Estimating Filamentary Structures: New Algorithms and Statistical Inference

Speaker: Wanli Qiao, George Mason University

Title: Estimating Filamentary Structures: New Algorithms and Statistical Inference

Abstract:  Filamentary structures, also known as ridges, extend the concept of density function modes, offering low-dimensional representations of point clouds as a new approach to manifold learning. The widely used Subspace Constrained Mean Shift (SCMS) algorithm for ridge estimation may overlook certain ridge segments. We introduce two new algorithms for ridge estimation, accompanied by theoretical guarantees of their convergence and consistency. Additionally, we explore asymptotic confidence regions for filamentary structures using bootstrap methods, considering the potential existence of ridge intersections to model the intriguing topology of filamentary structures.