2025/09/19 by Sigurd Gaukstad, Gaukstad, Sigurd, Mathias Karsrud Nordal +3
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Computational Geometry (cs.CG) #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 55N99 #Secondary 68U05 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2509.16102
openalex publication_date 2025/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The circular coordinates algorithm, a key tool in topological data analysis, relies on a theoretically unvalidated lifting step to convert cocycles from a prime field to integer coefficients. We provide a rigorous analysis of this procedure, establishing a criterion for its success. We also introduce a novel algebraic method to reduce any lifted cocycle to a cocycle with winding number 1, ensuring feature correctness. These principles are extended to homology cycles, solidifying the theoretical foundation of this widely used feature extraction technique.