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E.2. InternetAds data set φ (NMI) 1 0.8 0.6 0.4 0.2 0 CSPA rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (a) CSPA φ (NMI) λ 30 c 1 0.8 0.6 0.4 0.2 0 λ 40 c λ 50 c λ 75 c φ (NMI) 1 0.8 0.6 0.4 0.2 0 ALSAD rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c λ 30 c (e) ALSAD λ 40 c EAC rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (b) EAC λ 50 c λ 75 c φ (NMI) λ 30 c 1 0.8 0.6 0.4 0.2 0 λ 40 c λ 50 c λ 75 c φ (NMI) 1 0.8 0.6 0.4 0.2 0 KMSAD rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c λ 30 c (f) KMSAD λ 40 c HGPA rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (c) HGPA λ 50 c λ 75 c φ (NMI) λ 30 c 1 0.8 0.6 0.4 0.2 0 λ 40 c λ 50 c λ 75 c φ (NMI) 1 0.8 0.6 0.4 0.2 0 SLSAD rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c λ 30 c (g) SLSAD λ 40 c MCLA rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (d) MCLA Figure E.8: φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions using the rb-cos-i2 algorithm on the CAL500 data set. E.2 InternetAds data set In the following paragraphs, the results corresponding to the execution of self-refining multimodal consensus clustering on the InternetAds collection are presented. In this case, the modalities are object (i.e image) attributes and collateral image attributes (see appendix A.2.2 for a description). E.2.1 Consensus clustering per modality and across modalities In this section, the quality of the unimodal, multimodal and intermodal consensus clusterings obtained on the cluster ensembles generated upon the agglo-cos-upgma, direct-cos-i2, graph-cos-i2 and rb-cos-i2 clustering algorithms is evaluated. Firstly, the results corresponding to the agglo-cos-upgma cluster ensemble are depicted in figure E.9. The first thing to notice is the extremely low quality of the cluster ensemble components, regardless of the modality. This fact conditions the consensus clustering results obtained, which are also of very low quality. Moreover, in contrast to what has been observed in the rest of experiments, there exist very little differences among the performance of the distinct consensus functions employed. A very similar behaviour is observed in the experiments conducted on the direct-cos-i2 and rb-cos-i2 cluster ensembles (figures E.10 and E.12). However, pretty different results are obtained on the graph-cos-i2 cluster ensemble (see figure E.11). In this case, the execution of consensus clustering on the collateral and the multimodal modalities yields better results. 364 λ 50 c λ 75 c λ 30 c λ 40 c λ 50 c λ 75 c
φ (NMI) 1 0.8 0.6 0.4 0.2 0 object λ agglo−cos−upgma c E CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD (a) Modality 1 φ (NMI) 0.8 0.6 0.4 0.2 0 Appendix E. Experiments on multimodal consensus clustering collateral λ agglo−cos−upgma c 1 E CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD (b) Modality 2 φ (NMI) object+collateral λ agglo−cos−upgma c 1 0.8 0.6 0.4 0.2 0 E CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD (c) Multimodal φ (NMI) 1 0.8 0.6 0.4 0.2 0 λ c agglo−cos−upgma E CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD (d) Intermodal Figure E.9: φ (NMI) boxplots of the unimodal, multimodal and intermodal consensus clustering solutions using the agglo-cos-upgma algorithm on the InternetAds data set. φ (NMI) 1 0.8 0.6 0.4 0.2 0 object λ direct−cos−i2 c E CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD (a) Modality 1 φ (NMI) 1 0.8 0.6 0.4 0.2 0 collateral λ direct−cos−i2 c E CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD (b) Modality 2 φ (NMI) object+collateral λ direct−cos−i2 c 1 0.8 0.6 0.4 0.2 0 E CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD (c) Multimodal φ (NMI) 1 0.8 0.6 0.4 0.2 0 λ c direct−cos−i2 E CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD (d) Intermodal Figure E.10: φ (NMI) boxplots of the unimodal, multimodal and intermodal consensus clustering solutions using the direct-cos-i2 algorithm on the InternetAds data set. E.2.2 Self-refined consensus clustering across modalities The results of the application of the self-refining procedure on the intermodal consensus clustering λc are presented next. Again, the consensus clustering selected by the supraconsensus function, λ final c , is highlighted by a green vertical dashed line. Figures E.13, E.14 and E.16, which show the results corresponding to the agglo-cosupgma, direct-cos-i2 and rb-cos-i2 cluster ensembles, reveal that little is achieved by selfrefining in these cases. In contrast, the usual growing φ (NMI) patterns induced by selfrefining are observed in figure E.15, especially when the MCLA, ALSAD and KMSAD consensus functions are employed (see figures E.15(d), E.15(e) and E.15(f)). Unfortunately, the supraconsensus function mostly fails in selecting the top quality clustering in these cases. 365
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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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B.1. Clustering indeterminacies in
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