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Adversarially Regularized Graph Autoencoder for Graph Embedding
Shirui Pan, Ruiqi Hu, Guodong Long, Jing Jiang, Lina Yao, Chengqi Zhang
TL;DR
Graph embedding methods often overlook the distribution of latent codes, limiting representation quality on real-world graph data. This paper introduces ARGA and ARVGA, which encode topology and node content, reconstruct graph structure, and adversarially match latent codes to a prior. Experiments report that both methods outperform baselines in link prediction, node clustering, and graph visualization.
Problem
Existing graph embedding methods typically preserve topology or minimize reconstruction error while largely ignoring latent-code distributions.
Method
ARGA and ARVGA encode graph structure and node content, reconstruct graph structure, and adversarially regularize latent codes toward a prior distribution.
Results
ARGA and ARVGA outperform baselines in link prediction, node clustering, and graph visualization tasks.
Takeaways & Limitations
Adversarial regularization is presented as a way to learn robust graph representations while preserving graph structure and node content.
Takeaways & Limitations
The framework uses a simple Gaussian distribution as the latent prior.
Abstract
from arXiv · showhide
Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the latent codes from the graphs, which often results in inferior embedding in real-world graph data. In this paper, we propose a novel adversarial graph embedding framework for graph data. The framework encodes the topological structure and node content in a graph to a compact representation, on which a decoder is trained to reconstruct the graph structure. Furthermore, the latent representation is enforced to match a prior distribution via an adversarial training scheme. To learn a robust embedding, two variants of adversarial approaches, adversarially regularized graph autoencoder (ARGA) and adversarially regularized variational graph autoencoder (ARVGA), are developed. Experimental studies on real-world graphs validate our design and demonstrate that our algorithms outperform baselines by a wide margin in link prediction, graph clustering, and graph visualization tasks.
1 Introduction
Graph embedding simplifies graph analytics by learning compact representations, but many methods ignore latent-code distributions. The paper addresses this gap with adversarially regularized graph embedding variants evaluated across three unsupervised tasks.
- Graph embedding maps graph data into a low-dimensional feature space intended to preserve topology, node content, and side information for downstream analytics.
- Existing approaches mainly preserve graph structure or minimize reconstruction error while largely ignoring the distribution of latent codes.The paper links this omission to degenerate identity mappings and poor representations on sparse, noisy real-world graphs.
- The proposed framework jointly reconstructs graph structure and adversarially forces latent codes toward a prior distribution using graph structure and node content.Two variants are developed: ARGA and ARVGA.
- Experiments on benchmark graph datasets show that the proposed embeddings outperform other methods on three unsupervised tasks.
2 Related Work
Prior graph embedding work includes probabilistic, matrix factorization, and deep learning approaches, with methods differing in whether they use topology, content, or both. The paper positions adversarial regularization as a response to neglected latent distributions.
- Graph embedding methods include probabilistic models, matrix factorization algorithms, and deep learning approaches.Examples include DeepWalk, node2vec, LINE, GraRep, HOPE, M-NMF, SDNE, and DNGR.
- Topological methods learn from graph structure, whereas content-enhanced methods jointly exploit topology and node features.TADW and TriDNR are examples of content-enhanced approaches.
- Existing approaches largely ignore the latent distribution of embeddings, motivating the paper’s use of adversarial training.
- Unlike general-data adversarial autoencoders and graph methods using topology alone, the proposed approach handles both topological and content information.
3 Problem Definition and Framework
The framework maps graph structure and node content to low-dimensional node embeddings, reconstructs graph structure, and regularizes latent codes adversarially against a prior distribution. ARGA uses a graph autoencoder, while ARVGA replaces its upper tier with a variational graph autoencoder.
- A graph is represented by nodes, edges, and node content, with adjacency matrix A encoding links and X containing node features.
- ARGA uses a graph convolutional autoencoder, while ARVGA uses a variational graph autoencoder in the upper tier.
- The embedding function maps (A, X) to an embedding matrix Z whose rows are d-dimensional node vectors preserving topology and content.
- The graph convolutional autoencoder takes A and X as inputs, learns Z, and reconstructs graph structure A from that representation.
- Adversarial regularization trains a discriminator to distinguish encoder-generated latent codes from samples drawn from a prior distribution.
4 Proposed Algorithm
The proposed graph autoencoder uses graph structure and node content in a graph convolutional encoder, reconstructs graph structure, and regularizes latent codes adversarially toward a prior distribution. Two variants implement this framework: graph and variational graph encoders, yielding ARGA and ARVGA.
- Graph Convolutional Autoencoder: The graph convolutional autoencoder addresses how to integrate graph structure A and node content X while selecting graph information for decoder reconstruction.The paper reconstructs graph structure A rather than content X or both.
- Graph Convolutional Encoder Model: A graph convolutional network serves as the encoder, extending convolution to graph data and learning layer-wise transformations from structure and content.The encoder is built from a two-layer GCN.
- Adversarial Regularization: The framework develops graph and variational graph encoders, corresponding to adversarially regularized graph autoencoder and variational graph autoencoder variants.The variational encoder is optimized with a variational lower bound involving KL divergence.
- Graph Convolutional Encoder Model: The encoder maps input node features X through graph convolutions into a latent representation Z that captures graph structure and node content.The convolution takes Z^(l) as input and produces Z^(l+1); initially, Z^0 = X.
- Decoder Model: The decoder reconstructs graph structure by predicting whether links exist between node pairs from the graph embedding.This design also functions when node content is unavailable, including X = I.
- Adversarial Regularization: Adversarial training regularizes latent codes by making a discriminator distinguish prior samples from encoder outputs, then updating the encoder to confuse it.The framework uses a simple Gaussian prior and alternates discriminator and graph-autoencoder updates.
5 Experiments
Experiments evaluate ARGA and ARVGA on link prediction, node clustering, and graph visualization using real-world citation graphs. Results examine embedding dimensions and compare the proposed methods with established baselines.
- Experimental setup: The experiments use citation graphs whose nodes are scientific publications, edges are citation relationships, and features are unique document words.
- Link prediction: Link prediction compares ARGA and ARVGA with DeepWalk, Spectral Clustering, GAE, and VGAE using AUC and average precision.Each experiment is repeated 10 times, reporting mean scores with standard errors.
- Link prediction: Embedding performance steadily rises from 8 to 16 dimensions, fluctuates at 32, and remains good for both AP and AUC.
- Link prediction: Performance rises markedly when the embedding dimension increases to 64, 128, and 1024 neurons.
- Node clustering: Node clustering evaluates embeddings with K-means and reports accuracy, NMI, precision, F1, and ARI across Cora and Citeseer.
- Graph visualization: Cora visualization applies t-SNE to learned embeddings, comparing ARGA, VGAE, GAE, DeepWalk, and Spectral Clustering with colors representing groups.The reported visualization yields a more meaningful graph-data layout with adversarial training.
- Node clustering: On Citeseer, ARGA improves accuracy by 6.1% over K-means to 154.7% over GraphEncoder, F1 by 31.9% over TADW to 102.2% over DeepWalk, and NMI by 14.8% over K-means to 124.4% over VGAE.
6 Conclusion
The paper introduces adversarial graph embedding to regularize latent codes toward a prior distribution and reports improved performance across three graph-analysis tasks.
- The framework jointly learns an adversarial module and graph convolutional autoencoder to produce robust graph representations.
- Adversarial regularization enforces latent codes to match a prior distribution rather than leaving their data distribution unconstrained.
- The proposed ARGA and ARVGA algorithms outperform baselines in link prediction, node clustering, and graph visualization.