TESI DOCTORAL - La Salle

B.1.13 Summary
Appendix B. Experiments on clustering indeterminacies
So as to provide a summarized vision of the data representation and the clustering algorithm
selection indeterminacies across all the analyzed data sets, table B.2 presents the φ (NMI)
corresponding to the best clustering solution achieved by each one of the five families of
clustering algorithms employed in this work, namely agglomerative (agglo), biased agglomerative
(bagglo), direct, graph, repeated-bisecting (rb) and refined repeated-bisecting (rbr),
indicating the type of object representation employed in each case (either baseline, PCA,
ICA, NMF or RP).
There are several worth observing facts as regards the data representation indeterminacy.
Notice that, in some data sets (e.g. Zoo or miniNG), there exists a notable diversity as
regards the type of representation that yields the top clustering result for each family of
clustering algorithms. In contrast, in other data collections, there seems to exist a particular
object representation that apparently reveals the data set structure regardless of the type of
clustering algorithm applied. This behaviour is observed in the Iris and Balance collections,
and also, to a lesser extent, in the WDBC and Segmentation data sets. Moreover, notice
the variablility of these optimal object representations across the analyzed data sets, which
is a clear indicator of the clustering indeterminacy regarding data representations.
As far as the selection of the optimal clustering algorithm is concerned, it is important
to note that at least one representative of the five families of clustering algorithms employed
in this work reach the best absolute performance in at least one of the analyzed data sets,
which gives an idea of the algorithm selection indeterminacy. Moreover, notice that choosing
the wrong type of clustering algorithm may affect the quality of the clustering solution
dramatically (see the Ionosphere and Balance collections) or not (as in the Segmentation
data set).
B.2 Clustering indeterminacies in multimodal data sets
The goal of this section is to evaluate the effect of clustering indeterminacies in the context
of multimodal data collections. Along with the data representation and clustering algorithm
selection indeterminacies, multimodality introduces a further focus of uncertainty, as it is
not evident to decide whether the combination of the m modalities will benefit the quality
of the obtained clustering solution or not. And again, to make things worse, it is important
to recall that all these indeterminacies are local to each data collection, so, in general, it is
not possible to drawn universally valid conclusions.
As done in appendix B.1, we start by presenting the total number of individual clustering
solutions obtained by applying the 28 clustering algorithms extracted from the CLUTO
toolbox on all the data representations of the objects contained in the employed multimodal
data sets2 —see table B.3. Notice that the CAL500 and InternetAds collections lack the
NMF representations as they do not satisfy the necessary non-negativity constraints.
In the next paragraphs, we describe the clustering results obtained on the four multimodal
data sets, placing special emphasis on which data representations and modalities
lead to the best clustering results in each case.
2 See appendices A.1, A.2.2, and A.3.2 for a description of the clustering algorithms, the multimodal
collections and the multimodal objects representations employed in this work.
241