Essays about: "persistent homology"

Showing result 6 - 10 of 15 essays containing the words persistent homology.

  1. 6. From Relations to Simplicial Complexes: A Toolkit for the Topological Analysis of Networks

    University essay from KTH/Matematik (Avd.)

    Author : Johan Lord; [2021]
    Keywords : applied algebraic topology; complex networks; topological data analysis; brain network analysis;

    Abstract : We present a rigorous yet accessible introduction to structures on finite sets foundational for a formal study of complex networks. This includes a thorough treatment of binary relations, distance spaces, their properties and similarities. READ MORE

  3. 7. A comparative study on the unsupervised classification of rat neurons by their morphology

    University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Author : Sabrina Chowdhury; Added Kina; [2020]
    Keywords : ;

    Abstract : An ongoing problem regarding the automatic classification of neurons by their morphology is the lack of consensus between experts on neuron types. Unsupervised clustering using persistent homology as a descriptor for the morphology of neurons helps tackle the problem of bias in feature selection and has the potential of aiding neuroscience research in developing a framework for automatic neuron classification. READ MORE

  4. 8. 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

  5. 9. Statistical Learning and Analysis on Homology-Based Features

    University essay from KTH/Matematisk statistik

    Author : Jens Agerberg; [2020]
    Keywords : Applied topology; topological data analysis; TDA; persistent homology; machine learning; Topologisk dataanalys; maskininlärning;

    Abstract : Stable rank has recently been proposed as an invariant to encode the result of persistent homology, a method used in topological data analysis. In this thesis we develop methods for statistical analysis as well as machine learning methods based on stable rank. READ MORE

  6. 10. Classifying RGB Images with multi-colour Persistent Homology

    University essay from Linköpings universitet/Matematiska institutionen

    Author : Wolf Byttner; [2019]
    Keywords : Persistent Homology; Applied Algebraic Topology; Topological Data Analysis; Image Classification; CUB-200-2011;

    Abstract : In Image Classification, pictures of the same type of object can have very different pixel values. Traditional norm-based metrics therefore fail to identify objectsin the same category. Topology is a branch of mathematics that deals with homeomorphic spaces, by discarding length. READ MORE