TESI DOCTORAL - La Salle

Appendix B
Experiments on clustering
indeterminacies
The goal of this appendix is to present experimental evidences of the indeterminacies affecting
the practical selection of a specific clustering configuration introduced in chapter 1. In
particular, we focus on the indeterminacies regarding the selection of the data representation
and clustering algorithm that yields the best clustering results for both unimodal and
multimodal data collections.
As already noted in chapter 1, the evaluation of the clustering results is based on computing
the normalized mutual information φ (NMI) between a given label vector and the
ground truth that is not available to the clustering process, being only used with evaluation
purposes. Recall that φ (NMI) ranges from 0 to 1, the higher its value the more similar the
clustering result to the ground truth.
B.1 Clustering indeterminacies in unimodal data sets
In this section, we analyze which clustering configurations (data representation plus clustering
algorithm) give rise to the best partitioning of the unimodal data sets described in
section A.2.1. We aim to demonstrate the dependence between the quality of the clustering
results and the selection of the way objects are represented and clustered.
As described in section A.3.1, starting with the original data representation (denoted
as baseline), four additional representations have been created by applying several feature
extraction techniques with multiple dimensionalities, namely Principal Component Analysis
(PCA), Independent Component Analysis (ICA), Non-negative Matrix Factorization
(NMF) and Random Projection (RP) 1 .
On each distinct object representation, the 28 clustering algorithms from the CLUTO
toolbox presented in section A.1 have been applied, which gives rise to the number of partitions
per data representation presented in table B.1. Notice that, in those data sets not
satisfying non-negativity constraints, the NMF representation was not derived. Moreover,
1 The only exception to this rule is the MFeat data set, where no attribute transformation was applied,
as its original form already presents data representation diversity through the use of several features, see
section A.2.1.
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