Aiming to overcome distribution shift and label sparsity that hinder cross-domain generalization of Graph Neural Networks (GNNs), Unsupervised Graph Domain Adaptation (UGDA) transfers knowledge from a label-rich source to an unlabeled target graph. Yet in practice, strict privacy protocols often withhold the source graph, reducing UGDA to the more constrained Source-Free UGDA (SFUGDA) where only a pre-trained source GNN remains. In this setting, the source GNN serves as a simple, task-specific graph foundation model. Despite recent progress, existing source-free UGDA methods remain hampered by source-knowledge absence: deprived of source graphs, they lose the reference distribution needed to gauge domain shift and must lean on noisy target cues, incurring biased adaptation and catastrophic forgetting. To overcome this drawback, this paper devises Source-Free Graph foundation model Adaptation via pseudo-source Reconstruction (SFGAR), a two-stage SFUGDA framework that first generates pseudo-source graphs to recover the source distribution encoded in a frozen pre-trained GNN, then adversarially aligns these synthetic graphs with the unlabeled target. Theoretical analysis shows that this proxy alignment tightly bounds the target-domain generalization error. Extensive experiments on public benchmarks validate the state-of-the-art performance of SFGAR.

Defending against backdoor attacks on graphs has become increasingly critical. Existing methods predominantly focus on detecting and removing triggers by identifying inconsistencies between trigger and clean nodes. However, adversaries can design triggers that closely resemble clean nodes, making them challenging to detect. Therefore, understanding the mechanisms underlying backdoor attacks is crucial. In this work, we observe an interesting phenomenon: in backdoored models, specific ''backdoor neurons'' (embedding dimensions) are more likely to be activated, causing nodes to be misclassified to the target label. This is largely due to the graph structure, where malicious information propagates through node neighborhoods, activating specific neurons and target label. Based on this observation, we theoretically and empirically demonstrate how graph backdoor attacks exploit this propagation mechanism to effectively poison the target node's embedding. Meanwhile, we propose a novel defense called Graph Backdoor Neuron Defense (GBND) to identify, unlearn, and recover backdoor neurons. Specifically, we design a novel reverse engineering technique to identify triggers that activate backdoor neurons, and eliminate their harmful effects by asymmetric unlearning and recovering at the neuron level. Extensive experiments on four datasets validate the effectiveness of GBND in defending against backdoor attacks.

Accurate traffic flow forecasting is crucial for intelligent transportation systems and relies on effectively modeling complex spatio-temporal dependencies. Although recent graph-based deep learning methods have achieved promising results, most focus on pairwise neighbor relationships, limiting their ability to capture higher-order spatio-temporal interactions in the traffic network. To overcome this limitation, we propose a novel Multi-source information driven Spatio-Temporal HyperGraph learning for traffic forecasting (MSTHG), which is designed to capture richer relational and semantic information. MSTHG introduces a multi-source hypergraph fusion strategy that jointly models dynamic high-order spatial and temporal correlations. Specifically, we build a spatial hypergraph based on geographical proximity to represent high-order spatial dependencies, and a temporal-trend hypergraph leveraging mutual information to capture nonlinear similarities among traffic series. To enhance the semantic richness of node representations, we integrate key daily and weekly information along with periodic features derived from Fast Fourier Transform (FFT). Following the obtained hypergraph, node representations are learned through a hypergraph convolutional network and subsequently processed by a GRU-MLP fusion module, which is designed to capture both local and global temporal dependencies. Extensive experiments on real-world benchmark datasets demonstrate that MSTHG outperforms state-of-the-art baselines. The source code is https://github.com/April-leng/MSTHG.git.

Understanding the heterogeneity of population-level viral fitness dynamics, which reflect the interplay between intrinsic viral properties and population immunity, is critical for pandemic preparedness. However, how these dynamics vary across diverse immune backgrounds and mutational landscapes remain poorly characterized. We present Geno-GNN, a graph representation learning approach for retrospectively characterizing the viral fitness dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Geno-GNN accurately predicts angiotensin-converting enzyme 2 (ACE2) binding affinity and immune escape potential across multiple external datasets. Using Geno-GNN, we identified temporal patterns in SARS-CoV-2 fitness and detected varying rates of fitness change associated with distinct immune backgrounds. Virtual mutation scanning revealed two fitness trajectories: broad immune evasion at the cost of ACE2 affinity and ACE2 affinity maintenance at or above the Wuhan-Hu-1 level along with moderate immune escape. Notably, real-world SARS-CoV-2 variants predominantly followed the latter trajectory, sustaining ACE2 affinity via fixed mutations. These findings underscore the heterogeneous, immune-contextualized nature of viral fitness dynamics and the complex evolutionary pathways of SARS-CoV-2.

After training on a specific source domain, models can leverage domain generalization (DG) techniques to achieve superior and broader performance on new, unseen target domains. Existing DG often utilizes contrastive learning to learn domain-invariant features. The goal of contrastive learning is to learn effective representations of data, causing samples from the same category to cluster together in feature space, while samples from different categories are dispersed. Traditional contrastive learning is limited to a finite set of contrastive pairs for DG. To handle this problem, we consider sampling from an infinite number of contrastive pairs using a mixture of von Mises-Fisher (vMF) distributions on the unit hypersphere. We propose a novel method called Probability-guided Contrastive Learning (PgCL), which selects contrastive pairs based on estimated data distributions of samples from each category in feature space. Additionally, we derive the exact analytical formula for the expected contrastive loss. We conduct an empirical investigation of the error bounds of PgCL and demonstrate its performance by comparing it with several leading methods across a range of DG datasets.

Precise determination of HER2 subtype is essential for selecting appropriate targeted therapies in breast cancer. However, current HER2 assessment methods remain dependent on invasive tissue biopsies, which are limited by tumor heterogeneity and sampling bias. To address these challenges, this paper proposes a knowledge-guided multi-modal neural network (KMNet) for non-invasive HER2 subtyping by integrating clinical data and ultrasound images. KMNet introduces a Graph-based Clinical Feature encoder (GCF), which constructs a causal graph among clinical indicators based on medical knowledge and extracts high-order feature relationships via the Graph Convolutional Network (GCN). Meanwhile, the Convolutional Neural Network (CNN) and Vision Transformer (ViT)-based hybrid image encoder (CVUIF) captures both local details (calcifications and blood flow) and global dependencies between intra- and peritumoral regions. In addition, the Reduced Dimensional Fusion (RDF) module integrates key information from clinical graph features, ultrasound image features, and structured clinical data to construct a unified multi-modal representation for downstream HER2 subtyping task. Experiments were conducted on the private datasets (HER2USC) and the public datasets (BCW, BCa and SIIM-ISIC). Experimental results demonstrate that KMNet outperformed other reported state-of-the-art multi- modal algorithms in HER2 subtyping task, offering strong potential for clinical decision support in breast cancer treatment.

