Effective Higher-order Link Prediction and Reconstruction from Simplicial Complex Embeddings

Simone Piaggesi, André Panisson, Giovanni Petri

Keywords: representation learning, simplicial complexes, higher-order link prediction

TL;DR: Prediction and reconstruction of group-wise interactions with simplicial complex embeddings.

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.

Type Of Submission: Full paper proceedings track submission (max 9 main pages).

Agreement: Check this if you are okay with being contacted to participate in an anonymous survey.

Type Of Submission: Full paper proceedings track submission.

Software: https://github.com/simonepiaggesi/simplex2pred