TESI DOCTORAL - La Salle

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List of symbols OΛ: object co-association matrix of a soft clustering solution Λ π λ1 ,λ 2 : cluster correspondence vector between the hard clustering solutions λ1 and λ2 π Λ1 ,Λ 2 : cluster correspondence vector between the soft clustering solutions Λ1 and Λ2 P λ1 ,λ 2 : cluster permutation matrix between the hard clustering solutions λ1 and λ2 P Λ1 ,Λ 2 : cluster permutation matrix between the soft clustering solutions Λ1 and Λ2 ΠE: product rule voting score matrix related to a cluster ensemble E φ (ANMI) : average normalized mutual information φ (NMI) : normalized mutual information PERTDHCA: estimated running time of a parallel DHCA PRTDHCA: real running time of a parallel DHCA PERTRHCA: estimated running time of a parallel RHCA PRTRHCA: real running time of a parallel RHCA r: number of attributes of an object after a dimensionality reduction process R: set of object representations used for creating a cluster ensemble RHCA: random hierachical consensus architecture s: number of stages of a hierarchical consensus architecture S λ1 ,λ 2 : cluster similarity matrix between the hard clustering solutions λ1 and λ2 S Λ1 ,Λ 2 : cluster similarity matrix between the soft clustering solutions Λ1 and Λ2 SERTDHCA: estimated running time of a serial DHCA SRTDHCA: real running time of a serial DHCA SERTRHCA: estimated running time of a serial RHCA SRTRHCA: real running time of a serial RHCA ΣE: sum rule voting score matrix related to a cluster ensemble E w: power proportionality factor of the time complexity of a consensus function xi: d-dimensional column vector denoting the ith object contained in a data set X: d × n matrix denoting a data set xxxvi
Chapter 1 Framework of the thesis The information and communications technologies (ICT) play a key role in the construction of the so-called global knowledge society. In fact, the increasingly rapid development of the ICT and the democratization of their use have facilitated information generation and access –a basic component of knowledge acquisition– to large segments of population. Possibly, the most paradigmatic example of this evolution is the World Wide Web (WWW, or “the Web” for short), which offers almost universal access to information to over 1500 million users worldwide, experiencing a percentage increase of 336% since year 2000 (InternetWorldStats.com, accessed on February 2009). In parallel, this evolution has boosted the number of existing websites, which has grown exponentially up to over 215 millions (NetCraft.com, accessed on February 2009)—see figure 1.1. Quite obviously, this latter fact incides on the quality of the information available on the Web (e.g. webpages with replicated, erroneous or even forged content are commonly found), making it sometimes difficult to separate the wheat from the chaff. This is an example of how the development of the ICT entails two instrinsically contradictory consequences: while facilitating knowledge acquisition by making information easier to share and access, it has also fostered the generation of increasingly growing amounts of digital information, giving rise to the so-called data overload effect —a problem that started to attract the attention of researchers more than a decade ago (Fayyad, Piatetsky-Shapiro, and Smyth, 1996). Indeed, as computing technologies have become increasingly efficient in the compression, transmission, storage and manipulation of data, the real bottleneck has moved towards the user side: that is, human information interpretation capabilities are often exceeded by the sheer amount of data. Not seldom, this situation is aggravated by the existence of data inconsistencies, making knowledge extraction even more difficult. Although exemplified in the WWW context, the data overload effect is far from being exclusive to it. At a smaller scale, large amounts of scientific and social data are being generated and made either freely or commercially available. Examples of these include experimental or observational data sets in the physics, chemistry, biomedical, marketing, financial or social sciences fields, whose sizes can even range over the Terabyte (Valencia, 2002; Witten and Frank, 2005). In addition to boosting the volume of information repositories, the evolution of the ICT has also brought about an increase of data complexity (Hinneburg and Keim, 1998). 1
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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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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.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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