Multi-view learning aims to integrate multi-source information for a comprehensive data representation, which has gained widespread attention in image processing. Each view contains view-specific noise and joint features associated with other views, and thus exploring the specificity and consistency among views is a typical solution to deal with multi-view data for learning discriminative representations. In this paper, we present a theory-induced model, termed Adversarial Distribution Alignment Network (ADAN), which learns view-invariant features and alleviate the negative impact of view-specific noise. We first demonstrate the necessity of suppressing view-specific noise and capturing view-invariant features inspired by the theory of view generalization, and then derive two collaborative modules: a feature disentangler and an adversarial alignment module. In detail, the feature disentanglement separates view-specific noise and view-invariant features by minimizing the mutual information between them. Following this, a negative entropy is proposed to suppress the negative impact of view-specific noise. Meanwhile, the adversarial module uses the adversarial technique that can fit more complex data conformed to different distributions to adaptively align cross-view features so that features encoded in different views converge. Substantial experiments are constructed on multi-view datasets, demonstrating that ADAN can achieve more promising performance compared to other superior methods. Code is available at https://github.com/huangsuj/ADANet.

With the advancement of high-throughput sequencing technology, large amounts of multi-omics data have been accumulated. Due to the comprehensive representation of different molecular layers, multi-omics data enable a deep understanding of cancer analysis, including subtype classification, biomarker identification and so on. However, existing multi-omics integration methods either rely on complex feature engineering or fail to capture the heterogeneity of multi-source data. To integrate multi-omics data in a complementary and collaborative manner, we propose a Kolmogorov-Arnold Networks-based multi-omics integration analysis framework, termed MOKAN. In detail, MOKAN first employs a sample-weighted random sampler to reduce the difference in the number of samples involved in training. Then, to perform this data analysis, our proposed model, MOKAN, leverages KAN's architecture, utilizing its learnable edge-weight activation functions and flexible network structure. This design makes MOKAN particularly well-suited for handling multi-omics data by efficiently capturing diverse feature spaces across different omics layers. It integrates heterogeneous data types while preserving the unique contributions of each omics for comprehensive and accurate representation. Moreover, MOKAN employs KAN's decomposition property to break down high-dimensional complex data into multiple low-dimensional subspaces, each independently capturing a specific aspect of the data. These subspace representations are then systematically integrated through a one-dimensional function that overlays and combines their contributions, effectively reconstructing the global data structure. Experimental results demonstrate that our proposed model outperforms other existing methods in cancer classification tasks.

Multi‐view learning has emerged as a pivotal research area driven by the growing heterogeneity of real‐world data, and graph neural network-based models, modeling multi-view data as multi-view graphs, have achieved remarkable performance by revealing its deep semantics. However, by assuming cross‐view consistency, most approaches collect not only task-relevant (determinative) semantics but also symbiotic yet task-irrelevant (incidental) factors are collected to obscure model inference. Furthermore, these approaches often lack rigorous theoretical analysis that bridges training data to test data. To address these issues, we propose Target-oriented Graph Neural Network (TGNN), a novel framework that goes beyond traditional consistency by prioritizing task-relevant information, ensuring alignment with the target. Specifically, TGNN employs a class-level dual-objective loss to minimize the classification similarity between determinative and incidental factors, accentuating the former while suppressing the latter during model inference. Meanwhile, to ensure consistency between the learned semantics and predictions in representation learning, we introduce a penalty term that aims to amplify the divergence between these two types of factors. Furthermore, we derive an upper bound on the loss discrepancy between training and test data, providing formal guarantees for generalization to test domains. Extensive experiments conducted on three types of multi-view datasets validate the superiority of TGNN.

Graph Neural Networks (GNNs) have expressed remarkable capability in processing graph-structured data. Recent studies have found that most GNNs rely on the homophily assumption of graphs, leading to unsatisfactory performance on heterophilous graphs. While certain methods have been developed to address heterophilous links, they lack more precise estimation of high-order relationships between nodes. This could result in the aggregation of excessive interference information during message propagation, thus degrading the representation ability of learned features. In this work, we propose a Disparity-induced Structural Refinement (DSR) method that enables adaptive and selective message propagation in GNN, to enhance representation learning in heterophilous graphs. We theoretically analyze the necessity of structural refinement during message passing grounded in the derivation of error bound for node classification. To this end, we design a disparity score that combines both features and structural information at the node level, reflecting the connectivity degree of hopping neighbor nodes. Based on the disparity score, we can adjust the aggregation of neighbor nodes, thereby mitigating the impact of irrelevant information during message passing. Experimental results demonstrate that our method achieves competitive performance, mostly outperforming advanced methods on both homophilous and heterophilous datasets.

