Spectral Evolution with Approximated Eigenvalue Trajectories for Link Prediction

TL;DR

This paper introduces an improved spectral evolution model for large network growth, focusing on eigenvalue approximation and extrapolation, and demonstrates its effectiveness in predicting new links in social networks.

Contribution

It extends the spectral evolution model by providing a method to approximate eigenvalue trajectories and an algorithm to predict their evolution, enhancing link prediction accuracy.

Findings

Learning algorithms outperform kernel methods in link prediction.

Eigenvalue approximation improves spectral analysis of evolving networks.

Model effectively predicts new edges in social network data.

Abstract

The spectral evolution model aims to characterize the growth of large networks (i.e., how they evolve as new edges are established) in terms of the eigenvalue decomposition of the adjacency matrices. It assumes that, while eigenvectors remain constant, eigenvalues evolve in a predictable manner over time. This paper extends the original formulation of the model twofold. First, it presents a method to compute an approximation of the spectral evolution of eigenvalues based on the Rayleigh quotient. Second, it proposes an algorithm to estimate the evolution of eigenvalues by extrapolating only a fraction of their approximated values. The proposed model is used to characterize mention networks of users who posted tweets that include the most popular political hashtags in Colombia from August 2017 to August 2018 (the period which concludes the disarmament of the Revolutionary Armed Forces of Colombia). To evaluate the extent to which the spectral evolution model resembles these networks, link prediction methods based on learning algorithms (i.e., extrapolation and regression) and graph kernels are implemented. Experimental results show that the learning algorithms deployed on the approximated trajectories outperform the usual kernel and extrapolation methods at predicting the formation of new edges.