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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.17: 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 Balance 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. self-refining is applied, especially when the CSPA, ALSAD and KMSAD consensus functions are employed —more modest improvements are obtained when using MCLA or SLSAD, whereas none is attained when self-refining is based on EAC and HGPA. As regards the ability of the supraconsensus function to select the top quality clustering solution as the final one, it only suceeds when consensus is based on EAC, HGPA and MCLA. However, the φ (NMI) losses caused by suboptimal supraconsensus selection are, in general, moderate. D.2.10 BBC data set The application of the selection-based self-refining procedure on the BBC data set yields the φ (NMI) boxplots depicted in figure D.21. Notice that, in this very data collection, the cluster ensemble component λref selected via average φ (NMI) is very close (if not equal) to the maximum quality individual partition contained in the cluster ensemble E. Starting from this high quality reference point, the self-refining procedure manages to yield slightly better clusterings when it is based on the MCLA, ALSAD and KMSAD consensus functions. 354
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.18: 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 MFeat 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. Moreover, notice that, regardless of the consensus function employed, the supraconsensus function tends to select pretty high quality clustering solutions as the final ones. D.2.11 PenDigits data set Figure D.22 presents the φ (NMI) boxplots corresponding to the application of the selectionbased clustering self-refining procedure on the PenDigits data set. Recall that, due to its size, only the HGPA and MCLA consensus functions are executable on this data collection. As regards the results obtained, notice that the selected cluster ensemble component λref has a notably high quality. However, the results obtained when it is self-refined differ dramatically depending on the consensus function applied. In the case of HGPA, selfrefining brings about no quality gains, and the supraconsensus function correctly selects λref as the final clustering solution. In contrast, refined clusterings yielded by MCLA are capable of achieving slightly higher φ (NMI) values than the selected cluster ensemble component λref. However, supraconsensus conducts a suboptimal selection, as it does not choose the maximum quality refined clustering as the final partition. 355
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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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3.5. 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.4. Computationally optimal RHCA,
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