2022/12/26 by Brittany Terese Fasy, Fasy, Brittany Terese, Samuel Micka +7
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cell Image Analysis Techniques #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Metabolomics and Mass Spectrometry Studies #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2212.13206
openalex publication_date 2022/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in ℝd, the (augmented) persistent homology transform ((A)PHT) is a family of persistence diagrams, parameterized by directions in the ambient space. A recent advance in understanding the PHT used the framework of reconstruction in order to find finite a set of directions to faithfully represent the shape, a result that is of both theoretical and practical interest. In this paper, we improve upon this result and present an improved algorithm for graph -- and, more generally one-skeleton -- reconstruction. The improvement comes in reconstructing the edges, where we use a radial binary (multi-)search. The binary search employed takes advantage of the fact that the edges can be ordered radially with respect to a reference plane, a feature unique to graphs.