Federated Graph Learning (FGL) has emerged as a compelling paradigm for collaboratively training a global model while preserving the privacy of multi-source graphs. Nonetheless, FGL faces a critical challenge of data heterogeneity, where semantic and structural discrepancies across clients significantly degrade its performance. Although existing methods attempt to calibrate client-specific graph distributions during federated training, they inevitably fall short in aligning the optimization behaviors across clients due to dynamic parameter updates, thereby inducing a bottleneck in generalization improvement. To tackle this challenge, we propose a solution from a new perspective of prior refinement, which seeks to proactively harmonize client graph distributions before the federated training. In particular, we propose a Federated Graph Harmonization (FedGH) framework that exploits the generative strengths of graph diffusion models to perform prior refinement of local graphs. In a nutshell, FedGH designs a conditional diffusion mechanism on each client that synthesizes pseudo-graphs encapsulating both feature and structural priors, thereby facilitating explicit correction of inter-client distributional bias. On the server side, we employ the graph contrastive learning between various client-specific pseudo-graphs to incorporate the global information, subsequently guiding local data reconstruction. Importantly, model-agnostic FedGH can be seamlessly deployed as a plug-and-play module to be easily integrated with existing FGL architectures. Extensive experiments demonstrate that FedGH consistently outperforms state-of-the-art FGL baselines.

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.

Graph node clustering is a fundamental unsupervised task. Existing methods typically train an encoder through self-supervised learning and then apply K-means to the encoder output. Some methods use this clustering result directly as the final assignment, while others initialize centroids based on this initial clustering and then finetune both the encoder and these learnable centroids. However, due to their reliance on K-means, these methods inherit its drawbacks when the cluster separability of encoder output is low, facing challenges from the Uniform Effect and Cluster Assimilation. We summarize three reasons for the low cluster separability in existing methods: (1) lack of contextual information prevents discrimination between similar nodes from different clusters; (2) training tasks are not sufficiently aligned with the downstream clustering task; (3) the cluster information in the graph structure is not appropriately exploited. To address these issues, we propose conTrastive grapH clustEring by SwApping fUsed gRomov-wasserstein coUplingS (THESAURUS). Our method introduces semantic prototypes to provide contextual information, and employs a cross-view assignment prediction pretext task that aligns well with the downstream clustering task. Additionally, it utilizes Gromov-Wasserstein Optimal Transport (GW-OT) along with the proposed prototype graph to thoroughly exploit cluster information in the graph structure. To adapt to diverse real-world data, THESAURUS updates the prototype graph and the prototype marginal distribution in OT by using momentum. Extensive experiments demonstrate that THESAURUS achieves higher cluster separability than the prior art, effectively mitigating the Uniform Effect and Cluster Assimilation issues.

Federated prototype learning is in the spotlight as global prototypes are effective in enhancing the learning of local representation spaces, facilitating the ability to generalize the global model. However, when encountering domain-skewed data, conventional federated prototype learning is susceptible to two dilemmas: 1) Local prototypes obtained by averaging intra-class embedding carry domain-specific markers, the margins among aggregated global prototypes could be attenuated and detrimental to inter-class separation. 2) Local domain-skewed embedding may not exhibit a uniform distribution in Euclidean space, which is not conductive to the prototype-induced intra-class compactness. To address the two drawbacks, we go beyond conventional paradigm of federated prototype learning, and propose learnable semantic anchors with hyperspherical contrast (FedLSA) for domain-skewed data. Specifically, we eschew the pattern of yielding prototypes via averaging intra-class embedding and directly learn a set of semantic anchors aided by the global semantic-aware classifier. Meanwhile, the margins between anchors are augmented via pulling apart them, ensuring decent inter-class separation. To guarantee that local domain-skewed representations can be uniformly distributed, local data is projected into the hyperspherical space, and the intra-class compactness is achieved by optimizing the contrastive loss derived from the von Mises-Fisher distribution. Finally, extensive experimental results on three multi-domain datasets show the superiority of the proposed FedLSA compared to existing typical and state-of-the-state methods.

