Essays about: "persistent homology"
Showing result 1 - 5 of 7 essays containing the words persistent homology.
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1. Comparison in Barcode and Computing Time for Persistent Homology Applied to a Subset of a Point Cloud
University essay fromAbstract : At the intersection of topology and computer science lies the field of topological data analysis(TDA). TDA uses the concept of persistence to identify low dimensional topological features of data embedded in high dimensions. READ MORE
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2. Stability of Homology-Based Invariants in Data Analysis
University essay from KTH/Skolan för teknikvetenskap (SCI)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
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3. Classifying RGB Images with multi-colour Persistent Homology
University essay from Linköpings universitet/Matematiska institutionenAbstract : 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
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4. Illustrations of Data Analysis Using the Mapper Algorithm and Persistent Homology
University essay from KTH/Matematik (Avd.)Abstract : The Mapper algorithm and persistent homology are topological data analysis tools used for analyzing point cloud data. In addition a classification method is used as a part of the data analysis toolchain adopted in this thesis in order to serve as a distinguishing technique for two class labels. READ MORE
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5. Algorithms for Multidimensional Persistence
University essay from KTH/Matematik (Avd.)Abstract : The theory of multidimensional persistence was introduced in a paper by G. Carlsson and A. Zomorodian as an extension to persistent homology. The central object in multidimensional persistence is the persistence module, which represents the homology of a multi filtered space. READ MORE