Entropic graphs for manifold learning

We propose a new algorithm that simultaneously estimates the intrinsic dimension and intrinsic entropy of random data sets lying on smooth manifolds. The method is based on asymptotic properties of entropic graph constructions. In particular, we compute the Euclidean k-nearest neighbors (k-NN) graph over the sample points and use its overall total edge length to estimate intrinsic dimension and entropy. The algorithm is validated on standard synthetic manifolds.