[Paper Review] Paper-author bipartite graph from Semantic Scholar

Michaël Defferrard, Stefania Ebli+1 more|arXiv (Cornell University)|Oct 7, 2020

Topological and Geometric Data Analysis27 references57 citations

TL;DR

Simplicial Neural Networks (SNNs) generalize graph neural networks to data on simplicial complexes and use low-degree polynomial spectral filters to perform local convolutions, with experiments imputing missing citations in coauthorship complexes.

ABSTRACT

Paper-author bipartite graph created from Semantic Scholar's Open Research Corpus, version 2018-05-03. Vertices are papers (39,219,709 of them) in one part and authors (12,862,455 of them) in the other. A paper is connected to all its co-authors, and an author is connected to all the papers they wrote, leading to 139,268,795 edges. A citation count (the number of times the paper was cited) is available for each paper (from 0 to 37,230 citations per paper).

Motivation & Objective

• Motivate learning on data with higher-order relationships beyond pairwise edges.
• Propose a simplicial neural network framework leveraging coboundary/Laplacian operators to define local convolutions on simplicial complexes.
• Demonstrate the approach on missing data imputation in coauthorship complexes built from Semantic Scholar data.
• Explore transferability of learned filters across different coauthorship complexes.

Proposed method

• Model data as p-cochains on a finite simplicial complex K and define coboundary maps delta^p.
• Construct degree-p simplicial Laplacians L_i = L_i^up + L_i^down using delta and its adjoint.
• Define simplicial convolution as F_p^{-1}(F_p(c) F_p(c')) with F_p based on eigenvectors of L_p.
• Restrict convolutional filters to low-degree polynomials in the Laplacian eigenvalues to ensure locality and efficient, sparse computations (sum W_i L_p^i).
• Implement networks with multiple layers (e.g., 3 layers, 30 filters, N=5) and train with Adam to impute missing cochain values.
• Experiment on coauthorship complexes CC1 and CC2 derived from Semantic Scholar Open Research Corpus, imputing missing k-cochains (k=0,1,2) under varying missing rates.

Experimental results

Research questions

• RQ1 Can simplicial neural networks effectively learn from higher-order relationships encoded in simplicial complexes?
• RQ2 Do low-degree polynomial spectral filters provide effective, localized convolutions on simplicial complexes?
• RQ3 How well do SNNs impute missing data in coauthorship complexes, and how do they compare to simple baselines?
• RQ4 Do learned filters transfer across different coauthorship complexes?
• RQ5 What is the potential of SNNs for capturing topological structure in data beyond graphs?

Key findings

• SNNs outperform baselines that impute missing values by simple means or neighbor averages.
• With 30% missing citations on CC1, the reported baselines show substantially higher error than the SNNs (as summarized in Table 1).
• SNNs trained on CC2 can nearly match the performance of SNNs trained on CC1 when imputing on CC1, indicating transferability of learned filters across similar coauthorship structures.
• The approach demonstrates that spectral-based, localized convolutions on simplicial complexes can be learned and applied to higher-order data.
• The study provides qualitative and quantitative evidence that zero-error-like imputations concentrate near zero error for the SNN predictions.