Efficient and Robust Persistent Homology for Measures

@inproceedings{Buchet2015EfficientAR,
  title={Efficient and Robust Persistent Homology for Measures},
  author={M. Buchet and F. Chazal and S. Oudot and Don Sheehy},
  booktitle={SODA},
  year={2015}
}
A new paradigm for point cloud data analysis has emerged recently, where point clouds are no longer treated as mere compact sets but rather as empirical measures. A notion of distance to such measures has been defined and shown to be stable with respect to perturbations of the measure. This distance can easily be computed pointwise in the case of a point cloud, but its sublevel-sets, which carry the geometric information about the measure, remain hard to compute or approximate. This makes it… Expand
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