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5.5. Related publications modes jointly. This work introduces the application of audiovisual analysis and synthesis techniques based on Principal Component Analysis and Non-negative Matrix Factorization on facial audiovisual sequences. Furthermore, the applicability of the extracted audiovisual bases is analyzed throughout several experiments that evaluate the quality of audiovisual resynthesis using both objective and subjective criteria. 162
Chapter 6 Voting based consensus functions for soft cluster ensembles As outlined in section 1.2.1, clustering algorithms can be bisected into two large categories, depending on the number of clusters every object is assigned to. On one hand, hard (or crisp) clustering algorithms assign each object to a single cluster. For this reason, the result of applying a hard clustering process on a data set containing n objects is usually represented as a n-dimensional integer-valued row vector of labels (or labeling) λ, each component of which identifies to which of the the k clusters each object is assigned to, that is: λ =[λ1 λ2 ... λn] (6.1) where λi ∈ [1,k], ∀i ∈ [1,n]. On the other hand, soft (or fuzzy) clustering algorithms allow the objects to belong to all clusters to a certain extent. Thus, the results of their application for partitioning a data set containing n objects into k clusters is usually represented by means of a k×n real-valued clustering matrix Λ –see equation (6.2)–, the (i,j)th entry of which indicates the degree of association between the jth object and the ith cluster. ⎛ ⎜ Λ = ⎜ ⎝ λ11 λ12 ... λ1n λ21 λ22 ... λ2n . . .. λk1 λk2 ... λkn . ⎞ ⎟ ⎠ (6.2) where λij ∈ R, ∀i ∈ [1,k]and∀j ∈ [1,n]. For illustration purposes, we resort to the toy clustering example presented in chapter 2, in which clustering is conducted on the two-dimensional artificial data set presented in figure 6.1. This toy data collection contains n = 9 objects, and the desired number of clusters k is set to 3. If the classic k-means hard clustering algorithm is applied on this data set, the label vector presented in equation (6.3) is obtained. Recall that the labels λi contained in λ are purely symbolic (i.e. the labelings λ =[111222333]orλ =[333222111] represent exactly the same partition of the data). 163
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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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Page 222 and 223: 6.4. Experiments Data set Soft clus
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Page 239 and 240: References Ben-Hur, A., D. Horn, H.
Page 241 and 242: References Deerwester, S., S.-T. Du
Page 243 and 244: References Fred, A. and A.K. Jain.
Page 245 and 246: References Ingaramo, D., D. Pinto,
Page 247 and 248: 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.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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