Multiscale Estimation of Intrinsic Dimensionality of Point Cloud Data and Multiscale Analysis of Dynamic Graphs
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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.
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Rights for Collection: Undergraduate Honors Theses and Student papers