Generalized Category Discovery (GCD) aims to identify both known and novel categories in unlabeled data by leveraging knowledge from old classes. However, existing methods are limited to non-graph data; lack theoretical foundations to answer *When and how known classes can help GCD*. We introduce the Graph GCD task; provide the first rigorous theoretical analysis of *parametric GCD*. By quantifying the relationship between old and new classes in the embedding space using the Wasserstein distance W, we derive the first provable GCD loss bound based on W. This analysis highlights two necessary conditions for effective GCD. However, we uncover, through a Pairwise Markov Random Field perspective, that popular graph contrastive learning (GCL) methods inherently violate these conditions. To address this limitation, we propose SWIRL, a novel GCL method for GCD. Experimental results validate our (theoretical) findings and demonstrate SWIRL's effectiveness.

Federated graph learning (FGL) aims to collaboratively train a global graph neural network (GNN) on multiple private graphs with preserving the local data privacy. Besides the common cases of data heterogeneity in conventional federated learning, FGL faces the unique challenge of topology heterogeneity. Most of existing FGL methods alleviate the negative impact of heterogeneity by introducing global signals. However, the manners of creating increments might not be effective and significantly increase the computation amount. In light of this, we propose the FedATH, an FGL method with Alleviating Topology Heterogeneity from a causal perspective. Inspired by the causal theory, we argue that not all edges in a topology are necessary for the training objective, less topology information might make more sense. With the aid of edge evaluator, the local graphs are divided into causal and biased subgraphs. A dual-GNN architecture is used to encode the two subgraphs into corresponding representations. Thus, the causal representations are drawn closer to the training objective while the biased representations are pulled away from it. Further, the Hilbert-Schmidt Independence Criterion is employed to strengthen the separability of the two subgraphs. Extensive experiments on six real-world graph datasets are conducted to demonstrate the superiority of the proposed FedATH over the compared approaches.

To defend against privacy leakage of user data, differential privacy is widely used in federated learning, but it is not free. The addition of noise randomly disrupts the semantic integrity of the model and this disturbance accumulates with increased communication rounds. In this paper, we introduce a novel federated learning framework with rigorous privacy guarantees, named FedCEO, designed to strike a trade-off between model utility and user privacy by letting clients "C*ollaborate with Each Other". Specifically, we perform efficient tensor low-rank proximal optimization on stacked local model parameters at the server, demonstrating its capability to flexibly truncate high-frequency components in spectral space. This capability implies that our FedCEO can effectively recover the disrupted semantic information by smoothing the global semantic space for different privacy settings and continuous training processes. Moreover, we improve the SOTA utility-privacy trade-off bound by order of $\sqrt{d}$, where $d$ is the input dimension. We illustrate our theoretical results with experiments on representative datasets and observe significant performance improvements and strict privacy guarantees under different privacy settings. The *code is available at https://github.com/6lyc/FedCEO_Collaborate-with-Each-Other.

Multi-view graph clustering (MVGC) has been of widespread interest owing to the ability of capturing the complementary information among views, thereby enhancing the performance of node clustering. Despite the impressive achievements of existing methods, they are limited by a common deficiency, namely, the curse of local manifold while failing to perceive the global manifold structure. In light of this drawback, we propose a Consistent Context-Aware Representation Learning (CCARL) method for MVGC, aiming to learn node representations from global space rather than just local topology. Concretely, we define a set of anchors to establish the global coordinate, which are optimally mapped to multi-view graphs with minimal cost via fused Gromov-Wasserstein optimal transport. To fuse the complementary information in various views, the attention mechanism is employed to integrate multiple graph embeddings into a consistent representation. By transforming to the global coordinate connecting with anchors, the consistent representation captures the contextual information, and its clustering-friendliness is further enhanced through a self-training strategy. Finally, extensive experiments on four multi-view graph datasets demonstrate the effectiveness of the proposed CCARL over existing MVGC methods.

