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C.2. Estimation of the computationally optimal RHCA PERT RHCA (sec.) PERT RHCA (sec.) PERT RHCA (sec.) PERT RHCA (sec.) 10 2 10 0 10 3 10 2 10 1 10 0 10 3 10 2 10 1 10 0 10 3 10 2 10 1 10 0 s : number of stages 2 2 1 2 3 6 b : mini−ensemble size (a) Estimated RT, |dfA| =1 s : number of stages 5 4 3 3 2 2 1 2 3 4 6 7 30 60 b : mini−ensemble size (c) Estimated RT, |dfA| =10 s : number of stages 6 4 4 3 3 2 2 1 2 3 4 5 8 9 57 114 b : mini−ensemble size (e) Estimated RT, |dfA| =19 s : number of stages 7 5 4 3 3 2 2 1 2 3 4 5 10 11 84 168 b : mini−ensemble size (g) Estimated RT, |dfA| =28 CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD PRT RHCA (sec.) PRT RHCA (sec.) PRT RHCA (sec.) PRT RHCA (sec.) 10 2 10 0 10 3 10 2 10 1 10 0 10 3 10 2 10 1 10 0 10 3 10 2 10 1 10 0 s : number of stages 2 2 1 2 3 6 b : mini−ensemble size (b) Real RT, |dfA| =1 s : number of stages 5 4 3 3 2 2 1 2 3 4 6 7 30 60 b : mini−ensemble size (d) Real RT, |dfA| =10 s : number of stages 6 4 4 3 3 2 2 1 2 3 4 5 8 9 57 114 b : mini−ensemble size (f) Real RT, |dfA| =19 s : number of stages 7 5 4 3 3 2 2 1 2 3 4 5 10 11 84 168 b : mini−ensemble size (h) Real RT, |dfA| =28 Figure C.14: Estimated and real running times (RT) of the parallel RHCA implementation on the Mfeat data collection in the four diversity scenarios |dfA| = {1, 10, 19, 28}. 270 CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
Appendix C. Experiments on hierarchical consensus architectures C.3 Estimation of the computationally optimal DHCA The methodology for selecting the most computationally efficient implementation variant of deterministic hierarchical consensus architectures presented in section 3.3 –consisting of estimating the running time of several DHCA variants differing in the order diversity factors are associated to the stages of the hierarchical consensus architecture, selecting the one that yields the minimum running time, which is the one to be truly executed– has been applied on the Iris, Wine, Glass, Ionosphere, WDBC, Balance and MFeat unimodal data sets (see appendix A.2.1 for a description of these collections). In these experiments, the fully serial and parallel implementations of DHCA variants have been considered across the four experimental diversity scenarios employed in this work —see appendix A.4. The objective of this experiment is twofold: firstly, we seek to verify whether the proposed strategy succeeds in predicting the most computationally efficient DHCA variant. And secondly, we intend to analyze the conditions under which deterministic hierarchical consensus architectures are computationally advantageous compared to flat consensus clustering. We have followed the experimental design outlined next. – What do we want to measure? i) The time complexity of deterministic hierarchical consensus architectures. ii) The ability of the proposed methodology for predicting the computationally optimal DHCA variant, in both the fully serial and parallel implementations. iii) The predictive power of the proposed methodology based on running time estimation vs the computational optimality criterion based on designing the DHCA according to a decreasing diversity factor cardinality order, in both the fully serial and parallel implementations. – How do we measure it? i) The time complexity of the implemented serial and parallel DHCA variants is measured in terms of the CPU time required for their execution —serial running time (SRTDHCA) and parallel running time (PRTDHCA). ii) The estimated running times of the same DHCA variants –serial estimated running time (SERTDHCA) and parallel estimated running time (PERTDHCA)– are computed by means of the proposed running time estimation methodology, which is based on the measured running time of c = 1 consensus clustering process. Predictions regarding the computationally optimal DHCA variant will be successful in case that both the real and estimated running times are minimized by the same DHCA variant, and the percentage of experiments in which prediction is successful is given as a measure of its performance. In order to measure the impact of incorrect predictions, we also measure the execution time differences (in both absolute and relative terms) between the truly and the allegedly fastest DHCA variants in the case prediction fails. This evaluation process is replicated for a range of values of c ∈ [1, 20], so as to measure the influence of this factor on the prediction accuracy of the proposed methodology. iii) Both computationally optimal DHCA variants prediction approaches are compared in terms of the percentage of experiments in which prediction is successful, 271
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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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3.5. 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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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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