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math.AT2026
Lower Bounds for Approximating the Vietoris-Rips Filtration
Kenneth McCabe
The Vietoris-Rips filtration is a standard tool for analyzing the shape of data within topological data analysis. Beginning with seminal work of Sheehy, a substan…
math.AT2024
Sparse Approximation of the Subdivision-Rips Bifiltration for Doubling Metrics
Michael Lesnick, Kenneth McCabe
The Vietoris-Rips filtration, the standard filtration on metric data in topological data analysis, is notoriously sensitive to outliers. Sheehy's subdivision-Rips bifiltration $\ma…
math.AT2024
Nerve Models of Subdivision Bifiltrations
Michael Lesnick, Kenneth McCabe
We study the size of Sheehy's subdivision bifiltrations, up to homotopy. We focus in particular on the subdivision-Rips bifiltration of a metric space , the on…