Federated graph learning is focused on aggregating knowledge from multi-source graph data and training graph neural networks. Unlike the data that traditional federated learning needs to deal with, federated graph learning also needs to face additional topological information. Further, there are also biases in features and topologies among clients, increasing the difficulty of training models. Previous methods usually seek global calibration information, however, this approach may suffer from information bias caused by data skews, and it is also difficult to naturally combine feature and topology information. Therefore, adjusting the bias before it occurs will hopefully address the learning difficulties caused by the skew. In view of this, we employ background graph data, which works as reference information for local training, to proactively correct bias before it occurs. As a kind of graph data, background graphs are naturally capable of combining feature and topology information to accomplish bias correction among clients in a comprehensive way. Mixing strategy is employed on the background graph to additionally provide privacy-preserving capabilities. Graph generation methods are employed to restore the diversity of background graphs that are blurred by the mixing strategy. Extensive experiments on two real-world datasets demonstrate the sufficient motivation and effectiveness of the proposed method.

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.

Federated domain generalization addresses the crucial challenge of developing models that can generalize across diverse domains while maintaining data privacy in federated learning settings. Current approaches either compromise privacy constraints or focus narrowly on specific aspects of model invariance, often incurring significant computational overhead. We propose a novel approach FedDIM, which leverages the concept of “insight matrix” - a fine-grained representation of the model's decision-making process derived from element-wise products between feature vectors and classifier weights. By introducing a regularization term that promotes consistency between individual sample insight matrices and their class-wise mean representations, our method effectively captures both feature and classifier invariance. This approach not only maintains strict privacy requirements but also introduces minimal computational overhead as it utilizes intermediate computations already present in the forward pass. Extensive experiments demonstrate that our method achieves superior out-of-distribution generalization compared to existing federated learning approaches while being simple to implement. Our work provides a new perspective on achieving robust generalization in federated learning settings through the lens of decision-making processes.

Graph classification has long assumed a closed-world setting, limiting its applicability to real-world scenarios where new categories often emerge. To address this limitation, we introduce Graph-Level Novel Category Discovery (GLNCD), a new task aimed at identifying unseen graph categories without supervision from novel classes. We first adapt classical Novel Category Discovery (NCD) methods for images to the graph domain and evaluate these baseline methods on four diverse graph datasets curated for the GLNCD task. Our analysis reveals that these methods suffer a notable performance degradation compared to their image-based counterparts, due to two key challenges: (1) insufficient utilization of structural information in graph self-supervised learning (SSL), and (2) ineffective pseudo-labeling strategies based on ranking statistics (RS) that neglect graph structure. To alleviate these issues, we propose ProtoFGW-NCD, a framework consisting of two core components: ProtoFGW-CL, a novel graph SSL framework, and FGW-RS, a structure-aware pseudo-labeling method. Both components employ a differentiable Fused Gromov-Wasserstein (FGW) distance to effectively compare graphs by incorporating structural information. These components are built upon learnable prototype graphs, which enable efficient, parallel FGW-based graph comparisons and capture representative patterns within graph datasets. Experiments on four GLNCD benchmark datasets demonstrate the effectiveness of ProtoFGW-NCD.

Federated graph learning (FGL) is a privacy-preserving paradigm for modeling distributed graph data, designed to train a powerful global graph neural network. Existing FGL methods predominantly rely on label information during training, effective FGL in an unsupervised setting remains largely unexplored territory. In this paper, we address two key challenges in unsupervised FGL: 1) Local models tend to converge in divergent directions due to the lack of shared semantic information across clients. Then, how to align representation spaces among multiple clients is the first challenge. 2) Conventional federated weighted aggregation easily results in degrading the performance of the global model, then which raises another challenge, namely how to adaptively learn the global model parameters. In response to the two questions, we propose a tailored framework named FedPAM, which is composed of two modules: Representation Space Alignment (RSA) and Adaptive Global Parameter Learning (AGPL). RSA leverages a set of learnable anchors to define the global representation space, then local subgraphs are aligned with them through the fused Gromov-Wasserstein optimal transport, achieving the representation space alignment across clients. AGPL stacks local model parameters into third-order tensors, and adaptively integrates the global model parameters in a low-rank tensor space, which facilitates to fuse the high-order knowledge among clients. Extensive experiments on eight graph datasets are conducted, the results demonstrate that the proposed FedPAM is superior over classical and SOTA compared methods.

