Deep Manifold Graph Auto-Encoder for Attributed Graph Embedding

TL;DR

The paper tackles the crowding problem in attributed graph embeddings by moving beyond reconstruction-only objectives and enforcing topological alignment between input and latent spaces. It proposes DMVGAE/DMGAE, a variational graph auto-encoder augmented with a manifold-learning loss that preserves inter-node geodesic similarity across $G_X$, $\bar{G}_X$, and $G_{Z_i}$ using a $t$-distribution kernel with degrees of freedom $\nu$ and node-scale parameters $\sigma_i$. The approach yields state-of-the-art results on node clustering (ACC, NMI, F1) and link prediction (AUC, AP) on four benchmarks ($Cora$, $CiteSeer$, $PubMed$, $Wiki$). This work provides a principled way to integrate manifold geometry into probabilistic graph embeddings, improving stability and separability of representations for downstream tasks.

Abstract

Representing graph data in a low-dimensional space for subsequent tasks is the purpose of attributed graph embedding. Most existing neural network approaches learn latent representations by minimizing reconstruction errors. Rare work considers the data distribution and the topological structure of latent codes simultaneously, which often results in inferior embeddings in real-world graph data. This paper proposes a novel Deep Manifold (Variational) Graph Auto-Encoder (DMVGAE/DMGAE) method for attributed graph data to improve the stability and quality of learned representations to tackle the crowding problem. The node-to-node geodesic similarity is preserved between the original and latent space under a pre-defined distribution. The proposed method surpasses state-of-the-art baseline algorithms by a significant margin on different downstream tasks across popular datasets, which validates our solutions. We promise to release the code after acceptance.

Figures (1)

• Figure 1: Comparison of visualization results on Cora using UMAP. Colors represent label categories.