Spectral Recovery of Point Clouds from Noisy Geometric Graphs
Read the original on arXiv Statistics ML →The paper investigates how to recover low‑dimensional latent geometry from a random geometric graph built from noisy, high‑dimensional data. It analyzes a spectral embedding algorithm on the Signal+Noise Graph Model, where vertices are perturbed points and edges are added when their inner product exceeds a threshold. In the regime where both the number of points and ambient dimension grow, the authors prove that, under a spectral gap condition, the leading eigenvectors and eigenvalues of the adjacency matrix can approximately recover the original point cloud up to an orthogonal transformation, and demonstrate the method on nested spheres and high‑dimensional sinusoid curves.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Statistics ML.