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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.15: 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 Ionosphere 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. quality of that of the selected cluster ensemble component λref are obtained for most consensus functions —in fact, the clearest exceptions to this behaviour are EAC and HGPA. However, the supraconsensus function is not capable of selecting those better quality clusterings as the final partition in most cases, which again gives an idea of its limited performance. D.2.7 MFeat data set Figure D.18 presents the φ (NMI) boxplots of the clusterings obtained after applying the selection-based self-refining process on the MFeat data set. Notice how, for four out of the seven consensus functions (CSPA, MCLA, ALSAD and KMSAD), notable quality gains are obtained (i.e. at least one of the refined clusterings attains a higher φ (NMI) than the selected cluster ensemble component λref). Unfortunately, the supraconsensus function fails to select these high quality partitions as the final clustering solution λ c final, as it constantly selects λref as the optimal one, which is the correct option when self-refining is based on the EAC, HGPA and SLSAD consensus functions. 352
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.16: 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 WDBC 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.2.8 miniNG data set The application of the selection-based self-refining procedure on the miniNG data collection yields the boxplots presented in figure D.19. Notice that the selected cluster ensemble component λref is comparable to the best individual partitions contained in the ensemble E. Despite of this, the self-refining process manages to obtain even higher quality consensus clusterings when based on the CSPA, MCLA, ALSAD and KMSAD consensus functions. Unfortunately, the supraconsensus functions fails in most occasions in selecting the maximum φ (NMI) clustering —in fact, it conducts the correct election when the EAC, HGPA and SLSAD consensus functions are employed. D.2.9 Segmentation data set Figure D.20 presents the φ (NMI) boxplots of the selection-based self-refined clustering solutions obtained on the Segmentation data set. Despite the notable quality of the selected cluster ensemble component λref, notice that important quality gains are obtained when 353
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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 396 and 397: E.1. CAL500 data set φ (NMI) 1 0.8
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Page 402 and 403: E.3. Corel data set φ (NMI) 1 0.8
Page 410 and 411: F.1. Iris data set φ (NMI) 1 0.8 0
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Page 422 and 423: F.11. PenDigits data set φ (NMI) 1
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