Estimating the Reach of a Manifold

@article{Aamari2017EstimatingTR,
  title={Estimating the Reach of a Manifold},
  author={Eddie Aamari and Jisu Kim and Fr{\'e}d{\'e}ric Chazal and Bertrand Michel and Alessandro Rinaldo and Larry Wasserman LM-Orsay and Select and Datashape and UC San Diego and Ecn and Lmjl},
  journal={arXiv: Statistics Theory},
  year={2017}
}
  • Eddie Aamari, Jisu Kim, +8 authors Lmjl
  • Published 2017
  • Mathematics
  • arXiv: Statistics Theory
  • Various problems in manifold estimation make use of a quantity called the reach, denoted by $\tau\_M$, which is a measure of the regularity of the manifold. This paper is the first investigation into the problem of how to estimate the reach. First, we study the geometry of the reach through an approximation perspective. We derive new geometric results on the reach for submanifolds without boundary. An estimator $\hat{\tau}$ of $\tau\_{M}$ is proposed in a framework where tangent spaces are… CONTINUE READING

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