As an essential technique for Graph Contrastive Learning (GCL), Graph Augmentation (GA) improves the generalization capability of the GCLs by introducing different forms of the same graph. To ensure information integrity, existing GA strategies have been designed to simultaneously process the two types of information available in graphs: node attributes and graph topology. Nonetheless, these strategies tend to augment the two types of graph information separately, ignoring their correlation, resulting in limited representation ability. To overcome this drawback, this paper proposes a novel GCL framework with a Joint spectrAl augMentation, named GCL-JAM. Motivated the equivalence between the graph learning objective on an attribute graph and the spectral clustering objective on the attribute-interpolated graph, the node attributes are first abstracted as another type of node to harmonize the node attributes and graph topology. The newly constructed graph is then utilized to perform spectral augmentation to capture the correlation during augmentation. Theoretically, the proposed joint spectral augmentation is proved to perturb more inter-class edges and noise attributes compared to separate augmentation methods. Extensive experiments on homophily and heterophily graphs validate the effectiveness and universality of GCL-JAM.

Scene Graph Generation (SGG) aims to detect all objects and identify their pairwise relationships existing in the scene. Considering the substantial human labor costs, existing scene graph annotations are often sparse and biased, which result in confusion training with low-frequency predicates. In this work, we design a Semi-Supervised Clustering framework for Scene Graph Generation (SSC-SGG) that uses the sparse labeled data to guide the generation of effective pseudo-labels from unlabeled object pairs, thus enriching the labeled sample space, especially for low-frequency interaction samples. We approach from the perspective of clustering, reducing the problem of confirmation bias in a self-training manner. Specifically, we first enhance the model's robustness to feature extraction via prototype-based clustering, aggregating different relationship augmented features onto the same prototype. Secondly, we design a dynamic pseudo-label assignment algorithm based on a mini-batch, which adjusts the detection sensitivity to different frequency samples from the historical assignment. Finally, we conduct joint training on the pseudo-labels and the labeled data. We conduct experiments on various SGG models and achieve substantial overall performance improvements, demonstrating the effectiveness of SSC-SGG.

Graph Transformers (GTs), adept at capturing the locality and globality of graphs, have shown promising potential in node classification tasks. Most state-of-the-art GTs succeed through integrating local Graph Neural Networks (GNNs) with their global Self-Attention (SA) modules to enhance structural awareness. Nonetheless, this architecture faces limitations arising from scalability challenges and the trade-off between capturing local and global information. On the one hand, the quadratic complexity associated with the SA modules poses a significant challenge for many GTs, particularly when scaling them to large-scale graphs. Numerous GTs necessitated a compromise, relinquishing certain aspects of their expressivity to garner computational efficiency. On the other hand, GTs face challenges in maintaining detailed local structural information while capturing long-range dependencies. As a result, they typically require significant computational costs to balance the local and global expressivity. To address these limitations, this paper introduces a novel GT architecture, dubbed DUALFormer, featuring a dual-dimensional design of its GNN and SA modules. Leveraging approximation theory from Linearized Transformers and treating the query as the surrogate representation of node features, DUALFormer \emph{efficiently} performs the computationally intensive global SA module on feature dimensions. Furthermore, by such a separation of local and global modules into dual dimensions, DUALFormer achieves a natural balance between local and global expressivity. In theory, DUALFormer can reduce intra-class variance, thereby enhancing the discriminability of node representations. Extensive experiments on eleven real-world datasets demonstrate its effectiveness and efficiency over existing state-of-the-art GTs.

The distribution shifts and the scarcity of labels prevent graph learning methods, especially graph neural networks (GNNs), from generalizing across domains. Compared to Unsupervised Domain Adaptation (UDA) with embedding alignment, Unsupervised Graph Domain Adaptation (UGDA) becomes more challenging in light of the attribute and topology entanglement in the representation. Beyond embedding alignment, UGDA turns to topology alignment but is limited by the ability of the employed topology model and the estimation of pseudo labels. To alleviate this issue, this paper proposed a Disentangled Graph Spectral Domain adaptation (DGSDA) by disentangling attribute and topology alignments and directly aligning flexible graph spectral filters beyond topology. Specifically, Bernstein polynomial approximation, which mimics the behavior of the function to be approximated to a remarkable degree, is employed to capture complicated topology characteristics and avoid the expensive eigenvalue decomposition. Theoretical analysis reveals the tight GDA bound of DGSDA and the rationality of polynomial coefficient regularization. Quantitative and qualitative experiments justify the superiority of the proposed DGSDA.

Brain network analysis plays a critical role in brain disease prediction and diagnosis. Graph mining tools have made remarkable progress. Graph neural networks (GNNs) and Transformers, which rely on the message-passing scheme, recently dominated this field due to their powerful expressive ability on graph data. Unfortunately, by considering brain network construction using pairwise Pearson’s coefficients between any pairs of ROIs, model analysis and experimental verification reveal that the message-passing under both GNNs and Transformers can NOT be fully explored and exploited. Surprisingly, this paper observes the significant performance and efficiency enhancements of the Hadamard product compared to the matrix product, which is the matrix form of message passing, in processing the brain network. Inspired by this finding, a novel Brain Quadratic Network (BQN) is proposed by incorporating quadratic networks, which possess better universal approximation properties. Moreover, theoretical analysis demonstrates that BQN implicitly performs community detection along with representation learning. Extensive evaluations verify the superiority of the proposed BQN compared to the message-passing-based brain network modeling. Source code is available at https://github.com/LYWJUN/BQN-demo.

As a pivotal architecture in Self-Supervised Learning (SSL), Graph Contrastive Learning (GCL) has demonstrated substantial application value in scenarios with limited labeled nodes (samples). However, existing GCLs encounter critical issues in the graph augmentation and positive and negative sampling stemming from the lack of explicit supervision, which collectively restrict their efficiency and universality. On the one hand, the reliance on graph augmentations in existing GCLs can lead to increased training times and memory usage, while potentially compromising the semantic integrity. On the other hand, the difficulty in selecting TRUE positive and negative samples for GCLs limits their universality to both homophilic and heterophilic graphs. To address these drawbacks, this paper introduces a novel GCL framework called GRAph learning via Self-contraSt (GRASS). The core mechanism is node-attribute self-contrast, which specifically involves increasing the feature similarities between nodes and their included attributes while decreasing the similarities between nodes and their non-included attributes. Theoretically, the self-contrast mechanism implicitly ensures accurate node-node contrast by capturing high-hop co-inclusion relationships, thereby enabling GRASS to be universally applicable to graphs with varying degrees of homophily. Evaluations on diverse benchmark datasets demonstrate the universality and efficiency of GRASS. The dataset and code are available at URL: https://github.com/YukunCai/GRASS.

Session-based Recommendation (SBR) aims to predict users’ next interaction based on their current session without relying on long-term profiles. Despite its effectiveness in privacy-preserving and real-time scenarios, SBR remains challenging due to limited behavioral signals. Prior methods often overfit co-occurrence patterns, neglecting semantic priors like item attributes. Recent studies have attempted to incorporate item attributes (e.g., category) by assigning fixed embeddings shared across all sessions. However, such approaches suffer from two key limitations: 1) Static attribute encoding fails to reflect semantic shifts under different session contexts. 2) Semantic misalignment between attribute and item ID embeddings. To address these issues, we propose attribute association driven multi-task learning for SBR, dubbed A²D-MTL. It explicitly models item categories using cross-session context to capture user potential interests and designs an adaptive sparse attention mechanism to suppress noise. Experimental results on three public datasets demonstrate the superiority of our method in recommendation accuracy (P@20) and ranking quality (MRR@20), validating the model’s effectiveness.

