Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD

Anna V. Little, Jason Lee, Yoon-Mo Jung, Mauro Maggioni
2009 2009 IEEE/SP 15th Workshop on Statistical Signal Processing  
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 (hyperplane), one may analyse this situation by SVD, hoping the noise would perturb the rank k covariance matrix. When M is a nonlinear manifold,
more » ... 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.
doi:10.1109/ssp.2009.5278634 fatcat:5ecszykjl5cz7j7zlx4u3mfh5i