Federated learning enables collaborative training while preserving the privacy of all participants. However, the heterogeneity in data distribution across multiple training nodes poses significant challenges to the construction of federated models. Prior studies were dedicated to mitigating the effects of data heterogeneity by using global information as a blueprint and restricting the local update of the model for reaching a "hard consensus". But this practice makes it difficult to balance local and global information, and it neglects to negotiate amicably between local and global models to reach mutually agreeable results, called ``soft consensus". In this paper, a multiple-path solving method is proposed to balance global and local features and combine these two feature preference paths to reach a soft consensus. Rather than relying on global information as the sole criterion, a negotiation process is employed to address the same objective by accommodating diverse feature preferences, thereby facilitating the discovery of a more plausible solution through multiple distinct pathways. Considering the overwhelming power of local features during local training, a swapping strategy is applied to weaken them to balance the solution paths. Moreover, to minimize the additional communication cost caused by the introduction of multiple paths, the solution of the task network is converted into data adaptation to reduce the amount of parameter transmission. Extensive experiments are conducted to demonstrate the advantages of the proposed method.

Vertical federated learning (VFL) allows parties to build robust shared machine learning models based on learning from distributed features of the same samples, without exposing their own data. However, current VFL solutions are limited in their ability to perform inference on non-overlapping samples, and data stored on clients is often subject to loss due to various unavoidable factors. This leads to incomplete client data, where client missing features (MF) are frequently overlooked in VFL. The main aim of this paper is to propose a VFL framework to handle missing features (MFVFL), which is a tensor decomposition network-based approach that can effectively learn intra- and inter-client feature information from client data with missing features to improve VFL performance. In the proposed MFVFL method each client imputes missing values and encodes features to learn intra-feature information, and the server collects the uploaded feature embeddings as input to our developed low-rank tensor decomposition network to learn inter-feature information. Finally, the server aggregates the representations from tensor decomposition to train a global classifier. In the paper, we theoretically guarantee the convergence of MFVFL. In addition, differential privacy (DP) for data privacy protection is always used, and the proposed framework (MFVFL-DP) can deal with such degraded data by using a tensor robust PCA to alleviate the impact of noise while preserving data privacy. We conduct extensive experiments on six datasets of different sample sizes and feature dimensions, and demonstrate that MFVFL significantly outperforms state-of-the-art methods, especially under high missing ratios. The experimental results also show that MFVFL-DP possesses excellent denoising capabilities and illustrate that the noisy effect by the DP mechanism can be alleviated.

Federated learning provides a privacy-preserving modeling schema for distributed data, which coordinates multiple clients to collaboratively train a global model. However, data stored in different clients may be collected from diverse domains, and the resulting feature shift is prone to the degraded performance of global model. In this paper, we propose a Federated Domain-Independent Prototype Learning (FedDP) method with Alignments of Representation and Parameter Spaces for Feature Shift. Concretely, FedDP aims to eliminate the domain-specific information and explore the pure representations via information bottleneck, thus integrating the local and global domain-independent prototypes, respectively. To align the cross-domain representation spaces, the global domain-independent prototypes serve as the supervised signals to enable local intra-class representations to approach them. Further, to mitigate the divergences of optimization directions between multiple clients induced by the feature shift, the global representations are yielded by the global model on the client-side and guide the learning of local representations, thus unifying the parameter spaces of multiple local models. We derive the theoretical lower bound of the optimization objective based on mutual information, which is transformed into a computable loss. The proposed FedDP can be applied in the scenarios of homogeneous and heterogeneous models. Extensive experiments are conducted on three challenging multi-domain datasets. The experimental results illustrate the superiority of FedDP compared with state-of-the-art federated learning methods.

