A semi-supervised label-driven auto-weighted strategy for multi-view data classification

Generalized latent multi-view clustering with tensorized bipartite graph

Tensor-based multi-view spectral clustering algorithms use tensors to model the structure of multi-dimensional data to take advantage of the complementary information and high-order correlations embedded in the graph, thus achieving impressive clustering performance. However, these algorithms use linear models to obtain consensus, which prevents the learned consensus from adequately representing the nonlinear structure of complex data. In order to address this issue, we propose a method called Generalized Latent Multi-View Clustering with Tensorized Bipartite Graph (GLMC-TBG). Specifically, in this paper we introduce neural networks to learn highly nonlinear mappings that encode nonlinear structures in graphs into latent representations. In addition, multiple views share the same latent consensus through nonlinear interactions. In this way, a more comprehensive common representation from multiple views can be achieved. An Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework is designed to optimize the model. Experiments on seven real-world data sets verify that the proposed algorithm is superior to state-of-the-art algorithms.

Comprehensive Multiview Representation Learning via Deep Autoencoder-Like Nonnegative Matrix Factorization

Learning a comprehensive representation from multiview data is crucial in many real-world applications. Multiview representation learning (MRL) based on nonnegative matrix factorization (NMF) has been widely adopted by projecting high-dimensional space into a lower order dimensional space with great interpretability. However, most prior NMF-based MRL techniques are shallow models that ignore hierarchical information. Although deep matrix factorization (DMF)-based methods have been proposed recently, most of them only focus on the consistency of multiple views and have cumbersome clustering steps. To address the above issues, in this article, we propose a novel model termed deep autoencoder-like NMF for MRL (DANMF-MRL), which obtains the representation matrix through the deep encoding stage and decodes it back to the original data. In this way, through a DANMF-based framework, we can simultaneously consider the multiview consistency and complementarity, allowing for a more comprehensive representation. We further propose a one-step DANMF-MRL, which learns the latent representation and final clustering labels matrix in a unified framework. In this approach, the two steps can negotiate with each other to fully exploit the latent clustering structure, avoid previous tedious clustering steps, and achieve optimal clustering performance. Furthermore, two efficient iterative optimization algorithms are developed to solve the proposed models both with theoretical convergence analysis. Extensive experiments on five benchmark datasets demonstrate the superiority of our approaches against other state-of-the-art MRL methods.

Revisiting multi-view learning: A perspective of implicitly heterogeneous Graph Convolutional Network

Graph Convolutional Network (GCN) has become a hotspot in graph-based machine learning due to its powerful graph processing capability. Most of the existing GCN-based approaches are designed for single-view data. In numerous practical scenarios, data is expressed through multiple views, rather than a single view. The ability of GCN to model homogeneous graphs is indisputable, while it is insufficient in facing the heterophily property of multi-view data. In this paper, we revisit multi-view learning to propose an implicit heterogeneous graph convolutional network that efficiently captures the heterogeneity of multi-view data while exploiting the powerful feature aggregation capability of GCN. We automatically assign optimal importance to each view when constructing the meta-path graph. High-order cross-view meta-paths are explored based on the obtained graph, and a series of graph matrices are generated. Combining graph matrices with learnable global feature representation to obtain heterogeneous graph embeddings at various levels. Finally, in order to effectively utilize both local and global information, we introduce a graph-level attention mechanism at the meta-path level that allocates private information to each node individually. Extensive experimental results convincingly support the superior performance of the proposed method compared to other state-of-the-art approaches.

Imbalanced low-rank tensor completion via latent matrix factorization

Tensor completion has been widely used in computer vision and machine learning. Most existing tensor completion methods empirically assume the intrinsic tensor is simultaneous low-rank in all over modes. However, tensor data recorded from real-world applications may conflict with these assumptions, e.g., face images taken from different subjects often lie in a union of low-rank subspaces, which may result in a quite high rank or even full rank structure in its sample mode. To this aim, in this paper, we propose an imbalanced low-rank tensor completion method, which can flexibly estimate the low-rank incomplete tensor via decomposing it into a mixture of multiple latent tensor ring (TR) rank components. Specifically, each latent component is approximated using low-rank matrix factorization based on TR unfolding matrix. In addition, an effective proximal alternating minimization algorithm is developed and theoretically proved to maintain the global convergence property, that is, the whole sequence of iterates is convergent and converges to a critical point. Extensive experiments on both synthetic and real-world tensor data demonstrate that the proposed method achieves more favorable completion results with less computational cost when compared to the state-of-the-art tensor completion methods.