TESI DOCTORAL - La Salle

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List of Figures 3.11 Estimated and real running times of the serial and parallel dHCA implementations on the Zoo data collection in the |dfA| = 10 diversity scenario . . . . 3.12 Estimated and real running times of the serial and parallel dHCA implemen- 78 tations on the Zoo data collection in the |dfA| = 19 diversity scenario . . . . 3.13 Estimated and real running times of the serial and parallel dHCA implemen- 79 tations on the Zoo data collection in the |dfA| = 28 diversity scenario . . . . 3.14 Evolution of the accuracy of DHCA running time estimation as a function of 80 the number of consensus processes . . . . . . . . . . . . . . . . . . . . . . . 82 3.15 Running times of the computationally optimal RHCA, DHCA and flat consensus architectures on the Zoo data collection for the diversity scenario corresponding to a cluster ensemble of size l = 57 . . . . . . . . . . . . . . . 3.16 Running times of the computationally optimal RHCA, DHCA and flat consensus architectures on the Zoo data collection for the diversity scenario 89 corresponding to a cluster ensemble of size l = 570 . . . . . . . . . . . . . . 91 3.17 Running times of the computationally optimal RHCA, DHCA and flat consensus architectures on the Zoo data collection for the diversity scenario corresponding to a cluster ensemble of size l = 1083 . . . . . . . . . . . . . 92 3.18 Running times of the computationally optimal RHCA, DHCA and flat consensus architectures on the Zoo data collection for the diversity scenario corresponding to a cluster ensemble of size l = 1596 . . . . . . . . . . . . . 93 3.19 Running times of the computationally optimal serial RHCA, DHCA and flat consensus architectures across all data collections for all the diversity scenarios 95 3.20 Running times of the computationally optimal parallel RHCA, DHCA and flat consensus architectures across all data collections for all the diversity scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.21 φ 97 (NMI) of the consensus solutions yielded by the computationally optimal RHCA, DHCA and flat consensus architectures on the Zoo data collection for the diversity scenario corresponding to a cluster ensemble of size l =57 3.22 φ 99 (NMI) of the consensus solutions yielded by the computationally optimal RHCA, DHCA and flat consensus architectures on the Zoo data collection for the diversity scenario corresponding to a cluster ensemble of size l = 570 3.23 φ 100 (NMI) of the consensus solutions yielded by the computationally optimal RHCA, DHCA and flat consensus architectures on the Zoo data collection for the diversity scenario corresponding to a cluster ensemble of size l = 1083 100 3.24 φ (NMI) of the consensus solutions yielded by the computationally optimal RHCA, DHCA and flat consensus architectures on the Zoo data collection for the diversity scenario corresponding to a cluster ensemble of size l = 1596 101 3.25 φ (NMI) of the consensus solutions obtained by the computationally optimal parallel RHCA, DHCA and flat consensus architectures across all data collections for all the diversity scenarios . . . . . . . . . . . . . . . . . . . . . . 103 4.1 φ (NMI) boxplots of the self-refined consensus clustering solutions on the Zoo data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 xxiv
List of Figures 4.2 Decreasingly ordered φ (NMI) (wrt ground truth) values of the 300 clusterings included in the toy cluster ensemble (left), and their corresponding φ (ANMI) values (wrt the toy cluster ensemble) (right) . . . . . . . . . . . . . . . . . . 121 4.3 φ (NMI) boxplots of the selection-based self-refined consensus clustering solutions on the Zoo data collection . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.1 Block diagram of the proposed multimodal consensus clustering system . . 134 5.2 An example of a deterministic hierarchical consensus architecture DRM variant139 5.3 φ (NMI) boxplots of the unimodal, multimodal and intermodal consensus clustering solutions using the agglo-cos-upgma algorithm on the IsoLetters data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 5.4 φ (NMI) boxplots of the unimodal, multimodal and intermodal consensus clustering solutions using the direct-cos-i2 algorithm on the IsoLetters data set 143 5.5 φ (NMI) boxplots of the unimodal, multimodal and intermodal consensus clustering solutions using the graph-cos-i2 algorithm on the IsoLetters data set 143 5.6 φ (NMI) boxplots of the unimodal, multimodal and intermodal consensus clustering solutions using the rb-cos-i2 algorithm on the IsoLetters data set . . 144 5.7 φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions using the agglo-cos-upgma algorithm on the IsoLetters data set . . . . . . . 153 5.8 φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions using the direct-cos-i2 algorithm on the IsoLetters data set . . . . . . . . . 153 5.9 φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions using the graph-cos-i2 algorithm on the IsoLetters data set . . . . . . . . . 154 5.10 φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions using the rb-cos-i2 algorithm on the IsoLetters data set . . . . . . . . . . . 155 6.1 Scatterplot of an artificially generated two-dimensional data set containing n = 9 objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 6.2 φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus functions on the Zoo data collection . . . . . . . . . . . . . . . . . . . . 186 B.1 φ (NMI) histograms on the Zoo data set . . . . . . . . . . . . . . . . . . . . . 234 B.2 φ (NMI) histograms on the Iris data set . . . . . . . . . . . . . . . . . . . . . 235 B.3 φ (NMI) histograms on the Wine data set . . . . . . . . . . . . . . . . . . . . 236 B.4 φ (NMI) histograms on the Glass data set . . . . . . . . . . . . . . . . . . . . 236 B.5 φ (NMI) histograms on the Ionosphere data set . . . . . . . . . . . . . . . . . 237 B.6 φ (NMI) histograms on the WDBC data set . . . . . . . . . . . . . . . . . . . 237 B.7 φ (NMI) histograms on the Balance data set . . . . . . . . . . . . . . . . . . . 238 B.8 φ (NMI) histograms on the MFeat data set . . . . . . . . . . . . . . . . . . . 239 B.9 φ (NMI) histograms on the miniNG data set . . . . . . . . . . . . . . . . . . . 239 B.10 φ (NMI) histograms on the Segmentation data set . . . . . . . . . . . . . . . . 240 xxv
Page 1: C.I.F. G: 59069740 Universitat Ramo
Page 5: Resum En segmentar de forma no supe
Page 9: Abstract When facing the task of pa
Page 12 and 13: Contents 2.2.6 Consensus functions
Page 14 and 15: Contents A.5 Consensus functions .
Page 16 and 17: Contents D.2.5 WDBC data set . . .
Page 18 and 19: List of Tables 3.13 Relative percen
Page 20 and 21: List of Tables 5.15 Relative φ (NM
Page 23: List of Figures 1.1 Evolution of th
Page 27 and 28: List of Figures C.18 Estimated and
Page 29 and 30: List of Figures C.49 φ (NMI) of th
Page 31 and 32: List of Figures D.22 φ (NMI) boxpl
Page 33: List of Algorithms 6.1 Symbolic des
Page 36 and 37: List of symbols OΛ: object co-asso
Page 38 and 39: Chapter 1. Framework of the thesis
Page 40 and 41: 1.1. Knowledge discovery and data m
Page 42 and 43: 1.1. Knowledge discovery and data m
Page 44 and 45: 1.2. Clustering in knowledge discov
Page 54 and 55: 1.3. Multimodal clustering in clust
Page 56 and 57: 1.4. Clustering indeterminacies exe
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Page 62 and 63: 1.5. Motivation and contributions o
Page 64 and 65: Chapter 2. Cluster ensembles and co
Page 66 and 67: fuzzy consensus clustering solution
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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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D.1. Experiments on consensus-based
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D.2. Experiments on selection-based
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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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