TESI DOCTORAL - La Salle

Appendix B. Experiments on clustering indeterminacies
see that φ (NMI) values scattered in a range extending approximately from φ (NMI) =0.45 to
φ (NMI) =0.85 are obtained. It is important to notice that such diverse results are solely due
to the clustering algorithm selection indeterminacy, as this histogram presents the results
of running multiple distinct clustering algorithms on a single data representation.
If this analysis is extended to the remaining histograms (figures B.1(b) to B.1(e)), it can
be observed that the φ (NMI) scatter extends across an even wider range for each distinct type
of representation. This somehow gives an idea of the dependence between the quality of the
clustering results and the selection of the clustering algorithm. However, this conclusion
cannot be drawn as directly as in the baseline representation, given that histograms B.1(b)
to B.1(e) present the results of running the 28 algorithms on multiple representations with
distinct dimensionalities derived by each feature extraction technique. In other words,
the diversity observed in these histograms is produced by the joint effect of the clustering
algorithm and dimensionality reduction data representation selection indeterminacies.
However, if figures B.1(a) to B.1(e) are compared among themselves, the different histogram
distributions reveal the effect of the clustering indeterminacy regarding the type of
data representation. For example, clustering results on the NMF representations of this
data set span across a comparatively narrower and higher range of φ (NMI) values than their
PCA, ICA and RP counterparts, indicating that it is more probable to obtain better results
if clustering is run on NMF representations than on the remaining ones.
B.1.2 Iris data set
Compared to other data sets, a pretty small number of clustering solutions have been generated
on the Iris collection. Regardless of this fact, the effect of the clustering indeterminacies
can also be observed in figure B.2.
clustering count
10
5
Iris Baseline
0
0 0.5 1
φ (NMI)
(a) Baseline
clustering count
10
5
Iris PCA
0
0 0.5 1
φ (NMI)
(b) PCA
clustering count
10
5
Iris ICA
0
0 0.5 1
φ (NMI)
(c) ICA
clustering count
10
5
Iris NMF
0
0 0.5 1
φ (NMI)
(d) NMF
clustering count
10
5
Iris RP
0
0 0.5 1
φ (NMI)
(e) RP
Figure B.2: Histograms of the φ (NMI) values obtained on each data representations in the
Iris data set.
In this case, the wide span of the φ (NMI) histograms of the PCA and ICA representations
(figures B.2(b) and B.2(c)) is the clearest indicator of the representation dimensionality and
algorithm selection indeterminacies.
If the qualities of the clustering solutions obtained for the distinct types of object representation
are compared, we can observe that the highest φ (NMI) values are obtained using
the RP and the baseline representations.
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