TESI DOCTORAL - La Salle

φ (NMI) direct-cos-i2 graph-cos-i2
BBC 0.807 (P100) 0.603 (P83)
PenDigits 0.658 (P84) 0.829 (P99)
Chapter 1. Framework of the thesis
Table 1.1: Illustration of the clustering algorithm indeterminacy on the BBC and PenDigits
data sets clustered by the direct-cos-i2 and graph-cos-i2 algorithms.
index (Davies and Bouldin, 1979), Dunn’s index (Dunn, 1973), the Calinski-Harabasz index
(Calinski and Harabasz, 1974) or the I index (Maulik and Bandyopadhyay, 2002)) can be
applied for determining the most appropriate number of clusters by comparing the relative
merit of several clustering solutions obtained for distinct values of k (Halkidi, Batistakis,
and Vazirgiannis, 2002b)—unfortunately, the performance of these indices is data dependent,
which gives rise to a further indeterminacy (Xu and Wunsch II, 2005). And last, in
the context of mixture densities based clustering, the number of clusters can be determined
through the optimization of criterion functions such as the Akaike’s Information Criterion
(Akaike, 1974) or the Bayesian Inference Criterion (Schwarz, 1978), among others.
In this work, the number of clusters is assumed to be known from the start of the
clustering process, and k is set to be equal to the number of classes defined by the ground
truth of each data set. However, in a real-world scenario, this parameter should be tuned
using some of the previously mentioned techniques.
To illustrate the clustering algorithm selection indeterminacy, table 1.1 presents the
values of φ (NMI) (and their percentiles in the global φ (NMI) distribution of each case) obtained
from evaluating the clustering solutions yielded by the graph-cos-i2 and direct-cos-i2 (graphbased
and direct clustering algorithms using the cosine distance, respectively) operating on
the baseline data representation of the objects contained in the BBC and PenDigits data
sets 6 . As just mentioned, the desired number of clusters k is set to the number of classes
in each data set. It can be observed that these two algorithms, despite using the same
object similarity measure and optimizing the same criterion function, offer almost opposite
performances in these two specific data collections, so no absolute claims on the superiority
of none of them can be made.—see appendix B.1 for more experimental results regarding
the clustering algorithm selection indeterminacy.
It is worth noticing that the decision problems caused by the previously described clustering
indeterminacies are multiplied in the case of clustering multimodal data. In this
context, besides the data representation and clustering algorithm selection indeterminacies,
the clustering practitioner must face an additional set of questions with no clear answer,
such as:
– should one modality dominate the clustering process? If so, which one, and to which
extent?
– should the modalities be fused? If so, how should the fusion process be conducted?
To illustrate the effect of these and the aforementioned indeterminacies in a multimodal
clustering scenario, we have conducted several clustering experiments on the multimodal
data sets presented in appendix A.2.2.
6 Refer to appendices A.1, A.2 and A.3 for a detailed description of the clustering algorithms, the data
sets and the data representations employed in the experimental sections of this thesis.
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