2023/05/04 by Yossi Bokor Bleile, Bleile, Yossi Bokor
Computer Science · Engineering · Mathematics · #51-08 #55N31 #68T09 #Advanced Numerical Analysis Techniques #Algebra over a field #Algebraic Topology (math.AT) #Algebraic number #Algebraic structure #Algorithm #Artificial intelligence #Class (philosophy) #Combinatorics #Computational Geometry (cs.CG) #Computer science #Correctness #Digital Image Processing Techniques #Embedding #FOS: Computer and information sciences #FOS: Mathematics #Geometry #Mathematical analysis #Mathematics #Point (geometry) #Point cloud #Pure mathematics #Simple (philosophy) #Space (punctuation) #Theoretical computer science #Topological and Geometric Data Analysis #Topology (electrical circuits)
paper · pdf · doi:10.48550/arxiv.2305.02724
openalex publication_date 2023/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider a simple class of stratified spaces -- 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from computational geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding.