Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach

Federico Lopez, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:7090-7101, 2021.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-lopez21a, title = {Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach}, author = {Lopez, Federico and Pozzetti, Beatrice and Trettel, Steve and Strube, Michael and Wienhard, Anna}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {7090--7101}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/lopez21a/lopez21a.pdf}, url = {https://proceedings.mlr.press/v139/lopez21a.html}, 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.} }
Endnote
%0 Conference Paper %T Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach %A Federico Lopez %A Beatrice Pozzetti %A Steve Trettel %A Michael Strube %A Anna Wienhard %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-lopez21a %I PMLR %P 7090--7101 %U https://proceedings.mlr.press/v139/lopez21a.html %V 139 %X 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.
APA
Lopez, F., Pozzetti, B., Trettel, S., Strube, M. & Wienhard, A.. (2021). Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:7090-7101 Available from https://proceedings.mlr.press/v139/lopez21a.html.

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