[Paper Review] Factorizable Graph Convolutional Networks

Yiding Yang, Zunlei Feng+2 more|arXiv (Cornell University)|Oct 12, 2020

Advanced Graph Neural Networks20 references70 citations

TL;DR

FactorGCN disentangles a simple input graph into multiple factor graphs representing latent relations, performs relation-specific aggregations, and merges the results to produce interpretable, improved node features.

ABSTRACT

Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social network graph, users in different latent relationships like friends and colleagues, are usually connected via a bare edge that conceals such intrinsic connections. In this paper, we introduce a novel graph convolutional network (GCN), termed as factorizable graph convolutional network(FactorGCN), that explicitly disentangles such intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs, each of which represents a latent and disentangled relation among nodes. The features of the nodes are then aggregated separately in each factorized latent space to produce disentangled features, which further leads to better performances for downstream tasks. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets, and demonstrate that it yields truly encouraging results in terms of both disentangling and feature aggregation. Code is publicly available at https://github.com/ihollywhy/FactorGCN.PyTorch.

Motivation & Objective

• Motivate disentangling in irregular graph domains where multiple latent relations are collapsed into a single edge.
• Propose a graph convolutional framework that factors the input graph into several latent relation graphs.
• Enable block-wise, interpretable feature learning through factor-specific aggregation and merging.
• Demonstrate that graph-level disentangling improves both interpretability and task performance.

Proposed method

• Decompose the input graph into multiple factor graphs via a disentangle layer that uses edge-wise coefficients generated similarly to graph attention mechanisms.
• Apply a dedicated GCN on each factor graph to obtain latent features.
• Merge the per-factor features by concatenation to form the final node representations.
• Incorporate a discriminator head that encourages factor graphs to be structurally distinguishable, promoting diverse disentangled factors.
• Train with a combination of task loss and discriminator loss, balanced by a parameter lambda.
• Introduce and utilize graph edit-distance based GED_E and a C-Score metric to evaluate disentanglement quality.

Experimental results

Research questions

• RQ1 Can FactorGCN learn disentangled, latent relation graphs from a single input graph without edge-type labels?
• RQ2 Do factor-specific aggregations improve downstream tasks compared to standard GCNs and related disentangling methods?
• RQ3 Can the model quantify disentanglement quality with graph-based metrics like GED_E and C-Score?
• RQ4 Is FactorGCN a general GCN framework that remains competitive on standard graph classification benchmarks even without explicit edge-type information?

Key findings

• FactorGCN achieves state-of-the-art performance on both disentanglement metrics and downstream tasks on synthetic data.
• On ZINC, FactorGCN outperforms several baselines and matches the performance of edge-type aware methods despite not using edge information.
• FactorGCN consistently yields strong accuracy on graph classification datasets, often outperforming DL-based baselines and matching or surpassing state-of-the-art methods.
• Qualitative analyses show that learned factor graphs capture block-wise, disentangled latent features that correlate with improved downstream performance.
• Ablation shows the discriminator is crucial for disentanglement, and having a number of factor graphs near the ground truth improves results.