2009/07/01 by Frédéric Chazal, David Cohen‐Steiner, Leonidas Guibas +2 · 2 citations
Computer Science · Medicine · Biochemistry, Genetics and Molecular Biology · Mathematics · #Topological and Geometric Data Analysis #Advanced Neuroimaging Techniques and Applications #Cell Image Analysis Techniques #Metric space #Hausdorff space #Persistence (discontinuity) #Hausdorff distance #Point cloud #Mathematics #Metric (unit) #Compact-open topology #Stability (learning theory) #Point (geometry) #Signature (topology) #Topological data analysis #Computer science #Pure mathematics #Topological tensor product #Algorithm #Artificial intelligence #Geometry #Mathematical analysis #Machine learning
paper · doi:10.1111/j.1467-8659.2009.01516.x
openalex publication_date 2009/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
Abstract We introduce a family of signatures for finite metric spaces, possibly endowed with real valued functions, based on the persistence diagrams of suitable filtrations built on top of these spaces. We prove the stability of our signatures under Gromov‐Hausdorff perturbations of the spaces. We also extend these results to metric spaces equipped with measures. Our signatures are well‐suited for the study of unstructured point cloud data, which we illustrate through an application in shape classification.