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D.2. Experiments on selection-based self-refining 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 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.13: 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 Wine 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. solution λref is hardly surpassed by any of the refined consensus clustering solutions — in fact, this only happens when self-refining is based on the EAC and SLSAD consensus functions. In most cases, supraconsensus selects the selected cluster ensemble component λref as the final clustering solution. D.2.4 Ionosphere data set The application of the selection-based self-refining process on the Ionosphere data collection gives rise to modest quality increases, as depicted in figure D.15. Notice how only when the self-refining procedure is based on the CSPA and HGPA consensus functions, clustering solutions of higher φ (NMI) than λref are obtained. Furthermore, notice that the supraconsensus function selects, in most cases, the highest quality clustering solutions —unfortunately, the only exceptions occur when self-refining is based on CSPA and HGPA, i.e. the cases when self-refining introduces some significant quality gains. 350
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.14: 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 Glass 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.2.5 WDBC data set Figure D.16 presents the φ (NMI) boxplots corresponding to the selection-based self-refining process applied on the WDBC data set. Firstly, notice that the cluster ensemble component selected by means of the φ (ANMI) criterion –λref– is pretty close to the highest quality partition contained in the cluster ensemble. Secondly, the effect of self-refining is highly dependent on the consensus function employed. For instance, no quality gains are achieved when CSPA, EAC or HGPA are used. In contrast, φ (NMI) gains (although modest) are obtained when self-refining is conducted using the MCLA, ALSAD, KMSAD and SLSAD consensus functions. <strong>La</strong>st, notice that the supraconsensus function selects very high quality clusterings as the final partition. D.2.6 Balance data set As far as the performance of the selection-based self-refining process when applied on the Balance data collection, figure D.17 shows that self-refined clustering solutions of higher 351
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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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3.4. Flat vs. hierarchical consensu
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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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C.2. Estimation of the computationa
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C.4. Computationally optimal RHCA,
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Page 422 and 423: F.11. PenDigits data set φ (NMI) 1
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