Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach

• URL: http://arxiv.org/abs/2106.04941v1
• Date: Wed, 9 Jun 2021 09:33:33 GMT
• Title: Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach
• Authors: Federico L\'opez, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard
• Abstract summary: We propose the systematic use of symmetric spaces in representation learning, a class encompassing many of the previously used embedding targets. We develop a tool to analyze the embeddings and infer structural properties of the data sets. Our approach outperforms competitive baselines for graph reconstruction tasks on various synthetic and real-world datasets.
• Score: 7.752212921476838
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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