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α-Clusterable Sets

α-Clusterable Sets

This video was recorded at European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD), Athens 2011. In spite of the increasing interest into clustering research within the last decades, a unified clustering theory that is independent of a particular algorithm, or underlying the data structure and even the objective function has not be formulated so far. In the paper at hand, we take the first steps towards a theoretical foundation of clustering, by proposing a new notion of "clusterability" of data sets based on the density of the data within a specific region. Specifically, we give a formal definition of what we call "α-clusterable" set and we utilize this notion to prove that the principles proposed in Kleinberg's impossibility... Show More


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