As real-world data become increasingly heterogeneous, multi-view semi-supervised learning has garnered widespread attention. Although existing studies have made efforts towards this and achieved decent performance, they are restricted to shallow models and how to mine deeper information from multiple views remains to be investigated. As a recently emerged neural network, Graph Convolutional Network (GCN) exploits graph structure to propagate label signals and has achieved encouraging performance, and it has been widely employed in various fields. Nonetheless, research on solving multi-view learning problems via GCN is limited and lacks interpretability. To address this gap, in this paper we propose a framework termed Interpretable Multi-view Graph Convolutional Network (IMvGCN ^{1 1}Code is available at https://github.com/ZhihaoWu99/IMvGCN. ). We first combine the reconstruction error and Laplacian embedding to formulate a multi-view learning problem that explores the original space from feature and topology perspectives. In light of a series of derivations, we establish a potential connection between GCN and multi-view learning, which holds significance for both domains. Furthermore, we propose an orthogonal normalization method to guarantee the mathematical connection, which solves the intractable problem of orthogonal constraints in deep learning. In addition, the proposed framework is applied to the multi-view semi-supervised learning task. Comprehensive experiments demonstrate the superiority of our proposed method over other state-of-the-art methods.

Sparsity-constrained optimization problems are common in machine learning, such as sparse coding, low-rank minimization and compressive sensing. However, most of previous studies focused on constructing various hand-crafted sparse regularizers, while little work was devoted to learning adaptive sparse regularizers from given input data for specific tasks. In this paper, we propose a deep sparse regularizer learning model that learns data-driven sparse regularizers adaptively. Via the proximal gradient algorithm, we find that the sparse regularizer learning is equivalent to learning a parameterized activation function. This encourages us to learn sparse regularizers in the deep learning framework. Therefore, we build a neural network composed of multiple blocks, each being differentiable and reusable. All blocks contain learnable piecewise linear activation functions which correspond to the sparse regularizer to be learned. Furthermore, the proposed model is trained with back propagation, and all parameters in this model are learned end-to-end. We apply our framework to multi-view clustering and semi-supervised classification tasks to learn a latent compact representation. Experimental results demonstrate the superiority of the proposed framework over state-of-the-art multi-view learning models.

Multi-view subspace clustering aims to utilize the comprehensive information of multi-source features to aggregate data into multiple subspaces. Recently, low-rank tensor learning has been applied to multi-view subspace clustering, which explores high-order correlations of multi-view data and has achieved remarkable results. However, these existing methods have certain limitations: 1) The learning processes of low-rank tensor and label indicator matrix are independent. 2) Variable contributions of different views to the consistent clustering results are not discriminated. To handle these issues, we propose a unified framework that integrates low-rank tensor learning and spectral embedding (ULTLSE) for multi-view subspace clustering. Specifically, the proposed model adopts the tensor singular value decomposition (t-SVD) based tensor nuclear norm to encode the low-rank property of the self-representation tensor, and a label indicator matrix via spectral embedding is simultaneously exploited. To distinguish the importance of various views, we learn a quantifiable weighting coefficient for each view. An effective recursion optimization algorithm is also developed to address the proposed model. Finally, we conduct comprehensive experiments on eight real-world datasets with three categories. The experimental results indicate that the proposed ULTLSE is advanced over existing state-of-the-art clustering methods.

Deep multi-view representation learning focuses on training a unified low-dimensional representation for data with multiple sources or modalities. With the rapidly growing attention of graph neural networks, more and more researchers have introduced various graph models into multi-view learning. Although considerable achievements have been made, most existing methods usually propagate information in a single view and fuse multiple information only from the perspective of attributes or relationships. To solve the aforementioned problems, we propose an efficient model termed Dual Fusion-Propagation Graph Neural Network (DFP-GNN) and apply it to deep multi-view clustering tasks. The proposed method is designed with three submodules and has the following merits: a) The proposed view-specific and cross-view propagation modules can capture the consistency and complementarity information among multiple views; b) The designed fusion module performs multi-view information fusion with the attributes of nodes and the relationships among them simultaneously. Experiments on popular databases show that DFP-GNN achieves significant results compared with several state-of-the-art algorithms.

Multi-view learning is a promising research field that aims to enhance learning performance by integrating information from diverse data perspectives. Due to the increasing interest in graph neural networks, researchers have gradually incorporated various graph models into multi-view learning. Despite significant progress, current methods face challenges in extracting information from multiple graphs while simultaneously accommodating specific downstream tasks. Additionally, the lack of a subsequent refinement process for the learned graph leads to the incorporation of noise. To address the aforementioned issues, we propose a method named generative essential graph convolutional network for multi-view semi-supervised classification. Our approach integrates the extraction of multi-graph consistency and complementarity, graph refinement, and classification tasks within a comprehensive optimization framework. This is accomplished by extracting a consistent graph from the shared representation, taking into account the complementarity of the original topologies. The learned graph is then optimized through downstream-specific tasks. Finally, we employ a graph convolutional network with a learnable threshold shrinkage function to acquire the graph embedding. Experimental results on benchmark datasets demonstrate the effectiveness of our approach.