With the growing diversity of data sources, multi-view learning methods have attracted considerable attention. Among these, by modeling the multi-view data as multi-view graphs, multi-view Graph Neural Networks (GNNs) have shown encouraging performance on various multi-view learning tasks. The message passing is the critical mechanism empowering GNNs with superior capacity to process complex graph data. However, most multi-view GNNs are designed on the well-established overall framework, overlooking the intrinsic challenges of the message passing on multi-view scenarios. To clarify this, we first revisit the message passing mechanism from a Laplacian smoothing perspective, revealing the key to designing a multi-view message passing. Following the analysis, in this paper, we propose an enhanced GNN framework termed Confluent Graph Neural Networks (CGNN), with Cross-view Confulent Message Pssing (CCMP) tailored for multi-view learning. Inspired by the optimization of an improved multi-view Laplacian smoothing problem, CCMP contains three sub-modules that enable the interaction between graph structures and consistent representations, which makes it aware of consistency and complementarity information across views. Extensive experiments on four types of data including multi-modality data demonstrate that our proposed model exhibits superior effectiveness and robustness. The code is available at https://github.com/shumanzhuang/CGNN.

Graph Convolutional Network (GCN) has drawn widespread attention in data mining on graphs due to its outstanding performance and rigor theoretical guarantee. However, some recent studies have revealed that GCN-based methods may mine latent information insufficiently owing to the underutilization of the feature space . Besides, the unlearnable topology also significantly imperils the performance of GCN-based methods. In this paper, we conduct experiments to investigate these issues, finding that GCN does not fully consider the potential structure in the feature space, and a fixed topology deteriorates the robustness of GCN. Thus, it is desired to distill node features and establish a learnable graph. Motivated by this goal, we propose a framework dubbed G raph C onvolutional N etwork with e lastic t opology (GCNet 1 ). With the analysis of the optimization for the proposed flexible Laplacian embedding, GCNet is naturally constructed by alternative graph convolutional layers and adaptive topology learning layers. GCNet aims to deeply explore the feature space and employ the mined information to construct a learnable topology, which leads to a more robust graph representation. In addition, a set-level orthogonal loss is utilized to meet the orthogonal constraint required by the flexible Laplacian embedding and promote better class separability . Moreover, comprehensive experiments indicate that GCNet achieves remarkable performance and generalization on several real-world datasets.

Multi-omics data provides a wealth of information concerning disease mechanisms, which benefits the exploration of the intricate molecular phenomena underlying diseases. In recent years, considerable endeavors have been directed towards the combination of graph convolutional network, which has the powerful ability to gather information, with multi-omics learning methods to obtain more reliable results. For achieving this pursuit, an essential challenge is data integration. Against this backdrop, we propose a unified framework named multi-level knowledge integration with graph convolutional network, which effectively incorporates multiple prior knowledge and omics data to learn an intrinsic representation. In specific, the model consists of two subnetworks: an attribute-level module and a sample-level module. The former firstly aggregates the knowledge given by the prior biological graphs into low-dimensional embeddings, and then maximizes the consistency between these prior views via optimizing a contrastive loss for attaining the attribute-based representations. The latter leverages an encoder to dimensionalize the original multi-omics data to attain more dominant sample knowledge, and subsequently utilizes another contrastive loss to align these representations between multiple omics for learning the global sample-level information. Comprehensive experiments are performed to show that the proposed model surpasses other state-of-the-art methods.

In tensor-based multi-view learning methods, the self-representation based subspace clustering is widely researched, which is effective but heavy in high computational complexity. Furthermore, most of approaches learn the low-rank tensor representation and the final affinity matrix separately and ignore the difference between views. In this paper, we construct the target tensor composed of multiple normalized similarity matrices based on the Gaussian kernel function, which is constrained with the t-SVD based tensor nuclear norm to recover the low-rank part. The final affinity matrix is simultaneously learned via weighted multi-view fusion while optimizing the low-rank tensor, which suggests that each view is distributed to an adaptive weight. Moreover, the proposed method can be extended to semi-supervised classification through the collaborative optimization of the similarity tensor and the label indicator matrix. Extensive experiments conducted on four real-world datasets demonstrate the superiority of the proposed method compared with other state-of-the-art methods.