Dynamic Hyper-graph Regularized Non-negative Matrix Factorization

Nasr Ullah Khan, Luke Dickens

Keywords: Dynamic link prediction, dynamic graphs, hyper-graphs, graph regularization, non-negative matrix factorization, graph machine learning, time series analysis

TL;DR: We present a mathematical framework for dynamic hyper-graphs and a non-negative matrix factorization based algorithm for 1-step ahead prediction of the dynamic adjacency matrix.

Abstract: Recent advances in dynamic uni-graph methods make predictions about links between nodes at the current time, based on previous observations. The most powerful of these approaches are based on regularizing over previous graph laplacians with a greater emphasis placed on more recent observations as opposed to older observations. Concurrently, researchers have identified domains in which hyper-graph formulations of data provide more detailed information about relationships between entities when those relationships can be multi-factored. This work presents a natural synthesis of these two strands of work, extending regularization based on dynamic observations to hypergraphs. We present a modelling framework for dynamic hypergraphs, an algorithm for 1-step ahead prediction of the dynamic adjacency matrix, and experiments demonstrating the improved accuracy of this algorithm compared to dynamic uni-graph approaches.

Submission Type: Extended abstract (max 4 main pages).

Submission Number: 97