# 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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