Multiscale Estimation of Intrinsic Dimensionality of Data Sets

We present a novel approach for estimating the intrinsic dimensionality of certain point clouds: we assume that the points are sampled from a manifold M of dimension k , with k << D, and corrupted by D -dimensional noise. When M is linear, one may analyze this situation by SVD: with no noise one would obtain a rank k matrix, and noise may be treated as a perturbation of the covariance matrix. When M is a nonlinear manifold, global SVD may dramatically overestimate the intrinsic dimensionality. We introduce a multiscale version SVD and discuss how one can extract estimators for the intrinsic dimensionality that are highly robust to noise, while require a smaller sample size than current estimators.