Dynamic Clustering some unfinished business

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Dynamic Clustering(some unfinished business)

• Keith van Rijsbergen
• Glasgow
• October, 2002

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OUTLINE

• Introduction
• Scales
• Dissimilarity/Similarity
• Information-theoretic approach
• Static Clustering
• Dynamic Clustering
• Application

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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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Scales
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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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Information-theoretic approach I
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Information-theoretic approach II
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Navigation - Browsing
T-space
D-space
Duality is the key.
Class definition!
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Static Clustering

• dependence on rank-ordering of dissimilarity
• insensitive to small errors in DC
• preservation of well marked clusters
• stable under growth
• labelling independence
• invariance of ultrametric
• subject to 3 minimises distortion

T
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Dendrogram
.3
.2
.1
Spanning tree?
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Dynamic Clustering
Hilbert-Schmidt (A,B) trace(AB)
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Applications

• Image Retrieval
• Web Retrieval

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Ostension
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Conclusions
?