Structure-Feature Aligned Graph Learning via Alternating Constrained Optimization

D2GSL: Self-Supervised Dual-Layer Structure-Driven Graph Structure Learning

: Graph structure learning depends heavily on the integrity and reliability of graph data. However, real-world graphs often contain noise, missing information, and bias, thereby limiting the expressive capacity of existing models. Single-layer structure learning methods fail to simultaneously capture local interactions and the global structure. Furthermore, they rely excessively on high-quality labeled data, leading to label scarcity issues and high annotation costs. To address these challenges, we propose a self-supervised dual-layer structure-driven graph structure learning method, termed D2GSL. Specifically, D2GSL constructs a semantic similarity channel and a spectral feature channel to model node relationships from both local semantic and global spectral views. It introduces a hyperadjacency matrix that explicitly models inter-layer node correspondences and enables joint structural reconstruction across channels. The framework further applies structural reconstruction constraints and adopts a contrastive learning mechanism to enhance structural representations in a self-supervised setting. Comprehensive experimental results demonstrate that D2GSL consistently outperforms mainstream baseline models on public benchmark datasets and exhibits remarkable efficacy under label-scarcity conditions.

Unsupervised Graph Representation Learning with Complementary View Alignment

Unsupervised graph representation learning aims to derive meaningful node embeddings by capturing both structural and attribute information without relying on labeled data. Existing methods, such as GAEs, have demonstrated effectiveness but typically rely on message-passing mechanisms that assume homophily, leading to performance degradation on heterophilous graphs, where connected nodes exhibit dissimilar features. This homophily bias results in the loss of critical high-frequency components that are essential for identifying heterophilous patterns. To address these challenges, we propose \textsc{AlignGAE}, a novel extension of \textit{MaskGAE} that preserves the full frequency spectrum through complementary view alignment. Our framework introduces a dual-encoder architecture that separately processes structural and attribute information, incorporates node positional encoding to approximate Neighborhood Identity Distribution (NID), and employs dual reconstruction tasks for both edges and node attributes. We further propose theoretically grounded NID alignment strategies that ensure semantic consistency across views while preserving their distinct characteristics. Through comprehensive spectral analysis, we demonstrate that \textsc{AlignGAE} achieves optimal representation properties when the alignment loss converges. Extensive experiments across 12 benchmark datasets validate our approach, showing that \textsc{AlignGAE} outperforms state-of-the-art methods by up to 18.7\% on heterophilous graphs in node classification, while maintaining competitive performance on homophilous graphs. Our results establish a new paradigm for frequency-aware graph representation learning.

Enhancing Distance-Based Graph Autoencoders with Structural Penalties for Dynamic Graph Embedding

Graph autoencoders (GAEs) are widely used for learning representations of dynamic graphs. However, their optimisation objectives typically do not take structural heterogeneity across nodes into account. We propose three distance-based GAE variants that incorporate structural penalties into the reconstruction loss. All variants share a two-layer Graph Convolutional Network encoder and a Euclidean-distance decoder trained with distance-based reconstruction objectives. We extend sparsity-corrected loss with two node-level regularization terms: (i) a hub penalty based on degree centrality, and (ii) a penalty based on Natural Community Local Intrinsic Dimensionality (NC-LID). The paper is motivated by prior evidence linking high NC-LID to reduced embedding quality. The proposed methods are designed to emphasize reconstruction errors for structurally ambiguous nodes. Experiments on multiple dynamic graph data sets show that incorporating NC-LID-based regularization consistently improves reconstruction performance over the baseline without structural regularization and the method using hub-aware regularization. These findings highlight NC-LID as a useful structural signal for enhancing distance-based graph autoencoders in dynamic settings.

Global graph features unveiled by unsupervised deep learning

Graph Autoencoder Uncovering Descriptive Information (GAUDI), an unsupervised graph deep learning framework designed to capture both local details and global structure, is introduced, providing new insights into emergent phenomena across diverse scientific domains.

DiffGCC: diffusion-enhanced global–local graph contrastive clustering

DiffGCC is a generative graph contrastive clustering framework that couples global–local feature encoding with a latent-space diffusion denoising mechanism and substantially outperforms existing methods across ACC, NMI, ARI, and F1, with particularly strong gains on denser, noisier product graphs.

AdaGeM: Adaptive Geometric Learning on Manifolds for Hyper-Relational Knowledge Graphs