Symmetric spaces for graph embeddings

• Verfasst von: López, Federico [VerfasserIn]
• Verfasst von: Pozzetti, Maria Beatrice [VerfasserIn]
• Verfasst von: Trettel, Steve [VerfasserIn]
• Verfasst von: Strube, Michael [VerfasserIn]
• Verfasst von: Wienhard, Anna [VerfasserIn]
• Titel: Symmetric spaces for graph embeddings
• Titelzusatz: a Finsler-Riemannian approach
• Verf.angabe: Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard
• E-Jahr: 2021
• Jahr: 9 Jun 2021
• Umfang: 28 S.
• Fussnoten: Gesehen am 28.09.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), Artikel-ID 2106.04941, Seite 1-28
• DOI: doi:10.48550/arXiv.2106.04941
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Computer Science - Computational Geometry
• Sach-SW: Computer Science - Machine Learning
• Sach-SW: I.2
• K10plus-PPN: 1817329863

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.