Lossy compression of weighted graph adjacency matrices by transform coding

2026-07-16

AI Summary

This work addresses the challenge of efficiently compressing edge weights in weighted graph adjacency matrices by proposing a line-graph-based graph signal modeling approach. Specifically, edge weights are treated as graph signals defined on the line graph and are compressed through transform coding using graph filter banks, followed by quantization and entropy coding. The method innovatively introduces an edge smoothness metric that can be computed without explicitly constructing the line graph, enabling effective prediction of compression performance. Experimental results demonstrate that the proposed framework consistently outperforms existing matrix preprocessing techniques on both synthetic and real-world datasets, thereby validating its efficacy and practicality for lossy graph weight compression.

Abstract

In this paper, we propose a compression framework for weighted graphs in which the graph topology is transmitted losslessly and edge weights are compressed lossily. A challenge in the lossy compression of edge weights is that the underlying relationships between edges are ambiguous. To address this issue, we first transform the unweighted graph into the corresponding line graph, whose nodes represent the edges of the original graph and whose edges encode the relationships between them. The line graph transform allows us to regard edge weights as a graph signal defined on the line graph. Instead of transmitting the edge-weight vector, we first transform it with a graph filter bank on the line graph. Then, quantization and entropy coding are performed on the transformed coefficients of the edge weight vector. In addition to the lossy compression method, we formalize edge smoothness on the line graph and show that it serves as a measure of the difficulty of compression. The proposed smoothness measure can be easily calculated without converting to a line graph. This provides insight into the expected compression performance of a given weighted graph. Experiments on synthetic and real-world data validate the effectiveness of the proposed method by comparing it with existing matrix preprocessing methods.

Problem

• lossy compression
• weighted graph
• edge weights
• line graph
• graph signal

Innovation

• line graph transform
• graph signal processing
• lossy compression
• edge smoothness
• graph filter bank