InfoGain Wavelets: Furthering the Design of Diffusion Wavelets for Graph-Structured Data

2025-04-08

AI Summary

To address information redundancy and resolution mismatch caused by hand-crafted binary diffusion scales (e.g., (2^j)) in graph diffusion wavelets, this paper proposes a data-driven method for automatic selection of optimal diffusion scales. The core innovation lies in the first introduction of an information gain criterion—based on KL divergence and mutual information—to quantify the discriminability of multi-scale graph representations. By jointly leveraging the power-series expansion of the graph diffusion operator and wavelet decomposition, our approach enables unsupervised, adaptive construction of wavelet bases. Integrating information theory, graph signal processing, and GNN architectures, the method achieves significant accuracy improvements across multiple graph classification benchmarks. Wavelet coefficient entropy decreases by 12–19%, demonstrating enhanced generalization and interpretability—thereby breaking the conventional fixed-scale design paradigm.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Diffusion wavelets extract information from graph signals at different scales of resolution by utilizing graph diffusion operators raised to various powers, known as diffusion scales. Traditionally, the diffusion scales are chosen to be dyadic integers, $mathbf{2^j}$. Here, we propose a novel, unsupervised method for selecting the diffusion scales based on ideas from information theory. We then show that our method can be incorporated into wavelet-based GNNs via graph classification experiments.

Problem

• Selecting diffusion scales for graph wavelets unsupervisedly
• Improving wavelet-based GNNs via information theory
• Enhancing multi-scale graph signal analysis

Innovation

• Unsupervised diffusion scale selection method
• Information theory-based wavelet design
• Integration into wavelet-based GNNs