Duke Applied Mathematics

Publications [#243804] of Mauro Maggioni

Papers Published

1. Little, AV; Lee, J; Jung, YM; Maggioni, M, Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD, Ieee Workshop on Statistical Signal Processing Proceedings (December, 2009), pp. 85-88, IEEE [doi]
   (last updated on 2019/04/10)

   Abstract:
   The problem of estimating the intrinsic dimensionality of certain point clouds is of interest in many applications in statistics and analysis of high-dimensional data sets. Our setting is the following: the points are sampled from a manifold M of dimension k, embedded in ℝ D , with k < D, and corrupted by D-dimensional noise. When M is a linear manifold (hy-perplane), one may analyse this situation by SVD, hoping the noise would perturb the rank k covariance matrix. When M is a nonlinear manifold, SVD performed globally may dramatically overestimate the intrinsic dimensionality. We discuss a multiscale version SVD that is useful in estimating the intrinsic dimensionality of nonlinear manifolds. © 2009 IEEE.