Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach

We use curved spaces to more efficiently embed graphs that occur in machine learning problems.

AuthorsFederico Lopez, Beatrice Pozzetti, Steve Trettel, Michael Stube, Anna Wienhard
JournalProceedings of Machine Learning Research
CategoriesMachine Learning, Geometry, Experimental


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.

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