Graph Transformers (GTs), which effectively capture long-range dependencies and structural biases simultaneously, have recently emerged as promising alternatives to traditional Graph Neural Networks (GNNs). Advanced approaches for GTs to leverage topology information involve integrating GNN modules or modulating node attributes using positional encodings. Unfortunately, the underlying mechanism driving their effectiveness remains insufficiently understood. In this paper, we revisit these strategies and uncover a shared underlying mechanism—Cross Aggregation—that effectively captures the interaction between graph topology and node attributes. Building on this insight, we propose the Universal Graph Cross-attention Transformer (UGCFormer), a universal GT framework with linear computational complexity. The idea is to interactively learn the representations of graph topology and node attributes through a linearized Dual Cross-attention (DCA) module. In theory, this module can adaptively capture interactions between these two types of graph information, thereby achieving effective aggregation. To alleviate overfitting arising from the dual-channel design, we introduce a consistency constraint that enforces representational alignment. Extensive evaluations on multiple benchmark datasets demonstrate the effectiveness and efficiency of UGCFormer.

Graph Neural Networks(GNNs), such as Graph Convolutional Network, have exhibited impressive performance on various real-world datasets. However, many researches have confirmed that deliberately designed adversarial attacks can easily confuse GNNs on the classification of target nodes (targeted attacks) or all the nodes (global attacks). According to our observations, different attributes tend to be differently treated when the graph is attacked. Unfortunately, most of the existing defense methods can only defend at the graph or node level, which ignores the diversity of different attributes within each node. To address this limitation, we propose to leverage a new property, named Attribute-level Smoothness (ALS), which is defined based on the local differences of graph. We then propose a novel defense method, named GCN with Attribute-level Defense (ALD-GCN), which utilizes the ALS property to provide attribute-level protection to each attributes. Extensive experiments on real-world graphs have demonstrated the superiority of the proposed work and the potentials of our ALS property in the attacks.

The goal of single domain generalization is to use data from a single domain (source domain) to train a model, which is then deployed over several unknown domains for testing (target domains). This study introduces a practical approach diverging from traditional DG, which typically relies on multiple source domains. We focus on Single Long-Tailed Domain Generalization, which refers to a scenario in the context of long-tail distribution, where although minority classes may have fewer samples in a single domain, these minority classes could become more prevalent and dominant in other domains. We introduce the Graph Convolutional Mixture-of-Experts Learners Network for Long-Tailed Domain Generalization (GCML) as a solution to this problem. Our approach presents two novel tactics. Initially, we utilize an expert learning technique that is skill-diverse. In order to properly manage the unknown target domain, this entails training multiple specialists inside a single long-tailed source domain and combining their knowledge. Then, we use a graph convolutional network to facilitate domain generalization, leveraging joint data structure modeling to learn more domain-invariant feature. Experiments conducted on four established benchmarks reveal that our GCML algorithm outperforms contemporary domain generalization techniques, demonstrating its efficacy in this complex task.

Graph contrastive learning (GCL) is emerging as a pivotal technique in graph representation learning. However, recent research indicates that GCL is vulnerable to adversarial attacks, while existing robust GCL methods against adversarial attacks are inefficient and lack scalability due to the significant computational expenses of explicit adversarial attacks on the graph structure. To address the shortcomings of existing approaches, we propose an efficient and robust GCL via multiadversarial views training framework, called ERMAV. Specifically, the ERMAV generates two adversarial views by attacking both node attributes and latent representations on randomly sampled subgraphs. The method conducts explicit adversarial attacks on node attributes by attacking node attributes and implicit adversarial attacks on the graph structure by attacking latent representations, which avoids the costly computation of explicit graph structure attacks. Moreover, two efficient attack methods are developed to construct adversarial perturbations, which can dynamically generate different adversarial views to enhance sample diversity in the training phase. Furthermore, to validate the effectiveness and robustness of the proposed framework, extensive experiments of node classification on seven real-world datasets are conducted. Experimental results show that our ERMAV outperforms state-of-the-art GCL methods on the original graphs and is consistently more robust than existing robust GCL methods on a variety of attacked graphs. This demonstrates the strong robustness and great potential of our ERMAV in real-world applications.

High-dimensional gene expression data has gained considerable attention in diverse medical fields such as disease diagnosis, with the challenges of the dimensionality curse and exponentially growing computation. To analyze the data, feature selection is an essential step by reducing the dimensionality. However, most feature selection algorithms for high-dimensional gene expression data still suffer from low classification and poor generalization ability. An evolutionary algorithm is an effective paradigm for enhancing global search capability in feature selection. Inspired by the evolutionary algorithm Competitive Swarm Optimization, we propose a Multiobjective Dual-directional Competitive Swarm Optimization (MODCSO) method for feature selection from high-dimensional gene expression data. First, we design a competitive swarm optimization algorithm framework based on multi-objective optimization to evolve three objective functions simultaneously. Then, we introduce a dual-directional learning strategy that trains particles within the loser group using two distinct learning strategies. To assess the effectiveness and efficiency of the suggested algorithm, we evaluate MODCSO through extensive experiments on twenty high-dimensional gene expression datasets and three real-world biological datasets. Compared to various leading feature selection algorithms, our proposed algorithm MODCSO exhibits superior competitiveness for the high-dimensional feature selection task. Moreover, we provide other extensive analyses to demonstrate further the robustness and biological interpretability of MODCSO in handling high-dimensional gene expression data.

Graph Contrastive Learning (GCL), a Self-Supervised Learning (SSL) architecture tailored for graphs, has shown notable potential for mitigating label scarcity. Its core idea is to amplify feature similarities between the positive sample pairs and reduce them between the negative sample pairs. Unfortunately, most existing GCLs consistently present sub-optimal performances on both homophilic and heterophilic graphs. This is primarily attributed to two limitations of positive sampling, that is, incomplete local sampling and blind sampling. To address these limitations, this paper introduces a novel GCL framework with an adaptive positive sampling module, named grapH contrastivE Adaptive Positive Samples (HEATS). Motivated by the observation that the affinity matrix corresponding to optimal positive sample sets has a block-diagonal structure with equal weights within each block, a self-expressive learning objective incorporating the block and idempotent constraint is presented. This learning objective and the contrastive learning objective are iteratively optimized to improve the adaptability and robustness of HEATS. Extensive experiments on graphs and images validate the effectiveness and generality of HEATS.

