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F.5. WDBC data set φ (NMI) 1 0.8 0.6 0.4 0.2 IONOSPHERE 0 0 0.5 1 1.5 2 2.5 CPU time (sec.) CSPA EAC HGPA MCLA VMA BC CC PC SC Figure F.4: φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus functions on the Ionosphere data collection. CSPA EAC HGPA MCLA VMA BC CC PC SC CSPA ——— 0.0001 0.0001 × 0.0001 0.0002 0.0002 × × EAC 0.0001 ——— 0.0001 0.0001 0.0001 × × 0.0001 0.0001 HGPA 0.0001 0.0001 ——— 0.0008 0.0001 0.0001 0.0001 0.0033 0.0031 MCLA 0.012 0.0004 0.0492 ——— 0.0001 0.0009 0.0014 × × VMA 0.0336 0.0001 0.0001 × ——— 0.0001 0.0001 0.0001 0.0001 BC × 0.0001 0.0001 0.0002 0.0001 ——— × 0.0003 0.0003 CC × 0.0001 0.0001 0.0002 0.0001 × ——— 0.0004 0.0004 PC 0.0312 0.0001 0.0001 × × 0.0001 0.0001 ——— × SC 0.0302 0.0001 0.0001 × × 0.0001 0.0001 × ——— Table F.4: Significance levels p corresponding to the pairwise comparison of soft consensus functions using a t-paired test on the Ionosphere 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 ×. in this data set –k = 2– does not penalize CondorcetConsensus), while EAC is the least efficient option. As far as the quality of the consensus clustering solutions is concerned, PC and SC get to match VMA as the best performing consensus functions, showing smaller dispersion in φ (NMI) terms than BC, CC and MCLA. If the statistical significance of the CPU time and φ (NMI) differences between consensus functions is evaluated –see table F.5– it can be observed that PC and SC are, in execution time terms, equivalent to CSPA and MCLA. As regards the quality of the consensus clustering solutions, no significant differences are observed between VMA, BC, CC, PC and SC, which, as aforementioned, turn out to be the best performing consensus functions. 378
φ (NMI) 1 0.8 0.6 0.4 0.2 Appendix F. Experiments on soft consensus clustering WDBC 0 0 2 4 6 CPU time (sec.) CSPA EAC HGPA MCLA VMA BC CC PC SC Figure F.5: φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus functions on the WDBC data collection. CSPA EAC HGPA MCLA VMA BC CC PC SC CSPA ——— 0.0001 0.0001 × 0.0001 0.0001 0.0002 × × EAC 0.0001 ——— 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 HGPA 0.0001 0.0001 ——— 0.0026 0.0001 0.0001 0.0001 0.0267 0.0249 MCLA 0.0001 0.0001 0.0001 ——— 0.0001 0.0002 0.0004 × × VMA 0.0001 0.0001 0.0001 0.0057 ——— 0.0001 0.0001 0.0001 0.0001 BC 0.0001 0.0001 0.0001 × × ——— × 0.0001 0.0001 CC 0.0001 0.0001 0.0001 × × × ——— 0.0001 0.0001 PC 0.0001 0.0001 0.0001 0.0025 × × × ——— × SC 0.0001 0.0001 0.0001 0.0103 × × × × ——— Table F.5: Significance levels p corresponding to the pairwise comparison of soft consensus functions using a t-paired test on the WDBC 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.6 Balance data set In this section, the performance of the soft consensus functions is compared through a set of consensus clustering experiments conducted on the Balance data set. Figure F.6 depicts the diagram that qualitatively compares the nine consensus functions in terms of CPU time required for their execution and the φ (NMI) of the consensus clustering solutions they yield. As regards the former aspect, we can observe that VMA, PC and SC are the most efficient consensus functions, and the differences between them, though small, are statistically significant according to the results of the t-paired tests presented in table F.6. Moreover, we can also observe that the BC and CC consensus functions achieve a mid-range time complexity, being slower than MCLA and HGPA, but faster than CSPA and EAC. <strong>La</strong>st, as far as the quality of the consensus clustering solutions is concerned, there is a high degree of equality between consensus functions. In fact, the differences between the top 379
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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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