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Applied topology 7: How do you recover the shape of a dataset?
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Applied topology 7: How do you recover the shape of a dataset?
Abstract: Given a point cloud dataset, we explain how you can "blur your vision" in order to try to recover the underlying shape from which that dataset might have been sampled. We blur our vision by growing balls around each data point, and then considering the union of the balls. It is possible to also represent these thickenings via simplicial complexes (vertices, edges, triangles, tetrahedra, etc), including for example the Cech or Vietoris-Rips simplicial complex. This video is a preview to persistent homology, which we will discuss next!
This video accompanies the class "Topological Data Analysis" at Colorado State University:
Abstract: Given a point cloud dataset, we explain how you can "blur your vision" in order to try to recover the underlying shape from which that dataset might have been sampled. We blur our vision by growing balls around each data point, and then considering the union of the balls. It is possible to also represent these thickenings via simplicial complexes (vertices, edges, triangles, tetrahedra, etc), including for example the Cech or Vietoris-Rips simplicial complex. This video is a preview to persistent homology, which we will discuss next!
This video accompanies the class "Topological Data Analysis" at Colorado State University:
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