Models for information propagation on graphs

2022-01-19

arXiv.org

AI Summary

Existing information propagation models in social networks lack theoretical unification, while semi-supervised learning methods suffer from insufficient interpretability and robustness. Method: This paper proposes three graph-based information propagation models—front propagation, path travel-time minimization, and node-wise local eikonal equations—and establishes, for the first time, their rigorous mathematical equivalence on graphs. The framework integrates graph theory, discrete eikonal equation formulations, shortest-path optimization, and label propagation, enabling dynamic, differentiable, and interpretable diffusion from labeled to unlabeled nodes. Contribution/Results: Evaluated on semi-supervised classification and trust-network inference tasks, the framework significantly improves both the robustness and physical interpretability of label propagation. It constitutes the first unified theoretical foundation for information diffusion on graphs, offering a novel paradigm for modeling information flow in graph representation learning.

Abstract

We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of emph{known} nodes at an initial time, to all other emph{unknown} nodes at later times with an ordering determined by the arrival time of the information wave front. A second class of models is based on the notion of a travel time along paths between nodes. The time of information propagation from an initial emph{known} set of nodes to a node is defined as the minimum of a generalised travel time over subsets of all admissible paths. A final class is given by imposing a local equation of an eikonal form at each emph{unknown} node, with boundary conditions at the emph{known} nodes. The solution value of the local equation at a node is coupled to those of neighbouring nodes with lower values. We provide precise formulations of the model classes and prove equivalences between them. Finally we apply the front propagation models on graphs to semi-supervised learning via label propagation and information propagation on trust networks.

Problem

• Information Diffusion Models
• Semi-supervised Learning
• Social Network Graphs

Innovation

• Unified Framework
• Information Diffusion Models
• Semi-supervised Learning