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Creators/Authors contains: "Lewis, Robert R."

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  1. ; ; (, IEEE International Conference on Data Mining)
    Topological Data Analysis (TDA) utilizes concepts from topology to analyze data. In general, TDA considers objects similar based on a topological invariant. Topological invariants are properties of the topological space that are homeomorphic; resilient to deformation in the space. The Euler-Poincaré Characteristic is a classic topological invariant that represents the alternating sum of the vertices, edges, faces, and higherorder cells of a closed surface. Tracking the Euler characteristic over a topological filtration produces an Euler Characteristic Curve (ECC). This study introduces a computational technique to determine the ECC of R2 or R3 data; the technique generalizes to higher dimensions. This technique separates landscapes of lowerorder homologies utilizing triangulations of the space. 
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