Online Program Home
  My Program

All Times EDT

Abstract Details

Activity Number: 495 - Statistical Methods for Networks
Type: Contributed
Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #312567
Title: A Statistical Interpretation of Spectral Embedding: The Generalized Random Dot Product Graph
Author(s): Patrick Rubin-Delanchy and Joshua Cape* and Minh Tang and Carey Priebe
Companies: University of Bristol and University of Michigan and NC State University and Johns Hopkins University
Keywords: networks; random graphs; spectral clustering; Procrustes; dimensionality reduction; latent space

We study a latent position network model that generalizes random dot product graphs. We show that for both the normalized Laplacian and the adjacency matrix, the vector representations of nodes obtained by spectral embedding, using the largest eigenvalues by magnitude, provide strongly consistent latent position estimates with asymptotically Gaussian error, up to indefinite orthogonal transformation. The mixed membership and standard stochastic block models constitute special cases where the latent positions live respectively inside or on the vertices of a simplex, crucially, without assuming the underlying block connectivity probability matrix is positive-definite. Estimation via spectral embedding can therefore be achieved by respectively estimating this simplicial support, or fitting a Gaussian mixture model. In the latter case, the use of K-means (with Euclidean distance), as has been previously recommended, is suboptimal and for identifiability reasons unsound. Empirical improvements in link prediction and the potential to uncover latent structure are demonstrated in a cyber-security example.

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

Back to the full JSM 2020 program