Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach
Federico Lopez, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard
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.
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.}
}