Temporal Link Prediction using Matrix and Tensor Factorizations

TL;DR

This paper explores matrix and tensor factorization techniques for predicting future links in evolving bipartite graphs, demonstrating their effectiveness especially when data exhibits periodic patterns.

Contribution

It introduces scalable matrix and tensor methods for temporal link prediction, extending Katz to bipartite graphs and leveraging tensor decompositions for periodic data.

Findings

Tensor methods outperform matrix methods on periodic data

Scalable SVD-based approximation improves computational efficiency

Both techniques are effective despite the problem's inherent difficulty

Abstract

The data in many disciplines such as social networks, web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this paper, we consider the problem of temporal link prediction: Given link data for times 1 through T, can we predict the links at time T+1? If our data has underlying periodic structure, can we predict out even further in time, i.e., links at time T+2, T+3, etc.? In this paper, we consider bipartite graphs that evolve over time and consider matrix- and tensor-based methods for predicting future links. We present a weight-based method for collapsing multi-year data into a single matrix. We show how the well-known Katz method for link prediction can be extended to bipartite graphs and, moreover, approximated in a scalable way using a truncated singular value decomposition. Using a CANDECOMP/PARAFAC tensor decomposition of the data, we illustrate the usefulness of exploiting the natural three-dimensional structure of temporal link data. Through several numerical experiments, we demonstrate that both matrix- and tensor-based techniques are effective for temporal link prediction despite the inherent difficulty of the problem. Additionally, we show that tensor-based techniques are particularly effective for temporal data with varying periodic patterns.