c
λ 10
c
λ 15
c
λ 20
c
λ 30
c
(f) KMSAD
λ 40
c
λ 10
c
λ 15
c
λ 20
c
(c) HGPA
λ 50
c
λ 75
c
φ (NMI)
0.8
0.6
0.4
0.2
λ 30
c
0
λ 40
c
λ 50
c
λ 75
c
φ (NMI)
MCLA agglo−cos−upgma
1
0.8
0.6
0.4
0.2
0
E λc
λ 2 c
λ 5 c
SLSAD agglo−cos−upgma
1
E λc
λ 2 c
λ 5 c
λ 10
c
λ 15
c
λ 20
c
λ 30
c
(g) SLSAD
λ 40
c
λ 10
c
λ 15
c
λ 20
c
(d) MCLA
Figure E.5: φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions
using the agglo-cos-upgma algorithm on the CAL500 data set.
E.1.2 Self-refined consensus clustering across modalities
In this section, the results of running the self-refining procedure on the intermodal consensus
clustering solution λc are evaluated. Firstly, the results of the process applied on
the cluster ensemble created by the compilation of the clusterings output by the agglo-cosupgma
clustering algorithm are presented in figure E.5. On each one of the seven boxplot
charts displayed (one per consensus function), the clustering solution selected by the supraconsensus
function, λfinal c , is highlighted by a green dashed vertical line. Notice that in
all cases there exists at least one self-refined consensus clustering λpi c that attains a higher
φ (NMI) than the non-refined consensus clustering solution, λc. However, the supraconsensus
function mostly fails to select the top quality clustering as the final partition of the data
—in fact, it only does so in the experiments based on the CSPA, ALSAD and KMSAD
consensus functions. This situation is a clear illustrative example of the advantages of the
proposed self-refining procedures and the shortcomings of the φ (NMI) based supraconsensus
function.
Figures E.6 to E.8 present the self-refining results obtained on the cluster ensembles
constructed upon the clusterings generated by the direct-cos-i2, graph-cos-i2 and rb-cosi2
clustering algorithms. Notice that, in most cases, the self-refining procedure yields at
least one clustering of superior quality than the non-refined consensus clustering solution.
Exceptions to this behaviour occur, for instance, when the KMSAD and EAC consensus
functions are employed for clustering combination on the direct-cos-i2 and graph-cos-i2
cluster ensembles (see figures E.6(f) and E.7(b), respectively). Again, the supraconsensus
function performs with modest accuracy, managing to select the top quality clustering
solution in some cases (see figure E.8(b)) and failing clamorously in others (as in figure
362
λ 50
c
λ 75
c
λ 30
c
λ 40
c
λ 50
c
λ 75
c