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Activity Number: 553
Type: Contributed
Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #318641
Title: Eigenvalue Concentration in the Finite-Dimensional Random Dot Product Graph Model
Author(s): Joshua Cape* and Minh Tang and Carey Priebe
Companies: The Johns Hopkins University and The Johns Hopkins University and The Johns Hopkins University
Keywords: random dot product graph ; concentration inequality ; eigenvalue ; matrix analysis ; signal-noise model

The application of random matrix theory to observed data structures (e.g. graphs) has led to general interest in eigenvalue concentration inequalities. Proofs for such inequalities often make the distinct eigenvalue assumption, which leads to the existence of eigengaps, followed by the application of canonical results such as the Davis-Kahan theorem.

We address the concentration of eigenvalues in the finite-dimensional random dot product graph model. More specifically, we prove under mild assumptions that the eigenvalues of the adjacency spectral embedding concentrate around the true eigenvalues even when the true eigenvalues have multiplicity. Our result extends naturally to a more general finite-dimensional signal-noise model with upper tail probability bounds.

Authors who are presenting talks have a * after their name.

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