Topological Inference of Manifolds with Boundary

Understand

Given a set of data points sampled from some underlying space, there are two important challenges in geometric and topological data analysis when dealing with sampled data: reconstruction -- how to assemble discrete samples into global structures, and inference -- how to extract geometric and topological information from data that are high-dimensional, incomplete and noisy.

• Niyogi et al.
• (2008) have shown that by constructing an offset of the samples using a suitable offset parameter could provide reconstructions that preserve homotopy types therefore homology for densely sampled smooth submanifolds of Euclidean space without boundary.
• Chazal et al.