Adaptive Manifold Clustering

We extend the theoretical study of a recently proposed nonparametric clustering algorithm called Adaptive Weights Clustering (AWC). In particular, we are interested in the case of high-dimensional data lying in the vicinity of a lower-dimensional non-linear submanifold with positive reach. After a slight adjustment and under rather general assumptions for the cluster structure, the algorithm turns out to be nearly optimal in detecting local inhomogeneities, while aggregating homogeneous data with a high probability. We also adress the problem of parameter tuning.