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5.3. Multimodal consensus clustering results 5.3.2 Self-refined consensus clustering across modalities In this section, we analyze the results of subjecting the intermodal consensus clustering solution λc to a self-refining procedure based on a cluster ensemble E, the components of which correspond to both unimodal and multimodal partitions. As described in chapter 4, the self-refining process is based on the creation of a select cluster ensemble Epi –containing a percentatge pi of the clusterings in E– followed by the application of a (either flat or hierarchical) consensus process on it, which yields a self-refined consensus clustering λ pi c . In this work, the refining consensus processes are conducted by means of a flat consensus architecture, and the set of percentages pi employed is pi = {2, 5, 10, 15, 20, 30, 40, 50, 75}. For this reason, the obtention of the final consensus clustering solution λ final c relies on the application of a supraconsensus selection function onto the set of self-refined clusterings λ pi c —see section 4.1 for a description of the φ (ANMI) -based supraconsensus function employed in this work. In the following paragraphs, the performances of these two processes (i.e. the self-refining procedure and the supraconsensus function) are evaluated separately. As in the previous section, the results of the execution of these processes on the IsoLetters data collection are described in detail next. Again, for brevity reasons, the presentation of the results corresponding to the CAL500, InternetAds and Corel data sets is deferred to appendix E. Evaluation of the multimodal self-refining process For starters, figure 5.7 depicts the results of the self-refining process using the multimodal cluster ensemble resulting from gathering the partitions output by the agglo-cos-upgma clustering algorithm of the CLUTO package. Each one of the seven boxplots presented (one per consensus function) shows, from left to right, the φ (NMI) values of the multimodal cluster ensemble E components, of the intermodal consensus clustering λc, and of the self-refined consensus clustering solutions λ pi c . The consensus clustering selected by the supraconsensus , is highlighted by a vertical green dashed line. Notice that, regardless of the consensus function employed, there always exists at least one self-refined consensus clustering solution that attains a φ (NMI) value that is statistically significantly higher than the one achieved by the non-refined version λc. In some cases, as when consensus is based on CSPA (figure 5.7(a)), relatively small φ (NMI) gains are obtained, specially if they are compared with the dramatic φ (NMI) increases brought about by selfrefining when, for instance, the EAC, HGPA or SLSAD consensus functions are employed (see figures 5.7(b), 5.7(c) and 5.7(g)). As regards the ability of the supraconsensus function to select the highest quality (either refined or non-refined) consensus clustering as the final partition of the data, it is to notice that it apparently performs reasonably well, as it mostly succeeds in picking up the clustering solution of maximum φ (NMI) as λfinal c . A deeper analysis of the supraconsensus function performance will be presented in the next section. Notice that the proposed intermodal consensus self-refining procedure shows a very similar behaviour in the experiments conducted on the multimodal cluster ensembles created upon the partitions output by the direct-cos-i2, thegraph-cos-i2 and the rb-cos-i2 clustering algorithms from the CLUTO toolbox —see figures 5.8, 5.9 and 5.10, respectively. function, λ final c 152
φ (NMI) CSPA agglo−cos−upgma 1 0.8 0.6 0.4 0.2 0 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (a) CSPA φ (NMI) λ 30 c λ 40 c λ 50 c λ 75 c φ (NMI) 1 0.8 0.6 0.4 0.2 0 Chapter 5. Multimedia clustering based on cluster ensembles EAC agglo−cos−upgma E λc λ 2 c λ 5 c ALSAD agglo−cos−upgma 1 0.8 0.6 0.4 0.2 0 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 λ 10 c λ 15 c λ 20 c (b) EAC λ 50 c λ 75 c φ (NMI) λ 30 c λ 40 c λ 50 c λ 75 c φ (NMI) HGPA agglo−cos−upgma 1 0.8 0.6 0.4 0.2 0 E λc λ 2 c λ 5 c KMSAD agglo−cos−upgma 1 0.8 0.6 0.4 0.2 0 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 λ 10 c λ 15 c λ 20 c (c) HGPA λ 50 c λ 75 c φ (NMI) λ 30 c λ 40 c λ 50 c λ 75 c φ (NMI) MCLA agglo−cos−upgma 1 0.8 0.6 0.4 0.2 0 E λc λ 2 c λ 5 c SLSAD agglo−cos−upgma 1 0.8 0.6 0.4 0.2 0 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c λ 30 c (g) SLSAD λ 10 c λ 15 c λ 20 c (d) MCLA Figure 5.7: φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions using the agglo-cos-upgma algorithm on the IsoLetters data set. φ (NMI) 1 0.8 0.6 0.4 0.2 0 CSPA direct−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 ALSAD direct−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c 0 λ 30 c (e) ALSAD λ 40 c EAC direct−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 KMSAD direct−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c 0 λ 30 c (f) KMSAD λ 40 c HGPA direct−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 λ 40 c SLSAD direct−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c λ 30 c (g) SLSAD λ 50 c λ 75 c λ 30 c λ 40 c MCLA direct−cos−i2 E λc λ 2 c λ 5 c λ 10 c λ 15 c λ 20 c (d) MCLA Figure 5.8: φ (NMI) boxplots of the self-refined intermodal consensus clustering solutions using the direct-cos-i2 algorithm on the IsoLetters data set. A comprehensive evaluation of the results of the intermodal consensus self-refining procedure is presented throughout the following paragraphs. This analysis considers the ex- 153 λ 40 c λ 50 c λ 75 c λ 30 c λ 40 c λ 50 c λ 75 c λ 50 c λ 75 c
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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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Page 149 and 150: - What do we want to measure? Chapt
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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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