  We investigate the question of studying spectral clustering in a Hilbert
space where the set of points to cluster are drawn i.i.d. according to an
unknown probability distribution whose support is a union of compact connected
components. We modify the algorithm proposed by Ng, Jordan and Weiss in order
to propose a new algorithm that automatically estimates the number of clusters
and we characterize the convergence of this new algorithm in terms of
convergence of Gram operators. We also give a hint of how this approach may
lead to learn transformation-invariant representations in the context of image
classification.
