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B.2. Clustering indeterminacies in multimodal data sets Data set Highest maximum φ (NMI) −→ Lowest maximum φ (NMI) agglo bagglo direct rb rbr graph Zoo NMF-13d PCA-13d baseline RP-12d RP-12d PCA-6d (0.865) (0.858) (0.853) (0.848) (0.848) (0.730) bagglo direct rb rbr agglo graph Iris baseline baseline baseline baseline baseline baseline (0.899) (0.899) (0.899) (0.899) (0.837) (0.821) direct rbr bagglo rb graph agglo Wine PCA-10d PCA-10d ICA-12d PCA-10d PCA-8d ICA-5d (0.836) (0.836) (0.802) (0.795) (0.755) (0.720) agglo direct rb rbr bagglo graph Glass RP-8d RP-5d PCA-3d PCA-6d PCA-4d PCA-3d (0.487) (0.442) (0.423) (0.418) (0.417) (0.392) graph agglo bagglo direct rb rbr Ionosphere PCA-8d PCA-31d RP-14d RP-9d RP-9d RP-9d (0.656) (0.314) (0.309) (0.234) (0.234) (0.234) graph bagglo direct rb rbr agglo WDBC NMF-3d NMF-3d NMF-3d NMF-3d NMF-3d RP-15d (0.637) (0.603) (0.563) (0.563) (0.563) (0.522) agglo bagglo rbr rb direct graph Balance PCA-3d PCA-3d PCA-3d PCA-3d PCA-3d PCA-3d (0.703) (0.411) (0.394) (0.388) (0.370) (0.324) graph rbr direct agglo bagglo rb MFeat PIX PIX PIX KAR PIX KAR (0.811) (0.676) (0.669) (0.664) (0.606) (0.585) rb rbr bagglo direct graph agglo miniNG baseline PCA-70d baseline ICA-50d PCA-50d NMF-50d (0.638) (0.597) (0.559) (0.558) (0.412) (0.377) graph rbr agglo bagglo rb direct Segmentation PCA-11d PCA-13d ICA-13d PCA-13d PCA-14d ICA-17d (0.786) (0.741) (0.733) (0.731) (0.728) (0.720) rbr direct graph agglo bagglo rb BBC baseline baseline ICA-5d ICA-5d ICA-5d baseline (0.808) (0.808) (0.777) (0.750) (0.744) (0.726) graph agglo rbr direct bagglo rb PenDigits NMF-13d ICA-9d NMF-9d NMF-10d NMF-11d NMF-7d (0.839) (0.724) (0.682) (0.681) (0.665) (0.648) Table B.2: Top clustering results obtained by each clustering algorithm family across all the unimodal data sets, sorted from highest to lowest φ (NMI) . 242
Appendix B. Experiments on clustering indeterminacies Data representation CAL500 Data set Corel InternetAds IsoLetters MM 28 28 28 28 Baseline M1 28 28 28 28 M2 28 28 28 28 MM 504 420 308 532 PCA M1 280 196 308 196 M2 140 224 392 532 MM 504 420 308 532 ICA M1 280 196 308 196 M2 140 224 392 532 MM – 420 – 532 NMF M1 – 196 – 196 M2 – 224 – 532 MM 504 420 308 532 RP M1 280 196 308 196 M2 140 224 392 532 Table B.3: Number of individual clusterings per data representation on each multimodal data set, where MM, M1 and M2 stand for multimodal, mode #1 and mode #2, respectively. B.2.1 CAL500 data set The φ (NMI) histograms presented in figure B.13 summarize the clustering results obtained by running the aforementioned twenty-eight algorithms on each type of object representation for each one of the two modalities, and for the multimodal representations as well. If the histograms are compared representationwise, we observe that all representations yield clustering solutions whose quality spans over similarly wide ranges below φ (NMI) =0.5. For a given modality, there exists no clearly superior object representation. However, if the histograms are compared across the modalities, it can be observed that better results are obtained when clustering is conducted on the audio modality of this data set, regardless of the type of representation employed. Moreover, the multimodal data representation seems to yield intermediate quality clustering results (i.e. slightly better than clustering on text only, but worse than clustering solely on audio), which reveals that the early fusion of acoustic and textual features is not beneficial in this case. B.2.2 Corel data set Figure B.14 presents the φ (NMI) histograms corresponding to the multimodal and unimodal clustering of the captioned images of the Corel data set. As regards the comparison across object representations, it can be observed that, specially for the image and multimodal modalities, the RP representation offers a large amount of good clustering solutions, whereas the quality of the clusterings obtained on the remaining representations is scattered over a wide range of φ (NMI) values. If the clustering results obtained on the two modalities are compared, we can see that the image modality is the one yielding the best clustering results (up to φ (NMI) =0.68), 243
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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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1.5. 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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3.5. 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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%of experiments relative % φ (NMI)
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5.1. Generation of multimodal clust
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5.2. Self-refining multimodal conse
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5.5. Related publications modes joi
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Chapter 6. Voting based consensus f
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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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Page 247 and 248: References Li, S.Z. and G. GuoDong.
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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.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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