Graph representations as hyperball clouds enable scalable autoencoding
GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representations
Machine Learning
Summary
Graphs are complex structures like social networks or molecule shapes, and turning whole graphs into simple codes is hard. The authors represent graphs as clouds of shapes called hyperballs, providing a unique way to order graph parts. They build a system called GeoGAE that uses Transformers to convert these clouds into compact graph summaries and then reconstruct the graph back. This helps capture both the overall shape and local details of graphs. Their tests on many datasets show GeoGAE can effectively encode and rebuild graphs.
What this means in practice
- •For machine learning engineers: Develop graph-based models that need compact, scalable graph summaries preserving global and local graph structures.
- •For chemoinformatics teams: Encode molecular graphs efficiently to improve tasks such as drug discovery or material design with graph embeddings.
Authors
Radosław Nowak, Anna Bielawska, Bogusz Stefańczyk, Maciej Sanocki, Paweł Wawrzyński
Abstract
Embedding structured objects into Euclidean spaces has enabled a wide range of successful machine learning applications. Such objects include words, documents, image patches, time series, and graph nodes. In contrast, embedding entire graphs remains a challenging problem. Existing methods either sustain the original order of the graph nodes or match the output nodes to the input ones, both of which create scalability issues. In this work, we propose a graph representation as a cloud of hyperballs, which allows us to define a specific, typically unique, node ordering. Based on this representation, we propose GeoGAE, an autoencoder, in which the Transformer encoder translates a hyperball cloud into a graph-level embedding, and the Transformer decoder translates the graph-level embedding back into the graph. This formulation enables the model to capture both the global graph structure and local relational patterns. We evaluate our method on multiple graph datasets, spanning various domains. The results demonstrate effectiveness of our method in encoding and reconstructing graphs from their embeddings.