Clustering with the Connectivity Kernel

Clustering aims at extracting hidden structure in dataset. While the problem offinding compact clusters has been widely studied in the literature, extractingarbitrarily formed elongated structures is considered a much harder problem. In this paper we present a novel clustering algorithm whichtackles the problem by a two step procedure: first the data are transformed in such a way that elongated structures become compact ones. In a second step, these new objects are clustered by optimizing a compactness-based criterion. The advantages of the method over related approaches are threefold: (i) robustness properties of compactness-based criteria naturally transfer to the problem of extracting elongated structures, leadingto a model which is highly robust against outlier objects; (ii) the transformed distances induce a Mercer kernel which allows us to formulate a polynomial approximation scheme to the generally N P-hard clustering problem; (iii) the new method does not contain free kernel parameters in contrast to methods like spectral clustering or mean-shift clustering.