Symmetric spaces for graph embeddings: a Finsler-Riemannian approach
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 t...
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| Main Authors: | , , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
9 Jun 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-28 |
| DOI: | 10.48550/arXiv.2106.04941 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2106.04941 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2106.04941 
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| Author Notes: | Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard |
| Summary: | 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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| Item Description: | Gesehen am 28.09.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2106.04941 |