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F.7. MFeat data set φ (NMI) 1 0.8 0.6 0.4 0.2 0 BALANCE 10 0 CPU time (sec.) CSPA EAC HGPA MCLA VMA BC CC PC SC Figure F.6: φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus functions on the Balance data collection. performing consensus functions (CSPA, VMA, PC and SC) are not statistically significant. CSPA EAC HGPA MCLA VMA BC CC PC SC CSPA ——— 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 EAC 0.0001 ——— 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 HGPA 0.0001 0.0003 ——— 0.0419 0.0001 0.0004 0.0001 0.0001 0.0001 MCLA 0.0291 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 0.0001 0.0001 VMA × 0.0001 0.0001 × ——— 0.0001 0.0001 0.0001 0.0001 BC 0.0139 0.0001 0.0001 × × ——— 0.0044 0.0001 0.0001 CC 0.0139 0.0001 0.0001 × × × ——— 0.0001 0.0001 PC × 0.0001 0.0001 × × 0.0322 0.0322 ——— × SC × 0.0001 0.0001 × × × × × ——— Table F.6: Significance levels p corresponding to the pairwise comparison of soft consensus functions using a t-paired test on the Balance data set. The upper and lower triangular sections of the table correspond to the comparison in terms of CPU time and φ (NMI) , respectively. Statistically non-significant differences (p >0.05) are denoted by the symbol ×. F.7 MFeat data set The results of the soft consensus clustering experiments conducted on the MFeat data set are presented in this section. For this purpose, figure F.7 depicts the diagram displaying the φ (NMI) vs CPU time mean ± 2-standard deviation regions corresponding to the nine soft consensus functions compared, and table F.7 presents the results of the statistical significance t-paired tests that compares them pairwise. In time complexity terms, VMA is the best performing consensus function, closely followed by MCLA, HGPA, PC and SC (the two latter being statistically equivalent). Among the two proposed positional voting based consensus functions, BC is clearly more efficient than CC. This probably is due to the larger number of classes (i.e. candidates) in this data set, which makes CC more costly due to the exhaustive pairwise candidate confrontation 380
Appendix F. Experiments on soft consensus clustering involved in the Condorcet voting method. However, executing CC takes approximately as long as running CSPA, and much less time than doing so with EAC, which is, by far, the least efficient consensus function. When the quality of the consensus clustering solutions delivered by these consensus functions is compared, we can see that PC, BC and CC obtain the highest φ (NMI) scores –with no significant differences among them–, closely followed by VMA, SC and CSPA. φ (NMI) 1 0.8 0.6 0.4 0.2 0 10 0 MFEAT CPU time (sec.) 10 2 CSPA EAC HGPA MCLA VMA BC CC PC SC Figure F.7: φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus functions on the MFeat data collection. CSPA EAC HGPA MCLA VMA BC CC PC SC CSPA ——— 0.0001 0.0001 0.0001 0.0001 0.0001 0.0022 0.0001 0.0001 EAC 0.0001 ——— 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 HGPA 0.0001 0.0001 ——— 0.0013 0.0001 0.0015 0.0001 0.0266 0.026 MCLA 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 × × VMA × 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 0.0001 BC 0.0007 0.0001 0.0001 0.0001 0.0034 ——— 0.0001 0.0001 0.0001 CC 0.0008 0.0001 0.0001 0.0001 0.0043 × ——— 0.0001 0.0001 PC 0.0382 0.0001 0.0001 0.0001 × × × ——— × SC × 0.0001 0.0001 0.0001 × 0.0024 0.003 × ——— Table F.7: Significance levels p corresponding to the pairwise comparison of soft consensus functions using a t-paired test on the MFeat data set. The upper and lower triangular sections of the table correspond to the comparison in terms of CPU time and φ (NMI) , respectively. Statistically non-significant differences (p >0.05) are denoted by the symbol ×. F.8 miniNG data set In this section we present the results of the soft consensus clustering experiments conducted on the miniNG data collection. The φ (NMI) vs CPU time diagram of figure F.8 reveals that three of the proposed voting based consensus functions (BC, PC and SC) constitute a good trade-off between consensus quality and time complexity. 381
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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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