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D.2. Experiments on selection-based self-refining φ (NMI) φ (NMI) 1 0.5 0 1 0.5 0 E λc λ c 2 λ c 5 λ c 10 HGPA E λc λ c 2 λ c 5 λ c 10 λ c 15 λ c 20 λ c 30 MCLA (a) RHCA λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 λ c 15 λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 φ (NMI) φ (NMI) 1 0.5 0 1 0.5 0 E λc λ c 2 λ c 5 λ c 10 HGPA E λc λ c 2 λ c 5 λ c 10 λ c 15 λ c 20 λ c 30 MCLA (b) DHCA λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 λ c 15 λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 Figure D.11: φ (NMI) boxplots of the cluster ensemble E, the original consensus clustering λc and the self-refined consensus clustering solutions λc p i output by the flat, RHCA, and DHCA consensus architectures on the PenDigits data collection across all the consensus functions employed. The green dashed vertical line identifies the clustering solution selected by the supraconsensus function in each experiment. D.2 Experiments on selection-based self-refining This section presents the results of the clustering self-refining procedure based on the selection of a cluster ensemble component λref by means of an average normalized mutual information (φ (ANMI) ) criterion —see section 4.3. The results are presented in a very similar fashion to that of the previous section, that is, by means of boxplot charts displaying the φ (NMI) of the cluster ensemble E, the selected cluster ensemble component λref and the self-refined consensus solutions λcpi , with pi = {2, 5, 10, 15, 20, 30, 40, 50, 60, 75, 90}. Moreover, the clustering solution designated to be the optimal according to the supraconsensus function is highlighted by a vertical green dashed line, which provides a simple and fast means for evaluating its performance qualitatively. D.2.1 Iris data set Figure D.12 presents the results of the selection-based self-refining procedure applied on the Iris data set. It can be observed that the selected cluster ensemble component λref is of notable quality —i.e. well above the median partition in the cluster ensemble E. Notice how the self-refining process brings about relevant φ (NMI) gains depending on the consensus function employed. This is the case of the CSPA, MCLA, ALSAD, KMSAD and SLSAD consensus functions. However, the supraconsensus function selects λref as the optimal partition, thus ignoring the improvements introduced by the self-refining process on the aforementioned cases. This again highlights the need for good performing supraconsensus functions. 348
φ (NMI) 1 0.5 0 E λref λ c 2 λ c 5 λ c 10 φ (NMI) HGPA 1 0.5 0 (c) HGPA φ (NMI) 1 0.5 0 E E Appendix D. Experiments on self-refining consensus architectures λref λ c 2 λ c 5 λ c 10 λ c 15 λ c 15 λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 CSPA (a) CSPA λref λ c 2 λ c 5 λ c 10 φ (NMI) KMSAD 1 0.5 0 E (f) KMSAD λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 λref λ c 2 λ c 5 λ c 10 λ c 15 λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 φ (NMI) MCLA 1 0.5 0 (d) MCLA φ (NMI) 1 0.5 0 E E λref λ c 2 λ c 5 λ c 10 λ c 15 λ c 15 λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 λref λ c 2 λ c 5 λ c 10 EAC (b) EAC φ (NMI) SLSAD 1 0.5 0 E (g) SLSAD λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 λref λ c 2 λ c 5 λ c 10 λ c 15 λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 ALSAD (e) ALSAD λ c 15 λ c 20 λ c 30 λ c 40 λ c 50 λ c 60 λ c 75 λ c 90 Figure D.12: φ (NMI) boxplots of the cluster ensemble E, the selected cluster ensemble component λref and the self-refined consensus clustering solutions λc p i on the Iris data collection across all the consensus functions employed. The green dashed vertical line identifies the clustering solution selected by the supraconsensus function in each experiment. D.2.2 Wine data set The results obtained by the application of the selection-based self-refining procedure on the Wine data collection are presented in figure D.13. Notice that the cluster ensemble component selected by means of average normalized mutual information criteria, λref, is nearly the top quality partition contained in the cluster ensemble E. In this case, the creation of select cluster ensembles brings about no quality gains, regardless of the consensus function employed. As regards the performance of the supraconsensus function, it selects λref as the final clustering solution in a majority of cases, choosing a noticeably worse partition in those experiments based on the KMSAD and CSPA consensus functions. D.2.3 Glass data set Figure D.14 presents the φ (NMI) boxplots corresponding to the selection-based self-refining procedure applied on the Glass data set. Notice how the notably high quality clustering 349
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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 4.2 Decreasingly or
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List of Figures C.18 Estimated and
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List of Figures C.49 φ (NMI) of th
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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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1.1. Knowledge discovery and data m
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1.2. Clustering in knowledge discov
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1.3. Multimodal clustering in clust
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1.4. Clustering indeterminacies exe
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1.4. Clustering indeterminacies The
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1.4. Clustering indeterminacies Dat
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1.5. Motivation and contributions o
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Chapter 2. Cluster ensembles and co
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fuzzy consensus clustering solution
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2.1. Related work on cluster ensemb
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2.2. Related work on consensus func
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3.1. Motivation - the computational
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3.1. Motivation An additional and v
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3.2. Random hierarchical consensus
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3.3. Deterministic hierarchical con
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3.5. Discussion Consensus Consensus
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3.5. Discussion separate clustering
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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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1. Given a cluster ensemble E conta
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%of experiments relative % φ (NMI)
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Publisher: Springer Series: Lecture
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5.1. Generation of multimodal clust
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5.2. Self-refining multimodal conse
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5.3. Multimodal consensus clusterin
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5.4. Discussion Data set Relative
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5.5. Related publications modes joi
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Chapter 6. Voting based consensus f
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6.2. Adapting consensus functions t
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6.3. Voting based consensus functio
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6.4. Experiments λc = 1 1 1 3 3 3
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6.4. Experiments Data set Soft clus
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6.4. Experiments CSPA EAC HGPA MCLA
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6.5. Discussion solutions on hard c
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Chapter 7 Conclusions The contribut
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Chapter 7. Conclusions of-the-art c
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Chapter 7. Conclusions Though put f
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Chapter 7. Conclusions clustering r
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Chapter 7. Conclusions hardened. Ou
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References Ben-Hur, A., D. Horn, H.
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References Deerwester, S., S.-T. Du
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References Fred, A. and A.K. Jain.
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References Ingaramo, D., D. Pinto,
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References Li, S.Z. and G. GuoDong.
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References Sebastiani, F. 2002. Mac
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References Topchy, A., A.K. Jain, a
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Appendix A Experimental setup A.1 T
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Appendix A. Experimental setup g. s
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A.2.1 Unimodal data sets Appendix A
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A.2.2 Multimodal data sets Appendix
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Appendix A. Experimental setup gene
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Appendix A. Experimental setup orig
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Appendix A. Experimental setup Data
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Appendix A. Experimental setup or N
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B.1. Clustering indeterminacies in
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C.1. Configuration of a random hier
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Page 396 and 397: E.1. CAL500 data set φ (NMI) 1 0.8
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