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5 - Learning Network Representations

from Part II - Representations

Published online by Cambridge University Press:  23 September 2025

Eric W. Bridgeford
Affiliation:
The Johns Hopkins University
Alexander R. Loftus
Affiliation:
The Johns Hopkins University
Joshua T. Vogelstein
Affiliation:
The Johns Hopkins University
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Summary

This chapter presents a framework for learning useful representations, or embeddings, of networks. Building on the statistical models from Chapter 4, we explore techniques to transform complex network data into vector representations suitable for traditional machine learning algorithms. We begin with maximum likelihood estimation for simple network models, then motivate the need for network embeddings by contrasting network dependencies with typical machine learning independence assumptions. We progress through spectral embedding methods, introducing adjacency spectral embedding (ASE) for learning latent position representations from adjacency matrices, and Laplacian spectral embedding (LSE) as an alternative approach effective for networks with degree heterogeneities. The chapter then extends to multiple network representations, exploring parallel techniques like omnibus embedding (OMNI) and fused methods such as multiple adjacency spectral embedding (MASE). We conclude by addressing the estimation of appropriate latent dimensions for embeddings. Throughout, we emphasize practical applications with code examples and visualizations. This unified framework for network embedding enables the application of various machine learning algorithms to network analysis tasks, bridging complex network structures and traditional data analysis techniques.

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