Geometry Helps to Compare Persistence Diagrams

@article{Kerber2016GeometryHT,
  title={Geometry Helps to Compare Persistence Diagrams},
  author={Michael Kerber and Dmitriy Morozov and Arnur Nigmetov},
  journal={ACM Journal of Experimental Algorithmics},
  year={2016},
  volume={22}
}
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft-Karp algorithm for bottleneck matching (based on previous work by Efrat el al.) and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a… CONTINUE READING
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Extracted Numerical Results

  • We set δ = 0.01 and compute the approximate bottleneck distance to the relative precision of δ, using k-d trees for the geometric version and constructing the layered graph combinatorially in the non-geometric version.

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