TESI DOCTORAL - La Salle

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4.2. Flat vs. hierarchical self-refining 1. Given a cluster ensemble E containing l ⎛ components: ⎞ λ1 ⎜ ⎜λ2 ⎟ E = ⎜ ⎟ ⎝ . ⎠ and a pre-computed consensus clustering solution λc, compute the φ (NMI) between λc and each of the components of the cluster ensemble, that is: λl φ (NMI) (λc, λk) , ∀k =1,...,l 2. Generate an ordered list Oφ (NMI) = {λ φ (NMI) 1, λ φ (NMI)2,...λφ (NMI)l} of cluster ensemble components ranked in decreasing order according to their φ (NMI) with respect λc. 3. Create a set of P select cluster ensembles Epi nents of Oφ (NMI): Epi = ⎛ λ φ (NMI) ⎜ ⎝ 1 λ φ (NMI) 2 ⎞ ⎟ . ⎟ ⎠ where pi ∈ (0, 100) , ∀i =1,...,P. λ φ (NMI) ⌊ p i 100 l⌉ pi by compiling the first ⌊ 100l⌉ compo- 4. Run a (flat or hierarchical) consensus architecture based on a consensus function F on Epi , obtaining a self-refined consensus clustering solution λc p i . 5. Apply the supraconsensus function on the non-refined consensus clustering solution λc and the set of self-refined consensus clustering solutions λc p i , i.e. select as the final consensus solution the one maximizing its φ (ANMI) with respect to the cluster ensemble E. Table 4.1: Methodology of the consensus self-refining procedure. 4.2 Flat vs. hierarchical self-refining In this section, we present several experiments regarding the application of the consensus self-refining procedure described in section 4.1 on the consensus clustering solutions output by the three consensus architectures described in chapter 3. In all cases, our main interest is focused on analyzing the qualities of the clusterings obtained by the proposed self-refining procedure, not on evaluating the computational aspects of the self-refining process, as the decision regarding whether it is implemented according to a hierarchical or a flat consensus architecture can be efficiently made using the running time estimation methodologies proposed in chapter 3. The experiments conducted follow the design described next. 112
– What do we want to measure? Chapter 4. Self-refining consensus architectures i) The quality of the self-refined consensus clusterings obtained by the proposed methodology when applied on the consensus clusterings output by the flat and allegedly fastest RHCA and DHCA consensus architectures. ii) The ability of the proposed self-refining procedure to obtain a consensus clustering of higher quality than that of a) its non-refined counterpart, and b) the highest and median quality cluster ensemble components. iii) The quality of the self-refined consensus clustering of maximum quality compared to its non-refined counterpart. iv) The ability of the supraconsensus function to select, in a fully unsupervised manner, the highest quality self-refined consensus clustering among the set of self-refined clusterings generated. v) We analyze whether self-refining constitutes a means for uniformizing the quality of the consensus clustering solutions yielded by the flat and allegedly fastest RHCA and DHCA consensus architectures, thus making it possible to decide, on computational grounds only, which is the most suitable consensus architecture for a given clustering problem. – How do we measure it? i) The quality of the self-refined consensus clusterings is measured in terms of the φ (NMI) with respect to the ground truth of each data collection. ii) The percentage of experiments in which the proposed self-refining procedure gives rise to at least one self-refined consensus clustering of higher quality than that of a) its non-refined counterpart, and b) the highest and median quality cluster ensemble components. iii) We measure the relative φ (NMI) percentage difference between the self-refined consensus clustering of maximum quality and its non-refined counterpart. iv) The precision of the supraconsensus function is measured in terms of the percentage of experiments in which it manages to select the highest quality self-refined consensus clustering. v) We compare the average variance between the φ (NMI) scores of the consensus clusterings λc yielded by the three evaluated consensus architectures (i.e. prior to self-refining) with the variance between the consensus clustering selected by the ) after the self-refining procedure is conducted. supraconsensus function (λ final c – How are the experiments designed? we only analyze the results of the consensus self-refining process executed on the highest diversity scenario (i.e. the one where cluster ensembles are created by applying the |dfA| = 28 clustering algorithms from the CLUTO clustering package). The reason for this is twofold: besides brevity, this limitation on our analysis avoids that the results of the self-refining process are masked by the consensus quality variability observed in lower diversity scenarios —recall that, in those cases, the quality of the consensus clustering solutions shows larger variances, as the cluster ensemble changes from experiment to experiment due to the random selection of |dfA| = {1, 10, 19} clustering algorithms, whereas exactly the same cluster ensemble is employed across the ten experiments in the highest diversity scenario. As 113
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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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5.5. 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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