TESI DOCTORAL - La Salle

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List of Tables 3.13 Relative percentage φ (NMI) gain between the consensus clustering solution and the median cluster ensemble component . . . . . . . . . . . . . . . . . . 104 3.14 Percentage of experiments in which the consensus clustering solution is better than the best cluster ensemble component . . . . . . . . . . . . . . . . . . . 105 3.15 Relative percentage φ (NMI) gain between the consensus clustering solution and the best cluster ensemble component . . . . . . . . . . . . . . . . . . . 105 4.1 Methodology of the consensus self-refining procedure . . . . . . . . . . . . . 112 4.2 Percentage of self-refining experiments in which one of the self-refined consensus clustering solutions is better than its non-refined counterpart . . . . 117 4.3 Relative φ (NMI) gain percentage between the top quality self-refined consensus clustering solutions with respect to its non-refined counterpart . . . . . . . 117 4.4 Percentage of experiments in which the best (non-refined or self-refined) consensus clustering solution is better than the best cluster ensemble component 118 4.5 Relative percentage φ (NMI) gain between the best (non-refined or self-refined) consensus clustering solution and the best cluster ensemble component . . . 118 4.6 Percentage of experiments in which the best (non-refined or self-refined) consensus clustering solution is better than the median cluster ensemble component119 4.7 Relative percentage φ (NMI) gain between the best (non-refined or self-refined) consensus clustering solution and the median cluster ensemble component . 119 4.8 φ (NMI) variance of the non-refined and the best non/self-refined consensus clustering solutions across the flat, RHCA and DHCA consensus architectures120 4.9 Percentage of experiments in which the supraconsensus function selects the top quality consensus clustering solution . . . . . . . . . . . . . . . . . . . . 120 4.10 Relative percentage φ (NMI) losses due to suboptimal self-refined consensus clustering solution selection by supraconsensus . . . . . . . . . . . . . . . . 121 4.11 Methodology of the cluster ensemble component selection-based consensus self-refining procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.12 Percentage of self-refining experiments in which one of the self-refined consensus clustering solutions is better than the selected cluster ensemble component reference λref . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.13 Relative φ (NMI) gain percentage between the top quality self-refined consensus clustering solutions with respect to the maximum φ (ANMI) cluster ensemble component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.14 Percentage of experiments where either the top quality self-refined consensus clustering solution or λref better the best cluster ensemble component, and relative φ (NMI) gain percentage with respect to it . . . . . . . . . . . . . . . 126 4.15 Percentage of experiments where either the top quality self-refined consensus clustering solution or λref better the median cluster ensemble component, and relative φ (NMI) gain percentage with respect to it . . . . . . . . . . . . . 126 xviii
List of Tables 4.16 Percentage of experiments in which the supraconsensus function selects the top quality clustering solution, and relative percentage φ (NMI) losses between the top quality clustering solution and the one selected by supraconsensus, averaged across the twelve data collections . . . . . . . . . . . . . . . . . . . 127 5.1 Range and cardinality of the dimensional diversity factor dfD per modality for each one of the four multimedia data sets . . . . . . . . . . . . . . . . . 136 5.2 Percentage of cluster ensemble components that attain a higher φ (NMI) than the unimodal and multimodal consensus clusterings, across the four multimedia data collections and the seven consensus functions . . . . . . . . . . . 145 5.3 Evaluation of the unimodal and multimodal consensus clusterings with respect to the best cluster ensemble component, across the four multimedia data collections and the seven consensus functions . . . . . . . . . . . . . . 148 5.4 Evaluation of the unimodal and multimodal consensus clusterings with respect to the median cluster ensemble component, across the four multimedia data collections and the seven consensus functions . . . . . . . . . . . . . . 149 5.5 Evaluation of the multimodal consensus clusterings with respect to their unimodal counterparts, across the four multimedia data collections and the seven consensus functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 5.6 Evaluation of the intermodal consensus clustering with respect to the unimodal and multimodal consensus clusterings, across the four multimedia data collections and the seven consensus functions . . . . . . . . . . . . . . . . . 151 5.7 Percentage of multimodal self-refining experiments in which one of the selfrefined consensus clustering solutions is better than its non-refined counterpart154 5.8 Relative φ (NMI) gain percentage between the top quality self-refined consensus clustering solutions with respect to its non-refined counterpart . . . . . . . 156 5.9 Percentage of the cluster ensemble components that attain a higher φ (NMI) score than the top quality self-refined consensus clustering solution . . . . . 156 5.10 Percentage of experiments in which the best (either non-refined or self-refined) consensus clustering solution is better than the best cluster ensemble component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.11 Relative φ (NMI) percentage difference between the top quality (either nonrefined or self-refined) consensus clustering solution with respect to the best ensemble component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.12 Percentage of experiments in which the top quality (either non-refined or self-refined) consensus clustering solution is better than the median cluster ensemble component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 5.13 Relative φ (NMI) percentage difference between the top quality (either nonrefined or self-refined) consensus clustering solution with respect to the median ensemble component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 5.14 Percentage of experiments in which the supraconsensus function selects the top quality consensus clustering solution . . . . . . . . . . . . . . . . . . . . 159 xix
Page 1: C.I.F. G: 59069740 Universitat Ramo
Page 5: Resum En segmentar de forma no supe
Page 9: Abstract When facing the task of pa
Page 12 and 13: Contents 2.2.6 Consensus functions
Page 14 and 15: Contents A.5 Consensus functions .
Page 16 and 17: Contents D.2.5 WDBC data set . . .
Page 20 and 21: List of Tables 5.15 Relative φ (NM
Page 23 and 24: List of Figures 1.1 Evolution of th
Page 25 and 26: List of Figures 4.2 Decreasingly or
Page 27 and 28: List of Figures C.18 Estimated and
Page 29 and 30: List of Figures C.49 φ (NMI) of th
Page 31 and 32: List of Figures D.22 φ (NMI) boxpl
Page 33: List of Algorithms 6.1 Symbolic des
Page 36 and 37: List of symbols OΛ: object co-asso
Page 38 and 39: Chapter 1. Framework of the thesis
Page 40 and 41: 1.1. Knowledge discovery and data m
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Page 44 and 45: 1.2. Clustering in knowledge discov
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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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D.1. Experiments on consensus-based
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D.2. Experiments on selection-based
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E.1. CAL500 data set φ (NMI) 1 0.8
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E.1. CAL500 data set φ (NMI) CSPA
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E.2. InternetAds data set φ (NMI)
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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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