Graphs with heterophily have been regarded as challenging scenarios for Graph Neural Networks (GNNs), where nodes are connected with dissimilar neighbors through various patterns. In this paper, we present theoretical understandings of heterophily for GNNs by incorporating the graph convolution (GC) operations into fully connected networks via the proposed Heterophilous Stochastic Block Models (HSBM), a general random graph model that can accommodate diverse heterophily patterns. Our theoretical investigation comprehensively analyze the impact of heterophily from three critical aspects. Firstly, for the impact of different heterophily patterns, we show that the separability gains are determined by two factors, i.e., the Euclidean distance of the neighborhood distributions and $\sqrt{\mathbb{E}\left[\operatorname{deg}\right]}$, where $\mathbb{E}\left[\operatorname{deg}\right]$ is the averaged node degree. Secondly, we show that the neighborhood inconsistency has a detrimental impact on separability, which is similar to degrading $\mathbb{E}\left[\operatorname{deg}\right]$ by a specific factor. Finally, for the impact of stacking multiple layers, we show that the separability gains are determined by the normalized distance of the $l$-powered neighborhood distributions, indicating that nodes still possess separability in various regimes, even when over-smoothing occurs. Extensive experiments on both synthetic and real-world data verify the effectiveness of our theory.

In real-world scenarios, networks (graphs) and their tasks possess unique characteristics, requiring the development of a versatile graph augmentation (GA) to meet the varied demands of network analysis. Unfortunately, most Graph Contrastive Learning (GCL) frameworks are hampered by the specificity, complexity, and incompleteness of their GA techniques. Firstly, GAs designed for specific scenarios may compromise the universality of models if mishandled. Secondly, the process of identifying and generating optimal augmentations generally involves substantial computational overhead. Thirdly, the effectiveness of the GCL, even the learnable ones, is constrained by the finite selection of GAs available. To overcome the above limitations, this paper introduces a novel unified GA module dubbed UGA after reinterpreting the mechanism of GAs in GCLs from a message-passing perspective. Theoretically, this module is capable of unifying any explicit GAs, including node, edge, attribute, and subgraph augmentations. Based on the proposed UGA, a novel generalized GCL framework dubbed Graph cOntrastive UnifieD Augmentations (GOUDA) is proposed. It seamlessly integrates widely adopted contrastive losses and an introduced independence loss to fulfill the common requirements of consistency and diversity of augmentation across diverse scenarios. Evaluations across various datasets and tasks demonstrate the generality and efficiency of the proposed GOUDA over existing state-of-the-art GCLs.

To make Graph Neural Networks (GNNs) meet the requirements of the Web, the universality and the generalization become two important research directions. On one hand, many universal GNNs are presented for semi-supervised tasks on both homophilic and non-homophilic graphs by distinguishing homophilic and heterophilic edges with the help of labels. On the other hand, self-supervised learning (SSL) algorithms on graphs are presented by leveraging the self-supervised learning schemes from computer vision and natural language processing. Unfortunately, graph universal self-supervised learning remains resolved. Most existing SSL methods on graphs, which often employ two-layer GCN as the encoder and train the mapping functions, can't alter the low-passing filtering characteristic of GCN. Therefore, to be universal, SSL must becustomized for the graph, i.e., learning the graph. However, learning the graph via universal GNNs is disabled in SSL, since their distinguishability on homophilic and heterophilic edges disappears without the labels. To overcome this difficulty, this paper proposes novel GrAph-customized Universal Self-Supervised Learning (GAUSS) by exploiting local attribute distribution. The main idea is to replace the global parameters with locally learnable propagation. To make the propagation matrix demonstrate the affinity between the nodes, the self-representative learning framework is employed with k-block diagonal regularization. Extensive experiments on synthetic and real-world datasets demonstrate its effectiveness, universality and robustness to noises.

Real-world graphs exhibit diverse structures, including homophilic and heterophilic patterns, necessitating the development of a universal Graph Contrastive Learning (GCL) framework. Nonetheless, the existing GCLs, especially those with a local focus, lack universality due to the mismatch between the input graph structure and the homophily assumption for two primary components of GCLs. Firstly, the encoder, commonly Graph Convolution Network (GCN), operates as a low-pass filter, which assumes the input graph to be homophilic. This makes it challenging to aggregate features from neighbor nodes of the same class on heterophilic graphs. Secondly, the local positive sampling regards neighbor nodes as positive samples, which is inspired by the homophily assumption. This results in feature similarity amplification for the samples from the different classes (i.e., FALSE positive samples). Therefore, it is crucial to feed the encoder and positive sampling of GCLs with homophilic graph structures. This paper presents a novel GCL framework, named gRaph cOntraStive Exploring uNiversality (ROSEN), designed to achieve this objective. Specifically, ROSEN equips a local graph structure inference module, utilizing the Block Diagonal Property (BDP) of the affinity matrix extracted from node ego networks. This module can generate the homophilic graph structure by selectively removing disassortative edges. Extensive evaluations validate the effectiveness and universality of ROSEN across node classification and node clustering tasks.

The current success of Graph Neural Networks (GNNs) usually relies on loading the entire attributed graph for processing, which may not be satisfied with limited memory resources, especially when the attributed graph is large. This paper pioneers to propose a Binary Graph Convolutional Network (Bi-GCN), which binarizes both the network parameters and input node attributes and exploits binary operations instead of floating-point matrix multiplications for network compression and acceleration. Meanwhile, we also propose a new gradient approximation based back-propagation method to properly train our Bi-GCN. According to the theoretical analysis, our Bi-GCN can reduce the memory consumption by an average of ∼ 31x for both the network parameters and input data, and accelerate the inference speed by an average of ∼ 51x, on three citation networks, i.e., Cora, PubMed, and CiteSeer. Besides, we introduce a general approach to generalize our binarization method to other variants of GNNs, and achieve similar efficiencies. Although the proposed Bi-GCN and Bi-GNNs are simple yet efficient, these compressed networks may also possess a potential capacity problem, i.e., they may not have enough storage capacity to learn adequate representations for specific tasks. To tackle this capacity problem, an Entropy Cover Hypothesis is proposed to predict the lower bound of the width of Bi-GNN hidden layers. Extensive experiments have demonstrated that our Bi-GCN and Bi-GNNs can give comparable performances to the corresponding full-precision baselines on seven node classification datasets and verified the effectiveness of our Entropy Cover Hypothesis for solving the capacity problem.

The formation of information cocoons, driven by limited disclosure and individual preferences, has resulted in the polarization of society. However, the underlying mechanisms and pathways to escape these cocoons remain unresolved. This article aims to solve it by developing an adaptive imitation process. In this process, the measurement of information cocoons across the population is based on Shannon’s information entropy, taking into account neighborhood information. Incorporating the Dirac function to formulate information distribution over networks, theoretical results are validated by numerical simulation experiments. Results show that individual backgrounds and preferences are crucial factors in the formation of information cocoons, and the severity of information cocoon production increases with an individual capacity to stick to oneself. Encouraging connections among diverse communities can effectively mitigate the intensity of information cocoons. This research contributes to the advancement of computational communication systems and offers insights toward dismantling informational boundaries.

