Threshold for Detecting High Dimensional Geometry in Anisotropic Random Geometric Graphs

@article{Brennan2022ThresholdFD,
  title={Threshold for Detecting High Dimensional Geometry in Anisotropic Random Geometric Graphs},
  author={Matthew Brennan and Guy Bresler and Brice Huang},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.14896}
}
In the anisotropic random geometric graph model, vertices correspond to points drawn from a high-dimensional Gaussian distribution and two vertices are connected if their distance is smaller than a specified threshold. We study when it is possible to hypothesis test between such a graph and an Erd˝os-R´enyi graph with the same edge probability. If n is the number of vertices and α is the vector of eigenvalues, [EM19] shows that detection is possible when n 3 ≫ ( k α k 2 / k α k 3 ) 6 and… 

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