Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning, a class encompassing many of the previously used embedding targets. This enables us to introduce a new method, the use of Finsler metrics integrated in a Riemannian optimization scheme, that better adapts to dissimilar structures in the graph. We develop a tool to analyze the embeddings and infer structural properties of the data sets. For implementation, we choose Siegel spaces, a versatile family of symmetric spaces. Our approach outperforms competitive baselines for graph reconstruction tasks on various synthetic and real-world datasets. We further demonstrate its applicability on two downstream tasks, recommender systems and node classification.
@article{arxiv.2106.04941,
title = {Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach},
author = {Federico López and Beatrice Pozzetti and Steve Trettel and Michael Strube and Anna Wienhard},
journal= {arXiv preprint arXiv:2106.04941},
year = {2021}
}