Emerging infectious diseases pose a growing threat to human society and have sparked extensive public discussions on social media. Although numerous efforts have been made in health data mining on social media, there is a lack of focus on quantitative comparisons across multiple platforms, despite their crucial role in the holistic social communication system. This study addresses this gap by developing a generalized regression model that considers the distinct attributes of social media platforms, including short-text, long-text, and Eastern or Western orientation. Using Monkeypox as an application case, this study examines differences among platforms based on four factors: user characteristics, text topics, text emotion, and text quality. The modeling and regression results reveal significant heterogeneity in public opinion expressions across different platforms, particularly between long-text and short-text platforms. Users on short-text platforms are more exposed to diverse information and tend to be susceptible to emotionally provocative content. On the other hand, users on long-text platforms prefer in-depth discussions and show greater receptivity to content infused with positive emotions. This study reveals the information bias brought by platform differences and contributes to data-driven modeling in social communication systems.

Scene Graph Generation (SGG) aims to detect all objects and identify their pairwise relationships in the scene. Recently, tremendous progress has been made in exploring better context relationship representations. Previous work mainly focuses on contextual information aggregation and uses de-biasing strategies on samples to eliminate the preference for head predicates. However, there remain challenges caused by indeterminate feature training. Overlooking the label confusion problem in feature training easily results in a messy feature distribution among the confused categories, thereby affecting the prediction of predicates. To alleviate the aforementioned problem, in this paper, we focus on enhancing predicate representation learning. Firstly, we propose a novel Adaptive Message Passing (AMP) network to dynamically conduct information propagation among neighbors. AMP provides discriminating representations for neighbor nodes under the view of de-noising and adaptive aggregation. Furthermore, we construct a feature-assisted training paradigm alongside the predicate classification branch, guiding predicate feature learning to the corresponding feature space. Moreover, to alleviate biased prediction caused by the long-tailed class distribution and the interference of confused labels, we design a Bi-level Curriculum learning scheme (BiC). The BiC separately considers the training from the feature learning and de-biasing levels, preserving discriminating representations of different predicates while resisting biased predictions. Results on multiple SGG datasets show that our proposed method AMP-BiC has superior comprehensive performance, demonstrating its effectiveness.

Heterogeneous information networks (HINs) are potent models of complex systems. In practice, many nodes in an HIN have their attributes unspecified, resulting in significant performance degradation for supervised and unsupervised representation learning. We developed an unsupervised heterogeneous graph contrastive learning approach for analyzing HINs with missing attributes (HGCA). HGCA adopts a contrastive learning strategy to unify attribute completion and representation learning in an unsupervised heterogeneous framework. To deal with a large number of missing attributes and the absence of labels in unsupervised scenarios, we proposed an augmented network to capture the semantic relations between nodes and attributes to achieve a fine-grained attribute completion. Extensive experiments on three large real-world HINs demonstrated the superiority of HGCA over several state-of-the-art methods. The results also showed that the complemented attributes by HGCA can improve the performance of existing HIN models.

Deepfake video detection has drawn significant attention from researchers due to the security issues induced by deepfake videos. Unfortunately, most of the existing deepfake detection approaches have not competently modeled the natural structures and movements of human faces. In this paper, we formulate the deepfake video detection problem into a graph classification task, and propose a novel paradigm named Facial Action Dependencies Estimation (FADE) for deepfake video detection. We propose a Multi-Dependency Graph Module (MDGM) to capture abundant dependencies among facial action units, and extracts subtle clues in these dependencies. MDGM can be easily integrated into the existing frame-level detection schemes to provide significant performance gains. Extensive experiments demonstrate the superiority of our method against the state-of-the-art methods.

Graph neural network (GNN) can be formulated as the multiplication of the topology-related matrix (adjacency or Laplacian matrix) and node attribute matrix, i.e., operation in node-wise. Unfortunately, this unified formula reveals two inherent drawbacks. Firstly, the topology and node attribute are not reciprocal but biased. From employment, the topology information is repeatedly employed, while the node attribute is only used once. From parameterization perspective, the node attribute is parameterized with highly expressive MLPs, while topology is not. Secondly, the graph topology can not be fully explored. Only the local pairwise relation is explored, but the mesoscopic community structure, which is one of the most prominent characteristics of networks, is ignored. To alleviate these issues, this paper proposes the Graph Reciprocal Network (GRN) by treating node attribute and topology reciprocal. Firstly, it is illustrated that the node can be regarded and utilized as another kind of attribute. Secondly, a novel node representation scheme is proposed from the theory of Quadratic Networks, with a theoretical guarantee of the fine-grained element-wise product of the representations of the topology and attribute. Extensive experiments demonstrate the superior performance and robustness of the proposed GRN.

Heterophily has been considered as an issue that hurts the performance of Graph Neural Networks (GNNs). To address this issue, some existing work uses a graph-level weighted fusion of the information of multi-hop neighbors to include more nodes with homophily. However, the heterophily might differ among nodes, which requires to consider the local topology. Motivated by it, we propose to use the local similarity (LocalSim) to learn node-level weighted fusion, which can also serve as a plug-and-play module. For better fusion, we propose a novel and efficient Initial Residual Difference Connection (IRDC) to extract more informative multi-hop information. Moreover, we provide theoretical analysis on the effectiveness of LocalSim representing node homophily on synthetic graphs. Extensive evaluations over real benchmark datasets show that our proposed method, namely Local Similarity Graph Neural Network (LSGNN), can offer comparable or superior state-of-the-art performance on both homophilic and heterophilic graphs. Meanwhile, the plug-and-play model can significantly boost the performance of existing GNNs.

Panoptic Scene Graph Generation (PSG) presents pixel-wise instance detection and localization, leading to comprehensive and precise scene graphs. Current methods employ conventional Scene Graph Generation (SGG) frameworks to solve the PSG problem, neglecting the fundamental differences between bounding boxes and masks, i.e., bounding boxes are allowed overlap but masks are not. Since segmentation from the panoptic head has deviations, non-overlapping masks may not afford complete instance information. Subsequently, in the training phase, incomplete segmented instances may not be well-aligned to annotated ones, causing mismatched relations and insufficient training. During the inference phase, incomplete segmentation leads to incomplete scene graph prediction. To alleviate these problems, we construct a novel two-stage framework for the PSG problem. In the training phase, we design a proposal matching strategy, which replaces deterministic segmentation results with proposals extracted from the off-the-shelf panoptic head for label alignment, thereby ensuring the all-matching of training samples. In the inference phase, we present an innovative concept of employing relation predictions to constrain segmentation and design a relation-constrained segmentation algorithm. By reconstructing the process of generating segmentation results from proposals using predicted relation results, the algorithm recovers more valid instances and predicts more complete scene graphs. The experimental results show overall superiority, effectiveness, and robustness against adversarial attacks.

Most Graph Neural Networks (GNNs) follow the message-passing scheme. Residual connection is an effective strategy to tackle GNNs' over-smoothing issue and performance reduction issue on non-homophilic networks. Unfortunately, the coarse-grained residual connection still suffers from class-imbalanced over-smoothing issue, due to the fixed and linear combination of topology and attribute in node representation learning. To make the combination flexible to capture complicated relationship, this paper reveals that the residual connection needs to be node-dependent, layer-dependent, and related to both topology and attribute. To alleviate the difficulty in specifying complicated relationship, this paper presents a novel perspective on GNNs, i.e., the representations of one node in different layers can be seen as a sequence of states. From this perspective, existing residual connections are not flexible enough for sequence modeling. Therefore, a novel node-dependent residual connection, i.e., Long Short-Term Graph Memory Network (LSTGM) is proposed to employ Long Short-Term Memory (LSTM), to model the sequence of node representation. To make the graph topology fully employed, LSTGM innovatively enhances the updated memory and three gates with graph topology. A speedup version is also proposed for effective training. Experimental evaluations on real-world datasets demonstrate their effectiveness in preventing over-smoothing issue and handling networks with heterophily.

