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C.4. Computationally optimal RHCA, DHCA and flat consensus comparison Running time comparison The characteristics of this data set –in particular, the low cardinalities of the diversity factors associated to it–, make flat consensus the fastest consensus architecture when compared to the serial implementations of RHCA and DHCA regardless of the diversity scenario —see figure C.44. The only exception is the MCLA consensus function, whose time complexity scales quadratically with the size of the ensemble, which penalizes the execution of one-step consensus processes in front of their hierarchical counterparts. A somewhat lighter version of this same behaviour is observed in the running time analysis of the parallel implementations of the HCA, which is presented in figure C.45. In this case, though, RHCA and DHCA are as fast or faster than flat consensus when the HGPA, MCLA and KMSAD consensus functions are employed. Consensus quality comparison As regards the quality of the consensus clustering solutions output by the three consensus architectures, figure C.46 shows the results obtained on the Balance data collection. It is to notice that the EAC and HGPA consensus functions yield, in general, the lowest quality results. For the remaining consensus functions, pretty similar quality consensus solutions are obtained by means of the three architectures, except for the ALSAD and SLSAD consensus function, where notable differences are observed between HCA and flat consensus. 310
CPU time (sec.) CPU time (sec.) CPU time (sec.) CPU time (sec.) 4.5 4 3.5 3 2.5 2 1.5 20 15 10 5 20 15 10 5 25 20 15 10 5 1 CSPA RHCA DHCA flat CSPA RHCA DHCA flat CSPA RHCA DHCA flat CSPA RHCA DHCA flat CPU time (sec.) CPU time (sec.) CPU time (sec.) CPU time (sec.) 70 60 50 40 30 20 10 70 60 50 40 30 20 10 0 70 60 50 40 30 20 10 0 70 60 50 40 30 20 10 0 EAC RHCA DHCA flat EAC RHCA DHCA flat EAC RHCA DHCA flat EAC RHCA DHCA flat Appendix C. Experiments on hierarchical consensus architectures CPU time (sec.) 0.3 0.25 0.2 0.15 0.1 0.05 0 HGPA RHCA DHCA flat CPU time (sec.) 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 MCLA RHCA DHCA flat CPU time (sec.) 80 70 60 50 40 30 20 10 0 ALSAD RHCA DHCA flat (a) Serial implementation running time, |dfA| =1 CPU time (sec.) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 HGPA RHCA DHCA flat CPU time (sec.) 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 MCLA RHCA DHCA flat CPU time (sec.) 70 60 50 40 30 20 10 0 ALSAD RHCA DHCA flat (b) Serial implementation running time, |dfA| =10 CPU time (sec.) 1.4 1.2 1 0.8 0.6 HGPA RHCA DHCA flat CPU time (sec.) 1.4 1.2 1 0.8 0.6 0.4 MCLA RHCA DHCA flat CPU time (sec.) 50 40 30 20 10 0 ALSAD RHCA DHCA flat (c) Serial implementation running time, |dfA| =19 CPU time (sec.) 1.6 1.4 1.2 1 0.8 HGPA RHCA DHCA flat CPU time (sec.) 2.5 2 1.5 1 MCLA RHCA DHCA flat CPU time (sec.) 40 35 30 25 20 15 10 5 0 ALSAD RHCA DHCA flat (d) Serial implementation running time, |dfA| =28 CPU time (sec.) CPU time (sec.) CPU time (sec.) CPU time (sec.) 10 8 6 4 2 0 16 14 12 10 8 6 4 2 0 15 10 5 0 20 15 10 5 KMSAD RHCA DHCA flat KMSAD RHCA DHCA flat KMSAD RHCA DHCA flat KMSAD RHCA DHCA flat CPU time (sec.) CPU time (sec.) CPU time (sec.) CPU time (sec.) 40 30 20 10 0 40 35 30 25 20 15 10 5 0 40 30 20 10 0 30 25 20 15 10 5 0 SLSAD RHCA DHCA flat SLSAD RHCA DHCA flat SLSAD RHCA DHCA flat SLSAD RHCA DHCA flat Figure C.44: Running times of the computationally optimal serial RHCA, DHCA and flat consensus architectures on the Balance data collection in the four diversity scenarios |dfA| = {1, 10, 19, 28}. 311
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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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E.1. CAL500 data set φ (NMI) 1 0.8
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E.1. CAL500 data set φ (NMI) CSPA
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E.2. InternetAds data set φ (NMI)
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E.3. Corel data set φ (NMI) 1 0.8
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F.1. Iris data set φ (NMI) 1 0.8 0
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F.3. Glass data set CSPA EAC HGPA M
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F.5. WDBC data set φ (NMI) 1 0.8 0
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F.7. MFeat data set φ (NMI) 1 0.8
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F.9. Segmentation data set φ (NMI)
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F.10. BBC data set φ (NMI) 1 0.8 0
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F.11. PenDigits data set φ (NMI) 1
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