Published:
2020-06-02
Proceedings:
Proceedings of the AAAI Conference on Artificial Intelligence, 34
Volume
Issue:
Vol. 34 No. 04: AAAI-20 Technical Tracks 4
Track:
AAAI Technical Track: Machine Learning
Downloads:
Abstract:
A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Random Dot Product Graph (RDPG), which can be fit using an efficient spectral method; however, this method is based on a heuristic that can fail, even in simple cases. Here, we consider a closely related latent space model, the Logistic RDPG, which uses a logistic link function to map from latent positions to edge likelihoods. Over this model, we show that asymptotically exact maximum likelihood inference of latent position vectors can be achieved using an efficient spectral method. Our method involves computing top eigenvectors of a normalized adjacency matrix and scaling eigenvectors using a regression step. The novel regression scaling step is an essential part of the proposed method. In simulations, we show that our proposed method is more accurate and more robust than common practices. We also show the effectiveness of our approach over standard real networks of the karate club and political blogs.
DOI:
10.1609/aaai.v34i04.5975
AAAI
Vol. 34 No. 04: AAAI-20 Technical Tracks 4
ISSN 2374-3468 (Online) ISSN 2159-5399 (Print) ISBN 978-1-57735-835-0 (10 issue set)
Published by AAAI Press, Palo Alto, California USA Copyright © 2020, Association for the Advancement of Artificial Intelligence All Rights Reserved