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C.4. Computationally optimal RHCA, DHCA and flat consensus comparison CPU time (sec.) CPU time (sec.) CPU time (sec.) CPU time (sec.) 20 18 16 14 12 10 8 6 4 25 20 15 10 20 19 18 17 16 15 14 13 12 23 22 21 20 19 18 17 16 15 CSPA RHCA DHCA flat CSPA RHCA DHCA flat CSPA RHCA DHCA flat CSPA RHCA DHCA flat CPU time (sec.) CPU time (sec.) CPU time (sec.) CPU time (sec.) 7000 6000 5000 4000 3000 2000 1000 0 3500 3000 2500 2000 1500 1000 500 0 2500 2000 1500 1000 500 0 2500 2000 1500 1000 500 0 EAC RHCA DHCA flat EAC RHCA DHCA flat EAC CPU time (sec.) 0.4 0.35 0.3 0.25 0.2 0.15 0.1 HGPA RHCA DHCA flat CPU time (sec.) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 MCLA RHCA DHCA flat CPU time (sec.) 3000 2500 2000 1500 1000 500 0 ALSAD RHCA DHCA flat (a) Parallel implementation running time, |dfA| =1 CPU time (sec.) 1.4 1.2 1 0.8 0.6 0.4 0.2 HGPA RHCA DHCA flat CPU time (sec.) 2.5 2 1.5 1 0.5 MCLA RHCA DHCA flat CPU time (sec.) 2000 1500 1000 500 0 ALSAD RHCA DHCA flat (b) Parallel implementation running time, |dfA| =10 RHCA DHCA flat EAC CPU time (sec.) 4 3.5 3 2.5 2 1.5 1 0.5 HGPA RHCA DHCA flat CPU time (sec.) 8 7 6 5 4 3 2 1 MCLA RHCA DHCA flat CPU time (sec.) 1000 800 600 400 200 0 ALSAD RHCA DHCA flat (c) Parallel implementation running time, |dfA| =19 RHCA DHCA flat CPU time (sec.) 7 6 5 4 3 2 1 HGPA RHCA DHCA flat CPU time (sec.) 15 10 5 0 MCLA RHCA DHCA flat CPU time (sec.) 1000 800 600 400 200 0 ALSAD RHCA DHCA flat (d) Parallel implementation running time, |dfA| =28 CPU time (sec.) CPU time (sec.) CPU time (sec.) CPU time (sec.) 250 200 150 100 50 300 250 200 150 100 50 350 300 250 200 150 100 50 500 400 300 200 100 0 KMSAD RHCA DHCA flat KMSAD RHCA DHCA flat KMSAD RHCA DHCA flat KMSAD RHCA DHCA flat CPU time (sec.) CPU time (sec.) CPU time (sec.) CPU time (sec.) 7000 6000 5000 4000 3000 2000 1000 0 2000 1500 1000 500 0 1600 1400 1200 1000 800 600 400 200 0 1600 1400 1200 1000 800 600 400 200 0 SLSAD RHCA DHCA flat SLSAD RHCA DHCA flat SLSAD RHCA DHCA flat SLSAD RHCA DHCA flat Figure C.48: Running times of the computationally optimal parallel RHCA, DHCA and flat consensus architectures on the MFeat data collection in the four diversity scenarios |dfA| = {1, 10, 19, 28}. 316
φ (NMI) φ (NMI) φ (NMI) φ (NMI) 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 CSPA E RHCA DHCA flat CSPA E RHCA DHCA flat CSPA E RHCA DHCA flat CSPA E RHCA DHCA flat φ (NMI) φ (NMI) φ (NMI) φ (NMI) 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 EAC Appendix C. Experiments on hierarchical consensus architectures E RHCA DHCA flat EAC E RHCA DHCA flat EAC E RHCA DHCA flat EAC E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 HGPA E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 MCLA E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 ALSAD E RHCA DHCA flat (a) φ (NMI) of the consensus solutions, |dfA| =1 φ (NMI) 1 0.8 0.6 0.4 0.2 0 HGPA E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 MCLA E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 ALSAD E RHCA DHCA flat (b) φ (NMI) of the consensus solutions, |dfA| =10 φ (NMI) 1 0.8 0.6 0.4 0.2 0 HGPA E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 MCLA E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 ALSAD E RHCA DHCA flat (c) φ (NMI) of the consensus solutions, |dfA| =19 φ (NMI) 1 0.8 0.6 0.4 0.2 0 HGPA E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 MCLA E RHCA DHCA flat φ (NMI) 1 0.8 0.6 0.4 0.2 0 ALSAD E RHCA DHCA flat (d) φ (NMI) of the consensus solutions, |dfA| =28 φ (NMI) φ (NMI) φ (NMI) φ (NMI) 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 KMSAD E RHCA DHCA flat KMSAD E RHCA DHCA flat KMSAD E RHCA DHCA flat KMSAD E RHCA DHCA flat φ (NMI) φ (NMI) φ (NMI) φ (NMI) 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 0.2 0 SLSAD E RHCA DHCA flat SLSAD E RHCA DHCA flat SLSAD E RHCA DHCA flat SLSAD E RHCA DHCA flat Figure C.49: φ (NMI) of the consensus solutions yielded by the computationally optimal RHCA, DHCA and flat consensus architectures on the MFeat data collection in the four diversity scenarios |dfA| = {1, 10, 19, 28}. 317
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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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E.3. Corel 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.3. Glass data set CSPA EAC HGPA M
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F.5. WDBC data set φ (NMI) 1 0.8 0
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F.7. MFeat data set φ (NMI) 1 0.8
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F.9. Segmentation data set φ (NMI)
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F.10. BBC data set φ (NMI) 1 0.8 0
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F.11. PenDigits data set φ (NMI) 1
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