Zigzag zoology: rips zigzags for homology inference

@inproceedings{Oudot2013ZigzagZR,
  title={Zigzag zoology: rips zigzags for homology inference},
  author={Steve Oudot and Don Sheehy},
  booktitle={Symposium on Computational Geometry},
  year={2013}
}
For points sampled near a compact set X, the persistence barcode of the Rips filtration built from the sample contains information about the homology of X as long as X satisfies some geometric assumptions. The Rips filtration is prohibitively large, however zigzag persistence can be used to keep the size linear. We present several species of Rips-like zigzags and compare them with respect to the signal-to-noise ratio, a measure of how well the underlying homology is represented in the… CONTINUE READING
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