Duke Applied Mathematics

Publications [#243806] of Mauro Maggioni

Papers Published

1. Little, AV; Jung, YM; Maggioni, M, Multiscale estimation of intrinsic dimensionality of data sets, Aaai Fall Symposium Technical Report, vol. FS-09-04 (December, 2009), pp. 26-33
   (last updated on 2019/04/10)

   Abstract:
   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. Copyright © 2009, Association for the Advancement of Artificial Intelligence. All rights reserved.