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CvR 1 Dynamic Clustering (some unfinished business) Keith van Rijsbergen Glasgow October, 2002

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CvR 2 OUTLINE Introduction Scales Dissimilarity/Similarity Information-theoretic approach Static Clustering Dynamic Clustering Application

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CvR 3 Introduction Theory…..where did it come from (Sneath and Sokal) Implementation….not yet Experimentation…..none Sneath and Sokal, Numerical Taxonomy (1973) Jardine and Sibson, Mathematical Taxonomy (1971) Van Rijsbergen, Information Retrieval (1979)

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CvR 4 Scales scaleoperationgroupstatistics nominalequalitypermutation 1:1 mode ordinalgreater/lessisotonic monotone median intervalequality/diff of intervals linear x=ax+b mean ratioequality of ratios similarity x=ax coeff of variation

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CvR 5 Dissimilarity/Similarity d(x,y) 0 for all x,y d(x,x) = 0 for all x d(x,y) = d(y,x) d(x,y) d(x,z) +d(z,y) {d(x,y) max [d(x,z), d(z,y)]}

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CvR 6 Information-theoretic approach I

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CvR 7 Information-theoretic approach II

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CvR 8 Navigation - Browsing T-space D-space Duality is the key. Class definition!

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CvR 9 Static Clustering 1.dependence on rank-ordering of dissimilarity 2.insensitive to small errors in DC 3.preservation of well marked clusters 4.stable under growth 5.labelling independence 6.invariance of ultrametric 7.subject to 3 minimises distortion T

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CvR 10 Dendrogram Spanning tree?

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CvR 11 Dynamic Clustering Hilbert-Schmidt: (A,B) = trace(AB)

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CvR 12 Applications Image Retrieval Web Retrieval

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CvR 13 Ostension

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CvR 14 Conclusions ?

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