Federated learning, as a privacy-preserving learning paradigm, restricts the access to data of each local client, for protecting the privacy of the parties. However, in the case of heterogeneous data settings, the different data distributions among clients usually lead to the divergence of learning targets, which is an essential challenge for federated learning. In this article, we propose a federated learning framework with a unified coding space, called FedUCS, for learning cross-client uniform coding rules to solve the problem of divergent targets among multiple clients due to heterogeneous data. A cross-client coordinator co-trained by multiple clients is used as a criterion of the coding space to supervise all clients coding to a uniform space, which is the significant contribution of this article. Furthermore, in order to appropriately retain historical information and avoid forgetting previous knowledge, a partial memory mechanism is applied. Moreover, in order to further enhance the distinguishability of the unified encoding space, supervised contrastive learning is used to avoid the intersection of the encoding spaces belonging to different categories. A series of experiments are performed to verify the effectiveness of the proposed method in a federated learning setting with heterogeneous data.

Federated learning enables multiple clients to collaboratively train a global model without revealing their local data. However, conventional federated learning often overlooks the fact that data stored on different clients may originate from diverse domains, and the resulting domain shift problem can significantly impair the performance of the global model. In this paper, we introduce Federated Semantic Prototype Learning (FedSeProto), a semantic prototype-based approach designed to address the domain shift issue in federated learning. The proposed method comprises two components: feature decoupling and feature alignment. Feature decoupling aims to learn semantic prototypes that can represent semantic information associated with specific categories, while feature alignment utilizes these semantic prototypes to facilitate learning of cross-client consistent features. Two key techniques are employed to achieve feature decoupling. On one hand, feature separation is achieved through the minimization of mutual information between semantic and domain features. On the other hand, the knowledge distillation is leveraged to ensure that both semantic and domain features carry the correct information. For feature alignment, intra-class semantic features are used to generate the local prototypes, which are further aggregated to the global prototypes. These global prototypes serve as guides during the local training process. Specifically, the local intra-class semantic features are driven to close to the corresponding global prototypes, thereby encouraging all clients to learn the globally consistent semantic features. Comprehensive experiments conducted on four challenging multi-domain datasets demonstrate the effectiveness of the proposed method compared with existing federated learning algorithms.

The heterogeneity issue in federated learning (FL) has attracted increasing attention, which is attempted to be addressed by most existing methods. Currently, due to systems and objectives heterogeneity, enabling clients to hold models of different architectures and tasks of different demands has become an important direction in FL. Most existing FL methods are based on the homogeneity assumption, namely, different clients have the same architectural models with the same tasks, which are unable to handle complex and multivariate data and tasks. To flexibly address these heterogeneity limitations, we propose a novel federated multi-task learning framework with the help of tensor trace norm, FedSAK. Specifically, it treats each client as a task and splits the local model into a feature extractor and a prediction head. Clients can flexibly choose shared structures based on heterogeneous situations and upload them to the server, which learns correlations among client models by mining model low-rank structures through tensor trace norm. Furthermore, we derive convergence and generalization bounds under non-convex settings. Evaluated on 6 real-world datasets compared to 13 advanced FL models, FedSAK demonstrates superior performance.

Multi-view data containing complementary and consensus information can facilitate representation learning by exploiting the intact integration of multi-view features. Because most objects in the real world often have underlying connections, organizing multi-view data as heterogeneous graphs is beneficial to extracting latent information among different objects. Due to the powerful capability to gather information of neighborhood nodes, in this article, we apply Graph Convolutional Network (GCN) to cope with heterogeneous graph data originating from multi-view data, which is still under-explored in the field of GCN. In order to improve the quality of network topology and alleviate the interference of noises yielded by graph fusion, some methods undertake sorting operations before the graph convolution procedure. These GCN-based methods generally sort and select the most confident neighborhood nodes for each vertex, such as picking the top- k nodes according to pre-defined confidence values. Nonetheless, this is problematic due to the non-differentiable sorting operators and inflexible graph embedding learning, which may result in blocked gradient computations and undesired performance. To cope with these issues, we propose a joint framework dubbed Multi-view Graph Convolutional Network with Differentiable Node Selection (MGCN-DNS), which is constituted of an adaptive graph fusion layer, a graph learning module, and a differentiable node selection schema. MGCN-DNS accepts multi-channel graph-structural data as inputs and aims to learn more robust graph fusion through a differentiable neural network. The effectiveness of the proposed method is verified by rigorous comparisons with considerable state-of-the-art approaches in terms of multi-view semi-supervised classification tasks, and the experimental results indicate that MGCN-DNS achieves pleasurable performance on several benchmark multi-view datasets.

