MDL-Pool: Adaptive Multilevel Graph Pooling Based on Minimum Description Length

TL;DR

MDL-Pool introduces an adaptive graph pooling method based on the MDL principle, effectively modeling hierarchical interdependencies and selecting optimal pooling depths for improved graph classification.

Contribution

It proposes a novel MDL-based pooling operator that explicitly accounts for hierarchical interdependencies and adapts to varying graph sizes, unlike fixed-depth approaches.

Findings

Competitive performance on standard graph classification datasets

Effective modeling of hierarchical interdependencies

Adaptive pooling depth selection improves accuracy

Abstract

Graph pooling compresses graphs and summarises their topological properties and features in a vectorial representation. It is an essential part of deep graph representation learning and is indispensable in graph-level tasks like classification or regression. Current approaches pool hierarchical structures in graphs by iteratively applying shallow pooling operators up to a fixed depth. However, they disregard the interdependencies between structures at different hierarchical levels and do not adapt to datasets that contain graphs with different sizes that may require pooling with various depths. To address these issues, we propose MDL-Pool, a pooling operator based on the minimum description length (MDL) principle, whose loss formulation explicitly models the interdependencies between different hierarchical levels and facilitates a direct comparison between multiple pooling alternatives with different depths. MDP-Pool builds on the map equation, an information-theoretic objective function for community detection, which naturally implements Occam's razor and balances between model complexity and goodness-of-fit via the MDL. We demonstrate MDL-Pool's competitive performance in an empirical evaluation against various baselines across standard graph classification datasets.