Given a set of data points sampled from some underlying space, there are two important
challenges in geometric and topological data analysis when dealing with sampled data …

We consider the problem of reconstructing the topology of a manifold $ M $ from a finite
sample of its points. For a submanifold of the Euclidean $ n $-space Niyogi, Smale and …

A standard problem in applied topology is how to discover topological invariants of data from
a noisy point cloud that approximates it. We consider the case where a sample is drawn from …

Let be a collection of subspaces of a finite‐dimensional real vector space V. Let L denote a
one‐dimensional subspace of V, and let θ (L, Vi) denote the principal angle between L and …

In the introduction to this thesis, we provide background information about nonlinear
manifolds. In particular, we highlight the geometry of matrix manifolds. We explore literature …

Numerical algebraic geometry (NAG) consists of a collection of numerical algorithms, based
on homotopy continuation, to approximate the solution sets of systems of polynomial …

In this thesis we explore a variety of topics in the intersection of Topology and Statistics. This
includes some object oriented data analysis of topological summary statistics, a method of …

Let C={V1, V2,..., Vk} be a finite collection of nontrivial subspaces of a finite dimensional real
vector space V. Let L denote a one dimensional subspace of V and let θ (L, Vi) denote the …