Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach
This work addresses the need for improved graph embeddings in machine learning applications, offering a novel approach that is incremental in combining existing concepts.
The paper tackled the problem of learning faithful graph representations by proposing the use of symmetric spaces and a Finsler-Riemannian method to better adapt to dissimilar graph structures, resulting in outperforming baselines on graph reconstruction tasks across synthetic and real-world datasets.
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.