Topo-Geometric Analysis of Variability in Point Clouds Using Persistence Landscapes.

ABSTRACT: Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects known as persistence diagrams. To better aid statistical analysis, a functional representation of the diagrams, known as persistence landscapes, enable use of functional data analysis and machine learning tools. Topological and geometric variabilities inherent in point clouds are confounded in both persistence diagrams and landscapes, and it is important to distinguish topological signal from noise to draw reliable conclusions on the structure of the point clouds when using persistence homology. We develop a framework for decomposing variability in pers

SUBMITTER: Matuk J 

PROVIDER: S-EPMC11636526 | biostudies-literature | 2024 Dec

REPOSITORIES: biostudies-literature