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C.2. Estimation of the computationally optimal RHCA richer), which boosts the size of the cluster ensemble. Firstly, figure C.3 depicts the results corresponding to the fully serial RHCA implementation across the four diversity scenarios (estimated running times on the left column, real running times on the right). The first remarkable fact is that SERTRHCA is a pretty accurate predictor of SRTRHCA, which can be easily verified if the pair of subfigures presented on each row of figure C.3 are compared. Again, RHCA becomes more computationally attractive as the size of the cluster ensemble increases (except for the EAC consensus function). Moreover, among the distinct RHCA variants executed in each experiment, the greatest efficiency is achieved by the ones with 2 or 3 stages. The estimated and real execution times of the parallel implementation of RHCA are depicted in figure C.4. As already observed in the previous data sets, PERTRHCA is a modestly accurate estimator of PRTRHCA, although it is a fairly good predictor of the most computationally efficient consensus architecture. Notice that, in the most diverse scenario (|dfA| = 28), the least time consuming RHCA variant is nearly two orders of magnitude faster than flat consensus —thus, it can be argued that being able to predict which RHCA configuration requires the least computation time constitutes a significantly advantageous strategy compared to the traditional one-step approach to consensus clustering. C.2.3 Glass data set This section presents the results of estimating the execution times of the fully serial and parallel implementations of RHCA in the four diversity scenarios for the Glass data set, which give rise to cluster ensembles of sizes l =29, 290, 551 and 812 each. Firstly, figure C.5 depicts both the estimated and real running times of several serial RHCA variants. These results are quite comparable to those obtained in the previous data collections. That is, except for the EAC consensus function, the RHCA variants with s =2ands = 3 stages become the most computationally efficient as the size of the cluster ensemble increases. Moreover, in the most diverse scenario (|dfA| = 28) flat consensus is not executable if the MCLA consensus function is employed as the clustering combiner, whereas hierarchical consensus does provide a means for obtaining a consolidated clustering solution upon the same cluster ensemble using this consensus function. Furthermore, notice that the proposed methodology for estimating the running time of serial RHCA yields fairly reliable predictions of their real execution time. And secondly, the results corresponding to the parallel implementation of RHCA are presented in figure C.6. Again, it can be observed that the estimated running time of the parallel RHCA is an arguably accurate approximation of the real execution time. However, notice that this lack of accuracy is tolerable inasmuch as i) the location of the minima of PERTRHCA mostly coincides with the minima of PRTRHCA —which means that the fastest consensus architecture is successfully predicted, and ii) the selection of a computationally suboptimal RHCA variant involves a light penalization in terms of real execution time. C.2.4 Ionosphere data set This section describes the results of the minimum complexity RHCA variant selection based on running time estimation. In the case of the Ionosphere data collection, cluster ensembles of sizes l =97, 970, 1843 and 2716 correspond to the four diversity scenarios where this 256
SERT RHCA (sec.) SERT RHCA (sec.) SERT RHCA (sec.) SERT RHCA (sec.) Appendix C. Experiments on hierarchical consensus architectures 5 10 4 3 3 2 2 1 1 s : number of stages 10 0 10 −1 2 3 4 5 6 22 45 b : mini−ensemble size (a) Estimated RT, |dfA| =1 8 5 5 4 4 3 3 2 2 1 10 2 s : number of stages 10 1 10 0 10 2 10 1 10 0 10 2 10 1 10 0 2 3 4 5 6 7 17 18 225 450 b : mini−ensemble size (c) Estimated RT, |dfA| =10 s : number of stages 9 6 5 4 4 3 3 2 2 1 2 3 4 5 8 9 23 24 427 855 b : mini−ensemble size (e) Estimated RT, |dfA| =19 s : number of stages 10 7 5 5 4 4 3 3 2 2 1 2 3 4 5 6 9 10 28 29 630 1260 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 SRT RHCA (sec.) SRT RHCA (sec.) SRT RHCA (sec.) SRT RHCA (sec.) 5 10 4 3 3 2 2 1 1 s : number of stages 10 0 10 −1 2 3 4 5 6 22 45 b : mini−ensemble size (b) Real RT, |dfA| =1 8 5 5 4 4 3 3 2 2 1 10 2 s : number of stages 10 1 10 0 10 2 10 1 10 0 10 2 10 1 10 0 2 3 4 5 6 7 17 18 225 450 b : mini−ensemble size (d) Real RT, |dfA| =10 s : number of stages 9 6 5 4 4 3 3 2 2 1 2 3 4 5 8 9 23 24 427 855 b : mini−ensemble size (f) Real RT, |dfA| =19 s : number of stages 10 7 5 5 4 4 3 3 2 2 1 2 3 4 5 6 9 10 28 29 630 1260 b : mini−ensemble size (h) Real RT, |dfA| =28 Figure C.3: Estimated and real running times (RT) of the serial RHCA implementation on the Wine data collection in the four diversity scenarios |dfA| = {1, 10, 19, 28}. 257 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
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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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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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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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