Most multi-view clustering methods based on shallow models are limited in sound nonlinear information perception capability, or fail to effectively exploit complementary information hidden in different views. To tackle these issues, we propose a novel Subspace-Contrastive Multi-View Clustering (SCMC) approach. Specifically, SCMC utilizes a set of view-specific auto-encoders to map the original multi-view data into compact features capturing its nonlinear structures. Considering the large semantic gap of data from different modalities, we project multiple heterogeneous features into a joint semantic space, namely the embedded compact features are passed through the self-expression layers to learn the subspace representations, respectively. In order to enhance the discriminability and efficiently excavate the complementarity of various subspace representations, we use the contrastive strategy to maximize the similarity between positive pairs while differentiate negative pairs. Thus, the graph regularization is employed to encode the local geometric structure within varying subspaces for optimizing the consistent affinity matrix. Furthermore, to endow the proposed SCMC with the ability of handling the multi-view out-of-samples, we develop a consistent sparse representation (CSR) learning mechanism over the in-samples. To demonstrate the effectiveness of the proposed model, we conduct a large number of comparative experiments on ten challenging datasets, and the experimental results show that SCMC outperforms existing shallow and deep multi-view clustering methods. In addition, the experimental results on out-of-samples illustrate the effectiveness of the proposed CSR.

Federated Learning (FL) provides a novel paradigm for privacy-preserving machine learning, enabling multiple clients to collaborate on model training without sharing private data. To handle multi-source heterogeneous data, Vertical Federated Learning (VFL) has been extensively investigated. However, in the context of VFL, the label information tends to be kept in one authoritative client and is very limited. This poses two challenges for model training in the VFL scenario. On the one hand, a small number of labels cannot guarantee to train a well VFL model with informative network parameters, resulting in unclear boundaries for classification decisions. On the other hand, the large amount of unlabeled data is dominant and should not be discounted, and it is worthwhile to focus on how to leverage them to improve representation modeling capabilities. To address the preceding two challenges, we first introduce supervised contrastive loss to enhance the intra-class aggregation and inter-class estrangement, which is to deeply explore label information and improve the effectiveness of downstream classification tasks. Then, for unlabeled data, we introduce a pseudo-label-guided consistency mechanism to induce the classification results coherent across clients, which allows the representations learned by local networks to absorb the knowledge from other clients, and alleviates the disagreement between different clients for classification tasks. We conduct sufficient experiments on four commonly used datasets, and the experimental results demonstrate that our method is superior to the state-of-the-art methods, especially in the low-label rate scenario, and the improvement becomes more significant.

In deep multi-view clustering, three intractable problems are posed ahead of researchers, namely, the complementarity exploration problem, the information preservation problem, and the cluster structure discovery problem. In this paper, we consider the deep multi-view clustering from the perspective of mutual information (MI), and attempt to address the three important concerns with a Mutual Information-Driven Multi-View Clustering (MIMC) method, which extracts the common and view-specific information hidden in multi-view data and constructs a clustering-oriented comprehensive representation. Specifically, three constraints based on MI are devised in response to three issues. Correspondingly, we minimize the MI between the common representation and view-specific representations to exploit the inter-view complementary information. Further, we maximize the MI between the refined data representations and original data representations to preserve the principal information. Moreover, to learn a clustering-friendly comprehensive representation, the MI between the comprehensive embedding space and cluster structure is maximized. Finally, we conduct extensive experiments on six benchmark datasets, and the experimental results indicate that the proposed MIMC outperforms other clustering methods.

