Effective Higher-Order Link Prediction and Reconstruction From Simplicial Complex Embeddings

Simone Piaggesi, André Panisson, Giovanni Petri
Proceedings of the First Learning on Graphs Conference, PMLR 198:55:1-55:17, 2022.

Abstract

Methods that learn graph topological representations are becoming the usual choice to extract features to help solve machine learning tasks on graphs. In particular, low-dimensional encoding of graph nodes can be exploited in tasks such as link prediction and network reconstruction, where pairwise node embedding similarity is interpreted as the likelihood of an edge incidence. The presence of polyadic interactions in many real-world complex systems is leading to the emergence of representation learning techniques able to describe systems that include such polyadic relations. Despite this, their application on estimating the likelihood of tuple-wise edges is still underexplored. Here we focus on the reconstruction and prediction of simplices (higher-order links) in the form of classification tasks, where the likelihood of interacting groups is computed from the embedding features of a simplicial complex. Using similarity scores based on geometric properties of the learned metric space, we show how the resulting node-level and group-level feature embeddings are beneficial to predict unseen simplices, as well as to reconstruct the topology of the original simplicial structure, even when training data contain only records of lower-order simplices.

Cite this Paper

BibTeX
@InProceedings{pmlr-v198-piaggesi22a, title = {Effective Higher-Order Link Prediction and Reconstruction From Simplicial Complex Embeddings}, author = {Piaggesi, Simone and Panisson, Andr{\'e} and Petri, Giovanni}, booktitle = {Proceedings of the First Learning on Graphs Conference}, pages = {55:1--55:17}, year = {2022}, editor = {Rieck, Bastian and Pascanu, Razvan}, volume = {198}, series = {Proceedings of Machine Learning Research}, month = {09--12 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v198/piaggesi22a/piaggesi22a.pdf}, url = {https://proceedings.mlr.press/v198/piaggesi22a.html}, abstract = {Methods that learn graph topological representations are becoming the usual choice to extract features to help solve machine learning tasks on graphs. In particular, low-dimensional encoding of graph nodes can be exploited in tasks such as link prediction and network reconstruction, where pairwise node embedding similarity is interpreted as the likelihood of an edge incidence. The presence of polyadic interactions in many real-world complex systems is leading to the emergence of representation learning techniques able to describe systems that include such polyadic relations. Despite this, their application on estimating the likelihood of tuple-wise edges is still underexplored. Here we focus on the reconstruction and prediction of simplices (higher-order links) in the form of classification tasks, where the likelihood of interacting groups is computed from the embedding features of a simplicial complex. Using similarity scores based on geometric properties of the learned metric space, we show how the resulting node-level and group-level feature embeddings are beneficial to predict unseen simplices, as well as to reconstruct the topology of the original simplicial structure, even when training data contain only records of lower-order simplices. } }
Endnote
%0 Conference Paper %T Effective Higher-Order Link Prediction and Reconstruction From Simplicial Complex Embeddings %A Simone Piaggesi %A André Panisson %A Giovanni Petri %B Proceedings of the First Learning on Graphs Conference %C Proceedings of Machine Learning Research %D 2022 %E Bastian Rieck %E Razvan Pascanu %F pmlr-v198-piaggesi22a %I PMLR %P 55:1--55:17 %U https://proceedings.mlr.press/v198/piaggesi22a.html %V 198 %X Methods that learn graph topological representations are becoming the usual choice to extract features to help solve machine learning tasks on graphs. In particular, low-dimensional encoding of graph nodes can be exploited in tasks such as link prediction and network reconstruction, where pairwise node embedding similarity is interpreted as the likelihood of an edge incidence. The presence of polyadic interactions in many real-world complex systems is leading to the emergence of representation learning techniques able to describe systems that include such polyadic relations. Despite this, their application on estimating the likelihood of tuple-wise edges is still underexplored. Here we focus on the reconstruction and prediction of simplices (higher-order links) in the form of classification tasks, where the likelihood of interacting groups is computed from the embedding features of a simplicial complex. Using similarity scores based on geometric properties of the learned metric space, we show how the resulting node-level and group-level feature embeddings are beneficial to predict unseen simplices, as well as to reconstruct the topology of the original simplicial structure, even when training data contain only records of lower-order simplices.
APA
Piaggesi, S., Panisson, A. & Petri, G.. (2022). Effective Higher-Order Link Prediction and Reconstruction From Simplicial Complex Embeddings. Proceedings of the First Learning on Graphs Conference, in Proceedings of Machine Learning Research 198:55:1-55:17 Available from https://proceedings.mlr.press/v198/piaggesi22a.html.

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