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E.3. Corel data set φ (NMI) 1 0.8 0.6 0.4 0.2 0 CSPA rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (a) CSPA φ (NMI) λ 30 c 1 0.8 0.6 0.4 0.2 0 λ 40 c λ 50 c λ 75 c φ (NMI) 1 0.8 0.6 0.4 0.2 0 ALSAD rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c λ 30 c (e) ALSAD λ 40 c EAC rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (b) EAC λ 50 c λ 75 c φ (NMI) λ 30 c 1 0.8 0.6 0.4 0.2 0 λ 40 c λ 50 c λ 75 c φ (NMI) 1 0.8 0.6 0.4 0.2 0 KMSAD rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c λ 30 c (f) KMSAD λ 40 c HGPA rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (c) HGPA λ 50 c λ 75 c φ (NMI) λ 30 c 1 0.8 0.6 0.4 0.2 0 λ 40 c λ 50 c λ 75 c φ (NMI) 1 0.8 0.6 0.4 0.2 0 SLSAD rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c λ 30 c (g) SLSAD MCLA rb−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (d) MCLA Figure E.24: φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions using the rb-cos-i2 algorithm on the Corel data set. 372 λ 40 c λ 50 c λ 75 c λ 30 c λ 40 c λ 50 c λ 75 c
Appendix F Experiments on soft consensus clustering This appendix presents the results of the consensus clustering experiments on soft cluster ensembles. The main purpose of these experiments is to compare the four voting based consensus functions put forward in chapter 6 –namely BordaConsensus (BC), CondorcetConsensus (CC), ProductConsensus (PC) and SumConsensus (SC)– with five state-of-the-art clustering combiners: the soft versions of the hypergraph based hard consensus functions CSPA, HGPA and MCLA (Strehl and Ghosh, 2002), and the evidence accumulation approach (EAC) (Fred and Jain, 2005) (see section 6.2), plus the voting-merging soft consensus function (VMA) of (Dimitriadou, Weingessel, and Hornik, 2002). Such comparison entails two aspects: the quality of the consensus clustering solutions obtained (measured in terms of normalized mutual information –φ (NMI) – with respect to the ground truth of each data set), and the time complexity of each consensus function (measured in terms of the CPU time required for their execution —see appendix A.6 for a description of the computational resources employed in this work). From a formal viewpoint, the results of these experiments are presented by means of a φ (NMI) vs. CPU time diagram, onto which the performance of each consensus function is described by means of a scatterplot covering the mean ± 2-standard deviation region of the corresponding magnitude (i.e. φ (NMI) and CPU time). Moreover, the statistical significance of the results is evaluated by means of Student’s t-tests that compare all the consensus functions on a pairwise basis, thus analyzing whether the hypothetical superiority of any of them is sustained on firm statistical grounds, using the traditional 95% confidence interval as a reference for distinguishing between significant and non significant differences. These soft consensus clustering experiments have been conducted on the twelve unimodal data collections employed in this work (see appendix A.2.1 for a description). The results corresponding to the Zoo data collection are presented in chapter 6, and the following paragraphs describe the results obtained on the eleven remaining data sets. 373
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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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6.4. 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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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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