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3.3. Deterministic hierarchical consensus architectures SERT DHCA (sec.) PERT DHCA (sec.) 10 1 10 0 |df A | = 28 , |df D | = 14 , |df R | = 5 ADR ARD DAR DRA RAD RDA flat DHCA variant 10 0 (a) Serial estimated running time |df A | = 28 , |df D | = 14 , |df R | = 5 ADR ARD DAR DRA RAD RDA flat DHCA variant (c) Parallel estimated running time CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD SRT DHCA (sec.) PRT DHCA (sec.) 10 1 10 0 |df A | = 28 , |df D | = 14 , |df R | = 5 ADR ARD DAR DRA RAD RDA flat DHCA variant 10 0 (b) Serial real running time |df A | = 28 , |df D | = 14 , |df R | = 5 ADR ARD DAR DRA RAD RDA flat DHCA variant (d) Parallel real running time CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD Figure 3.13: Estimated and real running times of the serial and parallel DHCA on the Zoo data collection in the diversity scenario corresponding to a cluster ensemble of size l = 1596. most numerous diversity factor to the first stage, the second most populated to the second DHCA stage, and so on) seems to give rise to the most computationally efficient serial DHCA variant. And secondly, the execution time of fully parallel DHCA appears to be pretty insensitive to the way diversity factors are associated to the stages of the hierarchical consensus architecture. In practice, these two latter facts may play down the accuracy of the computationally optimal consensus architecture prediction methodology presented in table 3.6, as it seems possible to make well-grounded aprioridecisions as regards the selection of the fastest deterministic hierarchical consensus architecture variant without need of any running time estimation. For this reason, the next section presents an exhaustive comparative evaluation of these two strategies for predicting the computationally optimal consensus architecture. Evaluation of the optimal DHCA prediction methodology based on running time estimation Following an analogous procedure as in section 3.2.4, we have computed the percentage of experiments in which the estimated and real running times are simultaneously minimized by the same consensus architecture. The impact of the failures of this prediction methodology is measured in terms of the absolute and relative differences between the real execution times –ΔRT– of the truly (i.e. the one minimizing SRTDHCA or PRTDHCA) and the allegedly (the one that minimizes SERTDHCA or PERTDHCA) computationally optimal consensus 80
Chapter 3. Hierarchical consensus architectures Serial DHCA Parallel DHCA Dataset % correct ΔRT % correct ΔRT predictions (sec.) (%) predictions (sec.) (%) Zoo 55.9 1.32 227.3 40.0 0.03 34.0 Iris 93.4 0.56 180.7 51.2 0.10 63.7 Wine 76.1 1.19 48.2 36.8 0.14 48.1 Glass 76.4 0.76 32.1 39.3 0.23 60.7 Ionosphere 83.2 11.9 33.1 47.9 1.38 46.5 WDBC 76.2 77.73 58.1 39.7 4.93 44.5 Balance 90.6 0.52 26.5 71.1 0.93 51.7 MFeat 88.6 5.40 27.4 68.4 5.83 28.9 average 80.0 12.57 78.0 49.3 1.70 47.3 Table 3.7: Evaluation of the minimum complexity DHCA variant estimation methodology in terms of the percentage of correct predictions and running time penalizations resulting from mistaken predictions. architectures. The results corresponding to an averaging across 20 independent running time estimation experiments are presented in table 3.7. It can be observed that, in the serial case, SERTDHCA is a pretty accurate predictor, achieving correct prediction rates of the computationally optimal consensus architecture superior to 75% in all but one of the data sets. The running time overheads associated to incorrect predictions are usually negligible in absolute terms (ΔRT (sec.)) —except for the WDBC data collection, where the large real execution times of any of the consensus architectures make any mistake costly. As regards the performance of the proposed methodology for predicting the most efficent parallel implementation of DHCA, its degree of accuracy is inferior than in the serial case –a circumstance already observed in the context of RHCA–, although the penalization caused by this lower level of precision ranges below one second of extra execution time, which constitutes an assumable cost from a practical viewpoint —the WDBC and MFeat data collections stand out as the exceptions to this rule, although the corresponding ΔRT (sec.) overheads (around five seconds) are again of little importance in practice. Finally, we have also evaluated the influence of employing the execution times of c>1 consensus executions for estimating the running times of the DHCA variants. Expectably, the larger c, the more accurate the running time estimation and, consequently, smaller running time overheads will be derived from incorrect predictions. On the flip side, however, this will slow down the prediction process —recall that, in the experiments presented up to now, c =1. As in section 3.2.4, a sweep of values of c ∈ [1, 20] has been conducted, computing the percentage of fastest consensus architecture correct predictions and the absolute and relative running time deviations associated to prediction errors at each step of the sweep, averaging the results of twenty independent runs of this experiment on each one of the eight unimodal data collections —see figure 3.14. It can be observed that, despite the gradual increase of correct predictions (figure 3.14(a)), the running time deviations suffer a steep decrease as soon as c = 4 consensus processes are employed for computing SERTDHCA. Moreover, notice that using larger val- 81
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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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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.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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