Uncertainty in Artificial Intelligence
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A Uniqueness Theorem for Clustering
Reza Zadeh, Shai Ben-David
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.
Keywords: null
Pages: 639-646
PS Link:
PDF Link: /papers/09/p639-zadeh.pdf
AUTHOR = "Reza Zadeh and Shai Ben-David",
TITLE = "A Uniqueness Theorem for Clustering",
BOOKTITLE = "Proceedings of the Twenty-Fifth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-09)",
ADDRESS = "Corvallis, Oregon",
YEAR = "2009",
PAGES = "639--646"

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