Modeling homophily and stochastic equivalence in symmetric relational data

TL;DR

This paper introduces the eigenmodel, a latent variable approach for symmetric relational data that unifies and generalizes existing models, demonstrating superior or comparable predictive performance on real datasets.

Contribution

The eigenmodel is a novel latent variable model based on eigenvalue decomposition that encompasses latent class and distance models, offering improved inference and prediction.

Findings

Eigenmodel generalizes latent class and distance models.

Eigenmodel achieves comparable or better predictive accuracy.

Model tested on three real datasets.

Abstract

This article discusses a latent variable model for inference and prediction of symmetric relational data. The model, based on the idea of the eigenvalue decomposition, represents the relationship between two nodes as the weighted inner-product of node-specific vectors of latent characteristics. This ``eigenmodel'' generalizes other popular latent variable models, such as latent class and distance models: It is shown mathematically that any latent class or distance model has a representation as an eigenmodel, but not vice-versa. The practical implications of this are examined in the context of three real datasets, for which the eigenmodel has as good or better out-of-sample predictive performance than the other two models.