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3.4. Flat vs. hierarchical consensus results obtained when the MCLA consensus function is employed as the basis of consensus architectures must be made with care, as flat consensus is not executable when it must be conducted on large cluster ensembles. For this reason, the boxplots presented in the MCLA column only reflect the φ (NMI) values corresponding to those experiments where the three consensus architectures are executable. In these cases, the best consensus clustering solutions are obtained by the flat and DHCA consensus architectures. A greater degree of evenness between consensus architectures is observed in the consensus functions that treat object similarity as object features, i.e. ALSAD, KMSAD and SLSAD —notice the large overlap between boxes. However, whereas DHCA yields slightly lower quality consensus clustering solutions than the RHCA and flat consensus architectures when the ALSAD and KMSAD consensus functions are employed, it is the flat consensus approach that attains the lowest φ (NMI) values among the SLSAD based consensus architectures. And secondly, if an inter-consensus functions comparison is conducted, we can conclude that the excellent performance of the EAC consensus function on the Zoo data collection apparently constitutes an exception to the rule, as –together with HGPA and SLSAD– it yields the lowest φ (NMI) values (i.e. the poorest consensus clustering solutions) when the results obtained across all the data sets and diversity scenarios are compiled. In contrast, CSPA, MCLA, ALSAD and KMSAD tend to yield comparatively better consensus clustering solutions in a global perspective. Following a more quantitative perspective, we have compared the quality of the consensus clustering solutions yielded by the three consensus architectures with the components of the cluster ensemble consensus is conducted upon. In particular, this comparison has taken into account the cluster ensemble components of median and maximum φ (NMI) with respect to the ground truth (referred to as the median ensemble component, orMEC,and best ensemble component, or BEC, respectively). This comparison makes sense inasmuch we focus the application of consensus clustering as a means for becoming robust to the inherent indeterminacies that affect the clustering problem. More specifically, the higher the φ (NMI) of the consensus clustering solution with respect to that of the cluster ensemble components, the higher robustness is achieved. The median and maximum φ (NMI) components are used as a summarized reference of the quality of the cluster ensemble contents. For this reason, we have evaluated i) the percentage of experiments in which the consensus clustering solution attains a higher φ (NMI) than the MEC and the BEC, and ii) the relative percentage φ (NMI) variation between the median and the best cluster ensemble components and the consensus clustering solution. As regards the first issue, table 3.12 presents the percentage of experiments (considering all data sets in the highest diversity scenario) where the consensus clustering solution is better than the median normalized mutual information cluster ensemble component (MEC). It can be observed that the average percentage of experiments (considering all data sets in the highest diversity scenario) where the consensus clustering solution is better than the MEC is 53.1%, which indicates than in more than the half of the experiments, consensus yields a clustering solution better than the one located halfway of the cluster ensemble components. When the relative percentage φ (NMI) gains between consensus clustering solutions and the MEC are computed, a reasonable average of 59% gain is obtained —see table 3.13 for a detailed presentation of the results per consensus function and consensus architecture. If such comparison is referred to the cluster ensemble component that best describes the group structure of the data in terms of normalized mutual information with respect to the 102
φ (NMI) φ (NMI) φ (NMI) φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 CSPA 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 CSPA 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 CSPA CSPA 0 RHCA DHCA flat φ (NMI) φ (NMI) φ (NMI) φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 EAC 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 EAC 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 EAC EAC 0 RHCA DHCA flat φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 HGPA 0 RHCA DHCA flat φ (NMI) Chapter 3. Hierarchical consensus architectures 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 MCLA 0 RHCA DHCA flat φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ALSAD 0 RHCA DHCA flat (a) φ (NMI) of the consensus solutions, |dfA| =1 φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 HGPA 0 RHCA DHCA flat φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 MCLA 0 RHCA DHCA flat φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ALSAD 0 RHCA DHCA flat (b) φ (NMI) of the consensus solutions, |dfA| =10 φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 HGPA 0 RHCA DHCA flat φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 MCLA 0 RHCA DHCA flat φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ALSAD 0 RHCA DHCA flat (c) φ (NMI) of the consensus solutions, |dfA| =19 φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 HGPA 0 RHCA DHCA flat φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 MCLA 0 RHCA DHCA flat φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ALSAD 0 RHCA DHCA flat (d) φ (NMI) of the consensus solutions, |dfA| =28 φ (NMI) φ (NMI) φ (NMI) φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 KMSAD 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 KMSAD 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 KMSAD 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 KMSAD 0 RHCA DHCA flat φ (NMI) φ (NMI) φ (NMI) φ (NMI) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 SLSAD 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 SLSAD 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 SLSAD 0 RHCA DHCA flat 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 SLSAD 0 RHCA DHCA flat Figure 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 the diversity scenarios corresponding to the use of |dfA| = {1, 10, 19 and 28} clustering algorithms. 103
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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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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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TESI DOCTORAL - La Salle

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