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Title: Homology-Separating Triangulated Euler Characteristic Curve
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.  more » « less
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Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
IEEE International Conference on Data Mining
Page Range / eLocation ID:
1089 to 1094
Medium: X
Sponsoring Org:
National Science Foundation
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