Stability of Density-Based Clustering
High density clusters can be characterized by the connected components of a level set L(lambda) = {x : p(x) > lambda} of the underlying probability density function p generating the data, at some appropriate level lambda >= 0. The complete hierarchical clustering can be characterized by a cluster tree T = boolean OR L-lambda(lambda). In this paper, we study the behavior of a density level set estimate (L) over cap(lambda) and cluster tree estimate (T) over cap based on a kernel density estimator with kernel bandwidth h. We define two notions of instability to measure the variability of (L) over cap(lambda) and (T) over cap as a function of h, and investigate the theoretical properties of these instability measures.
stability clustering level sets density estimation model selection