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TDA - Coggle Diagram

- - - - Pipeline
        
        Input : finite set of points with a notion of distance
        
        Points embedded in metric space
        
        Pairwise distance matrix
        
        Choice of the metric may be critical to reveal interesting topological and geometric feature of the data.
        
        Filtration: Simplicial Complex or a nested family of Simplicial Complex that reflects structure of data at different scales
        
        Information Extraction:
        
        Method: Persistent Homology
        
        Stability to perturbations and noise
        
        Therefore, important to understand the statistical behavior of the inferred features
        
        Use extracted information for inference and further use in Machine Learning
      - powerful approach to infer robust qualitative, and sometimes quantitative, information about the structure of data.
      - aims at providing well-founded mathematical, statistical and algorithmic methods to infer, analyze and exploit the complex topological and geometric structures underlying the data
      - Data often represented as point clouds in Euclidean Space or more general metric spaces
      - Library
        
        GUDHI