Partition and Code: learning how to compress graphs

TL;DR

This paper introduces a novel machine learning-based framework called Partition and Code for lossless graph compression, which decomposes graphs, learns probabilistic models, and encodes data efficiently, approaching theoretical entropy limits.

Contribution

It proposes a flexible, trainable graph compression method that outperforms traditional approaches and adapts to different graph distributions without domain-specific assumptions.

Findings

Theoretically proven to achieve near-optimal compression bounds.

Empirically demonstrates significant compression improvements on real-world networks.

Achieves linear or quadratic growth in compression gains with graph size.

Abstract

Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant patterns. On the other hand, most graph compression approaches rely on domain-dependent handcrafted representations and cannot adapt to different underlying graph distributions. This work aims to establish the necessary principles a lossless graph compression method should follow to approach the entropy storage lower bound. Instead of making rigid assumptions about the graph distribution, we formulate the compressor as a probabilistic model that can be learned from data and generalise to unseen instances. Our "Partition and Code" framework entails three steps: first, a partitioning algorithm decomposes the graph into subgraphs, then these are mapped to the elements of a small dictionary on which we learn a probability distribution, and finally, an entropy encoder translates the representation into bits. All the components (partitioning, dictionary and distribution) are parametric and can be trained with gradient descent. We theoretically compare the compression quality of several graph encodings and prove, under mild conditions, that PnC achieves compression gains that grow either linearly or quadratically with the number of vertices. Empirically, PnC yields significant compression improvements on diverse real-world networks.