Approximation of the multicover bifiltration

  • Abhishek Rathod (Purdue University)
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For a finite point set P $\subset{R^d}$, let $M_{r,k}$ denote the set of points in $R^d$ that are within distance r of at least k points in P. Allowing r and k to vary yields a 2-parameter family of spaces M, called the multicover bifiltration of P. It is a density-sensitive extension of the union-of-balls filtration commonly considered in TDA. It is robust to outliers in a strong sense, which motivates the problem of efficiently computing it (up to homotopy). A recent algorithm of Edelsbrunner and Osang computes a polyhedral model of M called the rhomboid bifiltration. In this work, we introduce an approximation of M (up to homotopy) which extends a version of the rhomboid tiling and devise an efficient algorithm to compute it.

The talk is based on joint work with Uli Bauer, Tamal Dey and Michael Lesnick.

Antje Vandenberg

MPI for Mathematics in the Sciences Contact via Mail

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