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B.1. Clustering indeterminacies in unimodal data sets clustering count Segmentation Baseline 40 30 20 10 0 0 0.5 1 φ (NMI) (a) Baseline clustering count 40 30 20 10 Segmentation PCA 0 0 0.5 1 φ (NMI) (b) PCA clustering count 40 30 20 10 Segmentation ICA 0 0 0.5 1 φ (NMI) (c) ICA clustering count 40 30 20 10 Segmentation RP 0 0 0.5 1 φ (NMI) (d) RP Figure B.10: Histograms of the φ (NMI) values obtained on each data representation in the Segmentation data set. clustering count 60 40 20 BBC Baseline 0 0 0.5 1 φ (NMI) (a) Baseline clustering count 60 40 20 BBC PCA 0 0 0.5 1 φ (NMI) (b) PCA clustering count 60 40 20 BBC ICA 0 0 0.5 1 φ (NMI) (c) ICA clustering count 60 40 20 BBC NMF 0 0 0.5 1 φ (NMI) (d) NMF clustering count 60 40 20 BBC RP 0 0 0.5 1 φ (NMI) (e) RP Figure B.11: Histograms of the φ (NMI) values obtained on each data representation in the BBC data set. B.1.12 PenDigits data set In this case, the distinct object representations present a reasonably similar behaviour according to the histograms depicted in figure B.12. Assuming a simplifying viewpoint, these can be decomposed into a negatively skewed peak with its acme around φ (NMI) =0.6, and two other narrow peaks, one located near φ (NMI) =0.8 and the other on the low range of the histogram. Thus, as opposed to what has been observed in other data collections, the application of the twenty-eight clustering algorithms on the distinct object representations yield comparable quality results in this data set. clustering count 30 20 10 PenDigits Baseline 0 0 0.5 1 φ (NMI) (a) Baseline clustering count 30 20 10 PenDigits PCA 0 0 0.5 1 φ (NMI) (b) PCA clustering count 30 20 10 PenDigits ICA 0 0 0.5 1 φ (NMI) (c) ICA clustering count 30 20 10 PenDigits NMF 0 0 0.5 1 φ (NMI) (d) NMF clustering count 30 20 10 PenDigits RP 0 0 0.5 1 φ (NMI) (e) RP Figure B.12: Histograms of the φ (NMI) values obtained on each data representation in the PenDigits data set. 240
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
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C.I.F. G: 59069740 Universitat Ramo
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Resum En segmentar de forma no supe
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Abstract When facing the task of pa
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Contents 2.2.6 Consensus functions
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Contents A.5 Consensus functions .
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Contents D.2.5 WDBC data set . . .
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List of Tables 3.13 Relative percen
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List of Tables 5.15 Relative φ (NM
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List of Figures 1.1 Evolution of th
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List of Figures C.18 Estimated and
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List of Figures D.22 φ (NMI) boxpl
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List of Algorithms 6.1 Symbolic des
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List of symbols OΛ: object co-asso
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Chapter 1. Framework of the thesis
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1.1. Knowledge discovery and data m
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Chapter 4 Self-refining consensus a
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Chapter 4. Self-refining consensus
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- What do we want to measure? Chapt
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φ (NMI) φ (NMI) φ (NMI) φ (NMI)
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φ (NMI) 0.8 0.78 0.76 0.74 0.72 0
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%of experiments relative % φ (NMI)
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6.4. Experiments CSPA EAC HGPA MCLA
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Page 247 and 248: References Li, S.Z. and G. GuoDong.
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E.1. CAL500 data set φ (NMI) 1 0.8
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F.1. Iris data set φ (NMI) 1 0.8 0
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F.11. PenDigits data set φ (NMI) 1
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