Multiscale Estimation of Intrinsic Dimensionality of Point Cloud Data and Multiscale Analysis of Dynamic Graphs

Abstract

In the first part of the thesis, we study the problem of estimating the intrinsic dimension of point cloud data sampled from a noisy manifold. We show that a multiscale algorithm succeeds with high probability. The second part of this thesis studies Dynamic Networks using a multiscale methodology. We propose a novel multiscale algorithm to analyze the dynamics of graphs and networks.