Source-linked AI summary
Factorizable Graph Convolutional Networks
Yiding Yang, Zunlei Feng, Mingli Song, Xinchao Wang
TL;DR
Graphs often collapse heterogeneous relations between entities into single edges, limiting explicit analysis of their latent structure. FactorGCN decomposes such graphs into interpretable factor graphs, aggregates features separately in each relation space, and reports strong disentanglement and downstream-task performance across five datasets. The framework also introduces quantitative graph-disentanglement metrics and supports multi-relation feature propagation.
Problem
Prior graph methods largely focus on local neighbor partitioning and do not disentangle latent multi-relations in irregular structural data.
Method
FactorGCN decomposes an input graph into interpretable factor graphs, applies topology-aware GCNs separately to them, and merges the resulting features.
Results
FactorGCN achieves state-of-the-art performance for disentanglement and downstream tasks across five datasets, including a large-margin result on ZINC.
Takeaways & Limitations
FactorGCN provides block-wise explainable features and supports multi-relation information propagation for graph-related tasks.
Takeaways & Limitations
Like all learning-based methods, FactorGCN is not free of error.
Abstract
from arXiv · showhide
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.
1 Introduction
FactorGCN addresses entangled latent relations in graph data by decomposing a simple graph into interpretable factor graphs and aggregating features within each relation space. Experiments report strong disentanglement and downstream-task performance across five datasets.
- Motivation: Prior graph disentangling methods focus on local neighbor partitioning and do not capture latent multi-relations or global graph context.CNN-based disentangling methods do not directly transfer to irregular graph data because grid-like and structural data differ.
- Method: FactorGCN decomposes an input graph into factor graphs representing disentangled relation spaces, applies separate GCNs, and concatenates their features into block-wise interpretable outputs.The resulting topology is preserved, allowing layers to be stacked for hierarchical disentanglement.
- Graph-level Disentangling: Graph-level disentangling accounts for global topological semantics and produces relation-specific interconnections and interpretable node features.This contrasts with approaches that disentangle only within local neighborhoods.
- Multi-relation Disentangling: FactorGCN supports multi-relation disentangling, allowing a center node to aggregate information from a neighbor under multiple relation types.For example, two users may be represented as both friends and residents of the same city.
- Evaluation: A graph edit-distance metric evaluates similarity between factor graphs and ground truth without requiring graph generation.The metric is designed for irregular domains where existing graph generative models have limited applicability.
- Results: Five-dataset experiments report state-of-the-art performance for both disentanglement and downstream tasks, including a large-margin result on ZINC.Without bond information, FactorGCN performs on par with a state-of-the-art method that explicitly uses edge-type information.
2 Related Work
Prior disentangled-representation work largely develops methods for CNNs and auto-encoders, while GCN research targets information extraction from non-grid structural data.
- Disentangled representation learning: Recent disentangled-representation learning commonly builds on auto-encoder architectures rather than handcrafted disentangled variables.The related work cites auto-encoder-based approaches as a dominant recent direction.
- Graph convolutional network: GCNs are designed for non-grid data and have achieved promising results on citation, social, and relational graphs.The cited applications span several structural-data settings.
3 Method
FactorGCN disentangles an input graph into diverse factor graphs, uses each to aggregate node information independently, and merges the resulting features. Its training combines the original task loss with a discriminator loss that encourages structurally distinct factor graphs.
- Disentangling Step: FactorGCN’s disentangle layer factorizes the input graph into several factor graphs representing separate structural spaces.It computes edge coefficients from transformed node features and uses each factor graph for subsequent processing.
- Disentangling Step: An additional discriminator head assigns unique labels to factor graphs and treats their distinction as a graph classification problem.The discriminator uses transformed features and factor-graph coefficients, while shared node features ensure discrimination depends on structural differences.
- Aggregation Step: FactorGCN aggregates neighborhood information independently in each factor graph, using the corresponding edge coefficients and normalization terms.Zero coefficients exclude corresponding neighbors from a factor-specific aggregation.
- Merging Step: Features produced by different factor graphs are concatenated to form each node’s output feature.Multiple disentangle layers can use different numbers of factor graphs to produce hierarchical disentanglement.
- Training Objective: The discriminator loss is combined with the original task loss as L = Lt + λ ∗Ld.Lt depends on the downstream task, while λ balances task learning against factor-graph discrimination.
4 Experiments
Experiments evaluate FactorGCN on synthetic, molecular, graph-classification, and node-classification datasets using qualitative, quantitative, and sensitivity analyses. Results indicate disentangled features and factor graphs alongside strong downstream performance.
- Experimental setups: Experiments use six datasets spanning synthetic graphs, molecular graphs, node classification, social networks, and bioinformatics graphs.The evaluation includes synthetic data with predefined factor graphs, ZINC, Pattern, COLLAB, IMDB-B, and MUTAG.
- Evaluation protocol: The evaluation combines qualitative visualization and feature-correlation analysis with downstream-task and disentanglement metrics.Downstream metrics include Micro-F1 and MAE, while disentanglement is assessed with GEDE and C-Score.
- Qualitative evaluation: FactorGCN produces more block-wise, independent latent features while retaining better downstream performance than the compared models on the synthetic dataset.GCN and MLP achieve high downstream performance with entangled features, whereas GAT has more independent features but degraded task performance.
- Quantitative evaluation: FactorGCN achieves better synthetic-dataset performance in both disentanglement and the original task, while overly many factor graphs reduce performance gains.The number of factors increases the performance gain until the disentanglement task becomes too challenging.
- Quantitative evaluation: On ZINC, FactorGCN achieves the best disentanglement and downstream-task performance without edge-type information, approaching GatedGCNE, which uses bond information.The broader evaluations also report consistently best performance across additional graph and node classification datasets.
- Ablation and sensitivity analysis: Removing the discriminator degrades both disentanglement and downstream performance, while using slightly more factors than the ground truth improves performance in practice.The sensitivity analysis varies λ and the number of factor graphs under the stated experimental settings.
5 Conclusion
FactorGCN performs graph convolution through graph-level disentangling, decomposing input graphs into interpretable factor graphs and producing topology-aware node features. It supports multi-relation disentangling and outperforms other methods on disentanglement and downstream tasks.
- FactorGCN decomposes an input graph into interpretable factor graphs and applies topology-aware convolutions to produce final node features.
- The resulting node features are block-wise explainable and beneficial to downstream tasks.
- FactorGCN enables multi-relation disentangling by allowing information propagation between two nodes in disjoint spaces.
- FactorGCN introduces two metrics for quantitative graph disentanglement evaluation.
- FactorGCN outperforms other methods on both disentanglement and downstream tasks, supporting its use as a general GCN framework.
Broader Impact
FactorGCN is presented as applicable to technical and social scenarios, including graph learning, disentangling, recommendation, and social analysis. Its predictions remain vulnerable to errors in the produced factor graphs, which can degrade inference and introduce undesirable bias.
- FactorGCN can serve as a general GCN framework for node classification in social networks and graph classification in molecular graphs.
- For disentangling tasks, FactorGCN generates factor graphs that reveal latent relations and can support recommendation decisions.
- Given sufficient data, FactorGCN can analyze social issues such as reasons for rapid epidemic spread in some areas.
- Incorrect disentangled factor graphs can downgrade subsequent inference and prediction results, possibly yielding undesirable bias.