Significant efforts have been focused on enhancing the utilization of multiple node features and topological structures in multi-view graph learning through explicit model-driven and implicit deep learning-based methodologies. The former excels in embedding prior knowledge, thereby offering theoretical interpretability but is limited in application flexibility due to manual parameter selection. In contrast, the latter leverages automatic differentiation, providing greater flexibility but lacking theoretical interpretability due to their opaque nature. Motivated by these observations, we propose an interpretable deep unfolding network for mutual-benefit multi-view graph learning, aiming to combine the strengths of both approaches. Specifically, we employ the Alternating Direction Method of Multipliers (ADMM) to solve a multi-view graph learning model with sparse and low-rank constraints. This solution is then integrated into deep unfolding networks to enhance interpretability. Furthermore, we convert optimization conditions into implicit losses and utilize automatic differentiation to update parameters, reducing the need for manual tuning and increasing flexibility. This integration optimizes multi-view learning for a graph representation that balances interpretability and flexibility. Empirical evaluations on six diverse datasets demonstrate the effectiveness and superiority of the proposed method over state-of-the-art approaches.

Multi-view representation learning, which utilizes multiple channels to improve perceptual accuracy, is recognized for its effectiveness in the analysis of multi-view data. However, deploying these methods in real-world scenarios presents two primary challenges. 1) Lack of Variegation: Multi-view representation techniques commonly observe along a singular axis, i.e., the attribute axis; 2) Insufficient Relationship: Most multi-view models lack mechanisms for exploring potential relationships between attribute axis and channel axis. To mitigate these obstacles, we design a Dual Impulse Network framework for multi-view representation learning (DIN) to train a feature representation. In this framework, a strategy observed along the channel axis and attribute axis simultaneously is introduced, and two different representations are generated by two analogous impulse networks, which are capable of extracting information corresponding to different axes. Furthermore, we incorporate an integration network that analyzes the potential relationship between attribute axis and channel axis to generate two attention matrices. The final two feature representations derived from these attention matrices are aggregated to amplify the expression of internal information. Comprehensive experimental results support the efficacy and superiority of the proposed framework, demonstrating improvements in classification performance compared to state-of-the-art methods.

Graph Neural Networks (GNNs) have become a powerful tool for learning representations from graph-structured data, leveraging the relationships between nodes and their features. Despite their success, they often lack interpretability due to the black-box nature of neural networks, and further development may be limited. Moreover, previous GNN-based multi-view methods typically rely on simple feature fusion techniques such as weighted averaging or concatenation, which fail to capture the complex dependencies between views. In this paper, we propose a novel framework, namely Interpretable Multi-View Feature Representation via physical partial differential equation (IMvFR), to address these limitations in the context of multi-view semi-supervised learning. By integrating GNNs with partial differential equations (PDEs), we model the evolution of multi-view feature representations as a dynamic process. This provides a natural and interpretable framework for understanding how information flows between different views, overcoming the black-box nature of traditional GNNs. Additionally, we formulate multi-view feature representations as an initial-value problem within the framework of PDEs, providing a clear and interpretable mechanism for label propagation and feature fusion, thus facilitating the acquisition of global and local information between views. Comprehensive experimental results on eight datasets demonstrate that the proposed method achieves superior performance compared with state-of-the-art methods.

Deep multi-view graph clustering seeks to integrate diverse graph feature sets and uncover consistent information across multiple views. While extensive prior research has utilized various neural network architectures to address multi-view graph clustering challenges, these approaches exhibit notable limitations: 1) The ''black-box'' nature of deep learning models, which obscures their internal mechanisms and impedes interpretability; 2) Insufficient efforts aim to capture low-dimensional representations through graphs that reflect intuitive clustering structures and reduce computational cost. To address these limitations, this paper introduces an interpretable multi-view graph clustering framework constructed with optimization-inspired modules. The proposed approach formulates low-dimensional clustering representation learning from graph matrices as an optimization problem, deriving an iterative solution rooted in this formulation. By seamlessly bridging this optimization process to a deep network architecture, the model learns a low-dimensional clustering representation for graph-structured data across multiple views while adhering to the iterative optimization principles and reducing computational costs. This transparent network design enhances the interpretability of multi-view clustering, enabling intuitive and human-understandable learning of clustering structures. Extensive experimental evaluations validate the proposed framework's superiority over state-of-the-art methods in multi-view clustering tasks while ensuring interpretability and reducing computational costs.

The emerging Graph Convolutional Networks (GCNs) have attracted widespread attention in graph learning, due to their good ability of aggregating the information between higher-order neighbors. However, real-world graph data contains high noise and redundancy, making it hard for GCNs to accurately depict the complete relationships between nodes, which seriously degrades the quality of graph representations. Moreover, existing studies commonly ignore the distribution difference between feature and semantic spaces in graphs, causing inferior model generalization. To address these challenges, we propose DIB-RGCN, a novel robust GCN framework, to explore the optimal graph representation with the guidance of the well-designed dual information bottleneck principle. First, we analyze the reasons for distribution differences and theoretically prove that minimal sufficient representations in specific spaces cannot promise optimal performance for downstream tasks. Next, we design new dual channels to regularize feature and semantic spaces, eliminating the sharing of task-irrelevant information between spaces. Different from existing denoising algorithms that adopt a random dropping manner, we innovatively replace potential noisy features and edges with local neighboring representations. This design lowers edge-specific coefficient assignment, alleviating the interference of original representations while retaining graph structures. Further, we maximize the sharing of task-relevant information between feature and semantic spaces to alleviate the difference between them. Using real-world datasets, extensive experiments demonstrate the robustness of the proposed DIB-RGCN, which outperforms state-of-the-art methods on classification tasks.