Entry-wise dissipation for singular vector perturbation bounds

04/01/2023

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by   Abhinav Bhardwaj, et al.

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Consider a random, symmetric perturbation of a symmetric, low rank matrix. The goal of this paper is to present entry-wise bounds on the perturbation of the singular vectors. In particular, our result shows that, under common incoherence assumptions, the entry-wise error is evenly dissipated. This improves a number of previous results and has algorithmic applications for many well known clustering problems, including the hidden clique, planted coloring, and planted bipartition.