Graph Neural Networks (GNNs) have been the standard toolkit for processing non-euclidean spatial data since their powerful capability in graph representation learning. Unfortunately, their training strategy for network parameters is inefficient since it is directly inherited from classic Neural Networks (NNs), ignoring the characteristic of GNNs. To alleviate this issue, experimental analyses are performed to investigate the knowledge captured in classifier parameters during network training. We conclude that the parameter features, i.e., the column vectors of the classifier parameter matrix, are cluster representations with high discriminability. And after a theoretical analysis, we conclude that the discriminability of these features is obtained from the feature propagation from nodes to parameters. Furthermore, an experiment verifies that compared with cluster centroids, the parameter features are more potential for augmenting the feature propagation between nodes. Accordingly, a novel GNN-specific training framework is proposed by simultaneously updating node representations and classifier parameters via a unified feature propagation scheme. Moreover, two augmentation schemes are implemented for the framework, named Full Propagation Augmentation (FPA) and Simplified Full Propagation Augmentation (SFPA). Specifically, FPA augmentates the feature propagation of each node with the updated classifier parameters. SFPA only augments nodes with the classifier parameters corresponding to their clusters. Theoretically, FPA is equivalent to optimizing a novel graph learning objective, which demonstrates the universality of the proposed framework to existing GNNs. Extensive experiments demonstrate the superior performance and the universality of the proposed framework.

Self-supervised learning is introduced to train graph neural networks (GNNs) by employing propagation-based GNNs designed for semi-supervised learning tasks. Unfortunately, this common choice tends to cause two serious issues. Firstly, global parameters cause the model lack the ability to capture the local property. Secondly, it is difficult to handle networks beyond homophily without label information. This paper tends to break through the common choice of employing propagation-based GNNs, which aggregate representations of nodes belonging to different classes and tend to lose discriminative information. If the propagation in each ego-network is just between the nodes from the same class, the obtained representation matrix should follow the low-rank characteristic. To meet this requirement, this paper proposes the Low-Rank Decomposition-based GNNs (LRD-GNN-Matrix) by employing Low-Rank Decomposition to the attribute matrix. Furthermore, to incorporate long-distance information, Low-Rank Tensor Decomposition-based GNN (LRD-GNN-Tensor) is proposed by constructing the node attribute tensor from selected similar ego-networks and performing Low-Rank Tensor Decomposition. The employed tensor nuclear norm facilitates the capture of the long-distance relationship between original and selected similar ego-networks. Extensive experiments demonstrate the superior performance and the robustness of LRD-GNNs.

Due to the simplicity, intuition and explanation, most Graph Neural Networks (GNNs) are proposed by following the pipeline of message passing. Although they achieve superior performances in many tasks, propagation-based GNNs possess three essential drawbacks. Firstly, the propagation tends to produce smooth effect, which meets the inductive bias of homophily, and causes two serious issues: over-smoothing issue and performance drop on networks with heterophily. Secondly, the propagations to each node are irrelevant, which prevents GNNs from modeling high-order relation, and cause the GNNs fragile to the attributes noises. Thirdly, propagation-based GNNs may be fragile to topology noise, since they heavily relay on propagation over the topology. Therefore, the propagation, as the key component of most GNNs, may be the essence of some serious issues in GNNs. To get to the root of these issue, this paper attempts to replace the propagation with a novel local operation. Quantitative experimental analysis reveals: 1) the existence of low-rank characteristic in the node attributes from ego-networks and 2) the performance improvement by reducing its rank. Motivated by this finding, this paper propose the Low-Rank GNNs, whose key component is the low-rank attribute matrix approximation in ego-network. The graph topology is employed to construct the ego-networks instead of message propagation, which is sensitive to topology noises. The proposed Low-Rank GNNs posses some attractive characteristics, including robust to topology and attribute noises, parameter-free and parallelizable. Experimental evaluations demonstrate the superior performance, robustness to noises and universality of the proposed Low-Rank GNNs.

Graph Neural Networks (GNNs) have been generalized to process the heterogeneous graphs by various approaches. Unfortunately, these approaches usually model the heterogeneity via various complicated modules. This article aims to propose a simple yet effective framework to assign adequate ability to the homogeneous GNNs to handle the heterogeneous graphs. Specifically, we propose Relation Embedding based Graph Neural Network (RE-GNN), which employs only one parameter per relation to embed the importance of distinct types of relations and node-type-specific self-loop connections. To optimize these relation embeddings and the model parameters simultaneously, a gradient scaling factor is proposed to constrain the embeddings to converge to suitable values. Besides, we interpret the proposed RE-GNN from two perspectives, and theoretically demonstrate that our RE-GCN possesses more expressive power than GTN (which is a typical heterogeneous GNN, and it can generate meta-paths adaptively). Extensive experiments demonstrate that our RE-GNN can effectively and efficiently handle the heterogeneous graphs and can be applied to various homogeneous GNNs.

Network embedding which is to learn a low dimensional representation of nodes in a network has been used in many network analysis tasks. Some network embedding methods, including those based on Generative Adversarial Networks (GAN) (a promising deep learning model), have been proposed recently. Existing GAN-based methods typically use GAN to learn a Gaussian distribution as a prior for network embedding, which makes it difficult to distinguish the node representation from Gaussian distribution. It did not apply the adversarial learning strategy on the representation mechanism but just on representation results. Thus, it does not make full use of the essential advantage of GAN, and leads to compromised performance of the method. To address this problem, we propose a novel adversarial learning framework consisting of three players for network embedding, which applies the adversarial learning strategy on the representation mechanism, called Adversarial representation mechanism GAN (ArmGAN). Specifically, the first two players, named encoder and competitor, aim to learn two different representation mechanisms (i.e., two ways projecting data onto latent space). They compete with each other to improve their representation mechanisms. The third player is the discriminator, which discriminate the representation mechanism of the encoder from that of the competitor. In addition, we design a perturbation strategy to produce fake networks from the original network, and feed the fake networks to the competitor to obtain a “fake” representation mechanism. We evaluated ArmGAN on a variety of tasks including node clustering, node classification, link prediction and visualization. Moreover, we compared ArmGAN with 10 state-of-the-art methods (including DGI, which is well-known for its high accuracy) on 7 real-world networks. The experimental results show the significant superiority of ArmGAN over the existing methods.

