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B.2. Clustering indeterminacies in multimodal data sets Data set Highest φ (NMI) −→ Lowest φ (NMI) CAL500 Corel InternetAds IsoLetters rbr direct agglo rb bagglo graph RP-M1 RP-M1 RP-M1 RP-M1 RP-M1 baseline-M1 120d 100d 100d 120d 120d – (0.411) (0.404) (0.401) (0.384) (0.381) (0.364) rbr graph direct rb bagglo agglo NMF-MM RP-MM NMF-MM NMF-MM baseline-M1 baseline-MM 550d 400d 450d 300d – – (0.675) (0.672) (0.671) (0.641) (0.624) (0.622) bagglo graph agglo direct rb rbr RP-M1 NMF-MM baseline-M2 NMF-M2 NMF-M2 NMF-M2 70d 150d – 550d 550d 550d (0.430) (0.319) (0.258) (0.087) (0.087) (0.087) rbr direct graph agglo rb bagglo PCA-MM PCA-MM PCA-MM RP-MM baseline-MM baseline-MM 100d 100d 100d 600d – – (0.897) (0.875) (0.846) (0.790) (0.751) (0.728) Table B.4: Top clustering results obtained by each clustering algorithm family across all the multimodal data sets, sorted from highest to lowest φ (NMI) . 248
Appendix C Experiments on hierarchical consensus architectures This appendix presents several experiments regarding self-refining hierarchical consensus architectures. C.1 Configuration of a random hierarchical consensus architecture In this section, we present some examples that describe, in detail, the configuration process of random hierarchical consensus architectures (RHCA). The aim is to demostrate how, given a cluster ensemble size l and a mini-ensemble size b, equations (C.1), (C.2) and (C.3) allow determining the number of stages s, the number of consensus per stage Ki and the effective size of each mini-ensemble bij of the corresponding RHCA. For starters, let us evaluate carefully the three RHCA examples presented in section 3.2. In these toy examples, the mini-ensemble size is set to b = 2, while the respective cluster ensembles have l =7, 8 and 9 components. The first step of the RHCA design process consists of determining the number of stages of the hierarchy, s, accordingtoequation (C.1). ⎧ ⎪⎩ ⌊log b (l)⌉ if ⎪⎨ s = ⌊logb (l)⌉−1 if ⌊log b (l)⌉ +1 if l b ⌊log b (l)⌉ l b ⌊log b (l)⌉ l b ⌊log b (l)⌉ ≤ 1and ≤ 1and > 1 l b ⌊log b (l)⌉−1 l b ⌊log b (l)⌉−1 > 1 =1 (C.1) Table C.1 presents the results of this computation for the three aforementioned examples (one row per example), specifying the values of the decision factors used for selecting one of the three options presented in equation (C.1). Once the number of stages of the RHCA is computed, the next step consists of determining how many consensus processes are to be executed at each RHCA stage. This factor, 249
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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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Page 239 and 240: References Ben-Hur, A., D. Horn, H.
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Page 243 and 244: References Fred, A. and A.K. Jain.
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Page 247 and 248: References Li, S.Z. and G. GuoDong.
Page 249 and 250: References Sebastiani, F. 2002. Mac
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Page 253 and 254: Appendix A Experimental setup A.1 T
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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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