With the rapidly growing attention to multi-view data in recent years, multi-view outlier detection has become a rising field with intense research. These researches have made some success, but still exist some issues that need to be solved. First, many multi-view outlier detection methods can only handle datasets that conform to the cluster structure but are powerless for complex data distributions such as manifold structures. This overly restrictive data assumption limits the applicability of these methods. In addition, almost the majority of multi-view outlier detection algorithms cannot solve the online detection problem of multi-view outliers. To address these issues, we propose a new detection method based on the local similarity relation and data reconstruction, i.e., the Self-Representation Method with Local Similarity Preserving for fast multi-view outlier detection (SRLSP). By using the local similarity structure, the proposed method fully utilizes the characteristics of outliers and detects outliers with an applicable objective function. Besides, a well-designed optimization algorithm is proposed, which completes each iteration with linear time complexity and can calculate each instance parallelly. Also, the optimization algorithm can be easily extended to the online version, which is more suitable for practical production environments. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of the proposed method on both performance and time complexity.

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.

The goal of multi-view learning is to learn latent patterns from various data sources. Most of previous research focused on fitting feature embedding in target tasks. There is very limited research on the connection between feature representations with hidden layers of neural networks. In this paper, a multi-view deep matrix factorization model is proposed to learn a shared feature representation. The proposed model automatically explores the most discriminative features of multi-view data and makes these features meet the requirements of specific applications. Here we explore the connection between deep learning and feature representations. First, the model constructs a scalable neural network with shared hidden layers for exploring a low-dimensional representations of all views. Second, the quality of representation matrix is evaluated via relaxed graph regularization and evaluators to improve the feature representation capability of matrix factorization. Finally, the effectiveness of the proposed method is verified through comparative experiments with eight state-of-the-art multi-view clustering algorithms on eight real-world datasets.

Multi-view clustering (MVC) aims at exploiting the consistent features within different views to divide samples into different clusters. Existing subspace-based MVC algorithms usually assume linear subspace structures and two-stage similarity matrix construction strategies, thereby posing challenges in imprecise low-dimensional subspace representation and inadequacy of exploring consistency. This paper presents a novel hierarchical representation for MVC method via the integration of intra-sample, intra-view, and inter-view representation learning models. In particular, we first adopt the deep autoencoder to adaptively map the original high-dimensional data into the latent low-dimensional representation of each sample. Second, we use the self-expression of the latent representation to explore the global similarity between samples of each view and obtain the subspace representation coefficients. Third, we construct the third-order tensor by arranging multiple subspace representation matrices and impose the tensor low-rank constraint to sufficiently explore the consistency among views. Being incorporated into a unified framework, these three models boost each other to achieve a satisfactory clustering result. Moreover, an alternating direction method of multipliers algorithm is developed to solve the challenging optimization problem. Extensive experiments on both simulated and real-world multi-view datasets show the superiority of the proposed method over eight state-of-the-art baselines.

Multi-view data often contain redundant information that cannot be simply spliced. Many existing methods for processing them by assigning weights to each view cannot capture features dynamically. Therefore, we propose a multi-view deep matrix factorization method via neural networks that captures semantic hierarchical information of the data and dynamically produces a consistent representation using the complementarity of multi-view features. Due to the usefulness of deep matrix factorization, the generated representation is easily interpretable. The proposed method yields a harmonized representation directly from multi-view data without an extra weight learning process. In addition, we use a multi-path network to search for a consensual solution and obtain an optimal result. Additional feature optimization is used to enhance the discriminative characterization of the representation matrix. Finally, experiments on four real-world datasets show that the proposed method is superior to state-of-the-arts.

Recent researches on multiview learning have received widespread attention due to the increasing generalization of multiview data. As an effective probabilistic model, random walk has also shown encouraging performance in various fields. To further exploit the potential of utilizing random walk schemes to address multiview learning problems, this article proposes a simple yet efficient multigraph random walk scheme for both multiview clustering and semisupervised classification tasks. The proposed model integrates random walk with multiview learning, and recursively learns a globally stable probability distribution matrix from multiple views, on the basis of which the label indicator is obtained in the scene of clustering or semisupervised classification. Furthermore, an adaptive weight vector is learned to incorporate the diversity and complementarity of multiview data. Besides, the relationships between the proposed scheme and spectral clustering, neighborhood embedding and manifold embedding are analyzed theoretically. Finally, comprehensive comparative experiments are conducted with several state-of-the-art multiview clustering and semisupervised classification methods on eight real-world datasets. The experimental results demonstrate the superiority of the proposed method in terms of both clustering and classification performance.

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.