By interpreting Graph Neural Networks (GNNs) as the message passing from the spatial perspective, their success is attributed to Laplacian smoothing. However, it also leads to serious over-smoothing issue by stacking many layers. Recently, many efforts have been paid to overcome this issue in semi-supervised learning. Unfortunately, it is more serious in unsupervised node representation learning task due to the lack of supervision information. Thus, most of the unsupervised or self-supervised GNNs often employ \textit{one-layer GCN} as the encoder. Essentially, the over-smoothing issue is caused by the over-simplification of the existing message passing, which possesses two intrinsic limits: blind message and uniform passing. In this paper, a novel Diverse and Interactive Message Passing (DIMP) is proposed for self-supervised learning by overcoming these limits. Firstly, to prevent the message from blindness and make it interactive between two connected nodes, the message is determined by both the two connected nodes instead of the attributes of one node. Secondly, to prevent the passing from uniformness and make it diverse over different attribute channels, different propagation weights are assigned to different elements in the message. To this end, a natural implementation of the message in DIMP is the element-wise product of the representations of two connected nodes. From the perspective of numerical optimization, the proposed DIMP is equivalent to performing an overlapping community detection via expectation-maximization (EM). Both the objective function of the community detection and the convergence of EM algorithm guarantee that DMIP can prevent from over-smoothing issue. Extensive evaluations on node-level and graph-level tasks demonstrate the superiority of DIMP on improving performance and overcoming over-smoothing issue.

Graph Neural Networks have been widely employed for multimodal fusion and embedding. To overcome over-smoothing issue, residual connections, which are designed for alleviating vanishing gradient problem in NNs, are adopted in Graph Neural Networks (GNNs) to incorporate local node information. However, these simple residual connections are ineffective on networks with heterophily, since the roles of both convolutional operations and residual connections in GNNs are significantly different from those in classic NNs. By considering the specific smoothing characteristic of graph convolutional operation, deep layers in GNNs are expected to focus on the data which can't be properly handled in shallow layers. To this end, a novel and universal Difference Residual Connections (DRC), which feed the difference of the output and input of previous layer as the input of the next layer, is proposed. Essentially, Difference Residual Connections is equivalent to inserting layers with opposite effect (e.g., sharpening) into the network to prevent the excessive effect (e.g., over-smoothing issue) induced by too many layers with the similar role (e.g., smoothing) in GNNs. From the perspective of optimization, DRC is the gradient descent method to minimize an objective function with both smoothing and sharpening terms. The analytic solution to this objective function is determined by both graph topology and node attributes, which theoretically proves that DRC can prevent over-smoothing issue. Extensive experiments demonstrate the superiority of DRC on real networks with both homophily and heterophily, and show that DRC can automatically determine the model depth and be adaptive to both shallow and deep models with two complementary components.

To alleviate the unfavorable effect of noisy topology in Graph Neural networks (GNNs), some efforts perform the local topology refinement through the pairwise propagation weight learning and the multi-channel extension. Unfortunately, most of them suffer a common and fatal drawback: irrelevant propagation to one node and in multi-channels. These two kinds of irrelevances make propagation weights in multi-channels free to be determined by the labeled data, and thus the GNNs are exposed to overfitting. To tackle this issue, a novel Orthogonal Propagation with Ego-Network modeling (OPEN) is proposed by modeling relevances between propagations. Specifically, the relevance between propagations to one node is modeled by whole ego-network modeling, while the relevance between propagations in multi-channels is modeled via diversity requirement. By interpreting the propagations to one node from the perspective of dimension reduction, propagation weights are inferred from principal components of the ego-network, which are orthogonal to each other. Theoretical analysis and experimental evaluations reveal four attractive characteristics of OPEN as modeling high-order relationships beyond pairwise one, preventing overfitting, robustness, and high efficiency.

Although existing Graph Neural Networks (GNNs) based on message passing achieve state-of-the-art, the over-smoothing issue, node similarity distortion issue and dissatisfactory link prediction performance can’t be ignored. This paper summarizes these issues as the interference between topology and attribute for the first time. By leveraging the recently proposed optimization perspective of GNNs, this interference is analyzed and ascribed to that the learned representation in GNNs essentially compromises between the topology and node attribute. To alleviate the interference, this paper attempts to break this compromise by proposing a novel objective function, which fits node attribute and topology with different representations and introduces mutual exclusion constraints to reduce the redundancy in both representations. The mutual exclusion employs the statistical dependence, which regards the representations from topology and attribute as the observations of two random variables, and is implemented with Hilbert-Schmidt Independence Criterion. Derived from the novel objective function, a novel GNN, i.e., Graph Neural Network Beyond Compromise (GNN-BC), is proposed to iteratively updates the representations of topology and attribute by simultaneously capturing semantic information and removing the common information, and the final representation is the concatenation of them. The performance improvements on node classification and link prediction demonstrate the superiority of GNN-BC on relieving the interference.

Although many graph convolutional neural networks (GCNNs) have achieved superior performances in semisupervised node classification, they are designed from either the spatial or spectral perspective, yet without a general theoretical basis. Besides, most of the existing GCNNs methods tend to ignore the ubiquitous noises in the network topology and node content and are thus unable to model these uncertainties. These drawbacks certainly reduce their effectiveness in integrating network topology and node content. To provide a probabilistic perspective to the GCNNs, we model the semisupervised node classification problem as a topology-constrained probabilistic latent space model, probabilistic graph convolutional network (PGCN). By representing the nodes in a more efficient distribution form, the proposed framework can seamlessly integrate the node content and network topology. When specifying the distribution in PGCN to be a Gaussian distribution, the transductive node classification problems can be solved by the general framework and a specific method, called PGCN with the Gaussian distribution representation (PGCN-G), is proposed. To overcome the overfitting problem in covariance estimation and reduce the computational complexity, PGCN-G is further improved to PGCN-G+ by imposing the covariance matrices of all vertices to possess the identical singular vectors. The optimization algorithm based on expectation-maximization indicates that the proposed method can iteratively denoise the network topology and node content with respect to each other. Besides the effectiveness of this top-down framework demonstrated via extensive experiments, it can also be deduced to cover the existing methods, graph convolutional network, graph attention network, and Gaussian mixture model and elaborate their characteristics and relationships by specific derivations.

Many efforts have been paid to enhance Graph Convolutional Network from the perspective of propagation under the philosophy that ``Propagation is the essence of the GCNNs". Unfortunately, its adverse effect is over-smoothing, which makes the performance dramatically drop. To prevent the over-smoothing, many variants are presented. However, the perspective of propagation can't provide an intuitive and unified interpretation to their effect on prevent over-smoothing. In this paper, we aim at providing a novel explanation to the question of "Why do attributes propagate in GCNNs?''. which not only gives the essence of the oversmoothing, but also illustrates why the GCN extensions, including multi-scale GCN and GCN with initial residual, can improve the performance. To this end, an intuitive Graph Representation Learning (GRL) framework is presented. GRL simply constrains the node representation similar with the original attribute, and encourages the connected nodes possess similar representations (pairwise constraint). Based on the proposed GRL, exiting GCN and its extensions can be proved as different numerical optimization algorithms, such as gradient descent, of our proposed GRL framework. Inspired by the superiority of conjugate gradient descent compared to common gradient descent, a novel Graph Conjugate Convolutional (GCC) network is presented to approximate the solution to GRL with fast convergence. Specifically, GCC adopts the obtained information of the last layer, which can be represented as the difference between the input and output of the last layer, as the input to the next layer. Extensive experiments demonstrate the superior performance of GCC.

