Donald R. Sheehy

Linear-Size Approximations to the Vietoris–Rips Filtration

The Vietoris–Rips filtration is a versatile tool in topological data analysis. It is a sequence of simplicial complexes built on a metric space to add topological structure to an otherwise disconnected set of points. It is widely used because it encodes useful information about the topology of the underlying metric space. This information is often extracted from its so-called persistence diagram. Unfortunately, this filtration is often too large to construct in full. We show how to construct an

Zigzag zoology: rips zigzags for homology inference

O(n)

New Bounds on the Size of Optimal Meshes

O(n)-size filtered simplicial complex on an

Approximate center points with proofs

n

Linear-size approximations to the vietoris-rips filtration

n-point metric space such that its persistence diagram is a good approximation to that of the Vietoris–Rips filtration. This new filtration can be constructed in