Approximating min-sum k-clustering in metric spaces
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A tutorial on spectral clustering
Statistics and Computing
Characterization, Stability and Convergence of Hierarchical Clustering Methods
The Journal of Machine Learning Research
Min-sum clustering of protein sequences with limited distance information
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
The optimum clustering framework: implementing the cluster hypothesis
Information Retrieval
Discerning linkage-based algorithms among hierarchical clustering methods
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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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.