Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Uniqueness Theorem for Clustering   Despite the widespread use of Clustering, there is distressingly little
general theory of clustering available. Questions like "What distinguishes a
clustering of data from other data partitioning?", "Are there any principles
governing all clustering paradigms?", "How should a user choose an appropriate
clustering algorithm for a particular task?", etc. are almost completely
unanswered by the existing body of clustering literature. We consider an
axiomatic approach to the theory of Clustering. We adopt the framework of
Kleinberg, [Kle03]. By relaxing one of Kleinberg's clustering axioms, we
sidestep his impossibility result and arrive at a consistent set of axioms. We
suggest to extend these axioms, aiming to provide an axiomatic taxonomy of
clustering paradigms. Such a taxonomy should provide users some guidance
concerning the choice of the appropriate clustering paradigm for a given task.
The main result of this paper is a set of abstract properties that characterize
the Single-Linkage clustering function. This characterization result provides
new insight into the properties of desired data groupings that make
Single-Linkage the appropriate choice. We conclude by considering a taxonomy of
clustering functions based on abstract properties that each satisfies.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org