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F.10. BBC data set φ (NMI) 1 0.8 0.6 0.4 0.2 0 10 0 BBC CPU time (sec.) 10 2 CSPA EAC HGPA MCLA VMA BC CC PC SC Figure F.10: φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus functions on the BBC data collection. CSPA EAC HGPA MCLA VMA BC CC PC SC CSPA ——— 0.0001 0.0001 0.0001 0.0001 0.0002 0.0012 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 ——— × 0.0001 0.0001 0.0001 × × MCLA 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 × × VMA 0.0456 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 0.0001 BC 0.004 0.0001 0.0001 0.0001 × ——— 0.0001 0.0002 0.0002 CC 0.004 0.0001 0.0001 0.0001 × × ——— 0.0001 0.0001 PC × 0.0001 0.0001 0.0001 × × × ——— × SC × 0.0001 0.0001 0.0001 × 0.0279 0.0279 × ——— Table F.10: Significance levels p corresponding to the pairwise comparison of soft consensus functions using a t-paired test on the BBC 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.10 BBC data set This section is devoted to the presentation of the results of the soft consensus clustering experiments conducted on the BBC data set. A qualitative description of them is provided by the φ (NMI) vs CPU time diagram of figure F.10, and the results of the statistical significance study of the differences between consensus functions is presented in table F.10. It can be observed that VMA is again the fastest consensus function. The confidence voting consensus functions (PC and SC) are, in statistical terms, as fast as MCLA and HGPA. The positional voting consensus functions (BC and CC) are slower than those, the former being also faster than CSPA, while the latter is slower than it. As regards the quality of the consensus clustering solutions obtained, CSPA, PC and SC yield the highest φ (NMI) scores, being equivalent from a statistical significance viewpoint. The BordaConsensus and CondorcetConsensus clustering combiners also deliver pretty good performances, together with the VMA consensus function, being notably better than MCLA (and far better than EAC and HGPA, which yield extremely poor consensus clustering 384
solutions). F.11 PenDigits data set Appendix F. Experiments on soft consensus clustering The results of the soft consensus clustering experiments conducted on the PenDigits data set are described in the following paragraphs. Due to the number of objects n contained in this collection, the CSPA and EAC consensus functions were not executable –as their space complexity scales quadratically with n. Thus, as a means for comparing the seven consensus functions applied on this data set, figure F.11 depicts the φ (NMI) vs CPU time mean ± 2-standard deviation regions corresponding to them. It can be observed that, in this case, the four voting based consensus functions proposed are the most time consuming. However, those based on confidence voting (PC and SC) are relatively comparable to HGPA and MCLA, while BC and CC are the most computationally costly (especially the latter). As in the previous cases, VMA is the most efficient of the consensus functions compared. When comparison is referred to the φ (NMI) of the consensus clustering solutions yielded by the seven consensus functions, we can observe that the highest quality is obtained by PC and SC, which match VMA in this aspect. The other two voting based consensus functions (BC and CC) perform slightly worse, but far better than MCLA and HGPA. 385
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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 370 and 371: D.1. Experiments on consensus-based
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Page 396 and 397: E.1. CAL500 data set φ (NMI) 1 0.8
Page 398 and 399: E.1. CAL500 data set φ (NMI) CSPA
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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 414 and 415: F.5. WDBC data set φ (NMI) 1 0.8 0
Page 416 and 417: F.7. MFeat data set φ (NMI) 1 0.8
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Page 422 and 423: F.11. PenDigits data set φ (NMI) 1
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