Essays about: "Daniel Lundin"

Found 2 essays containing the words Daniel Lundin.

  1. 1. Metrics for Multidimensional Persistence

    University essay from KTH/Matematik (Avd.)

    Author : Daniel Lundin; [2022]
    Keywords : topological data analysis; multidimensional persistence; persistence modules; metrics; noise systems; topologisk dataanalys; multidimensionell persistens; persistensmoduler; metriker; noise system;

    Abstract : A fundamental mathematical object in topological data analysis today is the persistence module. This thesis explores different metrics on multidimensional persistence modules, where spaces are parametrized along multiple dimensions. The focus is especially on metrics constructed by the use of so called noise systems, introduced by Scolamiero et al. READ MORE

  3. 2. Stability of Homology-Based Invariants in Data Analysis

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Daniel Lundin; [2020]
    Keywords : ;

    Abstract : In this thesis we will study the stability of the persistent homology pipeline used in topological data analysis. In particular, we will prove that persistent homology is 2-Lipschitz with respect to the Gromov-Hausdorff distance on the space of pseudometric spaces and interleaving distance on the space of parametrised vector spaces. READ MORE