Stability of Density-Based Clustering

11/11/2010

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by   Alessandro Rinaldo, et al.

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High density clusters can be characterized by the connected components of a level set L(λ) = {x: p(x)>λ} of the underlying probability density function p generating the data, at some appropriate level λ≥ 0. The complete hierarchical clustering can be characterized by a cluster tree T= _λ L(λ). In this paper, we study the behavior of a density level set estimate L(λ) and cluster tree estimate T based on a kernel density estimator with kernel bandwidth h. We define two notions of instability to measure the variability of L(λ) and T as a function of h, and investigate the theoretical properties of these instability measures.