Graph Neural Networks (GNNs) have achieved tremendous success in graph representation learning. Unfortunately, current GNNs usually rely on loading the entire attributed graph into network for processing. This implicit assumption may not be satisfied with limited memory resources, especially when the attributed graph is large. In this paper, we pioneer to propose a Binary Graph Convolutional Network (Bi-GCN), which binarizes both the network parameters and input node features. Besides, the original matrix multiplications are revised to binary operations for accelerations. According to the theoretical analysis, our Bi-GCN can reduce the memory consumption by an average of ~30x for both the network parameters and input data, and accelerate the inference speed by an average of ~47x, on the citation networks. Meanwhile, we also design a new gradient approximation based back-propagation method to train our Bi-GCN well. Extensive experiments have demonstrated that our Bi-GCN can give a comparable performance compared to the full-precision baselines. Besides, our binarization approach can be easily applied to other GNNs, which has been verified in the experiments.

Most attempts on extending Graph Neural Networks (GNNs) to Heterogeneous Information Networks (HINs) implicitly take the direct assumption that the multiple homogeneous attributed networks induced by different meta-paths are complementary. The doubts about the hypothesis of complementary motivate an alternative assumption of consensus. That is, the aggregated node attributes shared by multiple homogeneous attributed networks are essential for node representations, while the specific ones in each homogeneous attributed network should be discarded. In this paper, a novel Heterogeneous Graph Information Bottleneck (HGIB) is proposed to implement the consensus hypothesis in an unsupervised manner. To this end, information bottleneck (IB) is extended to unsupervised representation learning by leveraging self-supervision strategy. Specifically, HGIB simultaneously maximizes the mutual information between one homogeneous network and the representation learned from another homogeneous network, while minimizes the mutual information between the specific information contained in one homogeneous network and the representation learned from this homogeneous network. Model analysis reveals that the two extreme cases of HGIB correspond to the supervised heterogeneous GNN and the infomax on homogeneous graph, respectively. Extensive experiments on real datasets demonstrate that the consensus-based unsupervised HGIB significantly outperforms most semi-supervised SOTA methods based on complementary assumption.

Most of the existing GNNs can be modeled via the Uniform Message Passing framework. This framework considers all the attributes of each node in its entirety, shares the uniform propagation weights along each edge, and focuses on the uniform weight learning. The design of this framework possesses two prerequisites, the simplification of homophily and heterophily to the node-level property and the ignorance of attribute differences. Unfortunately, different attributes possess diverse characteristics. In this paper, the network homophily rate defined with respect to the node labels is extended to attribute homophily rate by taking the attributes as weak labels. Based on this attribute homophily rate, we propose a Diverse Message Passing (DMP) framework, which specifies every attribute propagation weight on each edge. Besides, we propose two specific strategies to significantly reduce the computational complexity of DMP to prevent the overfitting issue. By investigating the spectral characteristics, existing spectral GNNs are actually equivalent to a degenerated version of DMP. From the perspective of numerical optimization, we provide a theoretical analysis to demonstrate DMP's powerful representation ability and the ability of alleviating the over-smoothing issue. Evaluations on various real networks demonstrate the superiority of our DMP on handling the networks with heterophily and alleviating the over-smoothing issue, compared to the existing state-of-the-arts.

Heterogeneous information networks (HINs), also called heterogeneous graphs, are composed of multiple types of nodes and edges, and contain comprehensive information and rich semantics. Graph neural networks (GNNs), as powerful tools for graph data, have shown superior performance on network analysis. Recently, many excellent models have been proposed to process hetero-graph data using GNNs and have achieved great success. These GNN-based heterogeneous models can be interpreted as smooth node attributes guided by graph structure, which requires all nodes to have attributes. However, this is not easy to satisfy, as some types of nodes often have no attributes in heterogeneous graphs. Previous studies take some handcrafted methods to solve this problem, which separate the attribute completion from the graph learning process and, in turn, result in poor performance. In this paper, we hold that missing attributes can be acquired by a learnable manner, and propose a general framework for Heterogeneous Graph Neural Network via Attribute Completion (HGNN-AC), including pre-learning of topological embedding and attribute completion with attention mechanism. HGNN-AC first uses existing HIN-Embedding methods to obtain node topological embedding. Then it uses the topological relationship between nodes as guidance to complete attributes for no-attribute nodes by weighted aggregation of the attributes from these attributed nodes. Our complement mechanism can be easily combined with an arbitrary GNN-based heterogeneous model making the whole system end-to-end. We conduct extensive experiments on three real-world heterogeneous graphs. The results demonstrate the superiority of the proposed framework over state-of-the-art baselines.

Most of the existing Graph Neural Networks (GNNs) are deliberately designed for semi-supervised learning tasks, where supervision information (labelled node) is utilized to mitigate the oversmoothing problem of message passing. Unfortunately, the oversmoothing problem tends to be more severe in unsupervised tasks, since supervision information is not available. Since community structure/cluster is an essential characteristic of network, a natural approach to reduce the oversmoothing problem is to also constrain the node embeddings to maintain their own characteristics to prevent all the node embeddings from becoming too similar to be distinguished. In this paper, a novel Optimal Transport based Graph Neural Network (OT-GNN) is proposed to overcome the oversmoothing problem in unsupervised GNNs by imposing the equal-sized clustering constraints to the obtained node embeddings. To solve the combinatorial optimization problem, the constrained objective function of unsupervised GNN is relaxed to an Optimal Transport problem, and a fast version of the Sinkhorm-Knopp algorithm is adopted to handle large networks. Extensive experiments on node clustering and classification demonstrate the superior performance of our proposed OT-GNN.

Motivated by the capability of Generative Adversarial Network on exploring the latent semantic space and capturing semantic variations in the data distribution, adversarial learning has been adopted in network embedding to improve the robustness. However, this important ability is lost in existing adversarially regularized network embedding methods, because their embedding results are directly compared to the samples drawn from perturbation (Gaussian) distribution without any rectification from real data. To overcome this vital issue, a novel Joint Adversarial Network Embedding (JANE) framework is proposed to jointly distinguish the real and fake combinations of the embeddings, topology information and node features. JANE contains three pluggable components, Embedding module, Generator module and Discriminator module. The overall objective function of JANE is defined in a min-max form, which can be optimized via alternating stochastic gradient. Extensive experiments demonstrate the remarkable superiority of the proposed JANE on link prediction (3% gains in both AUC and AP) and node clustering (5% gain in F1 score).

Network embedding which is to learn a low dimensional representation of nodes in a network has been used in many network analysis tasks. Some network embedding methods, including those based on generative adversarial networks (GAN) (a promising deep learning technique), have been proposed recently. Existing GAN-based methods typically use GAN to learn a Gaussian distribution as a priori for network embedding. However, this strategy makes it difficult to distinguish the node representation from Gaussian distribution. Moreover, it does not make full use of the essential advantage of GAN (that is to adversarially learn the representation mechanism rather than the representation itself), leading to compromised performance of the method. To address this problem, we propose to use the adversarial idea on the representation mechanism, i.e. on the encoding mechanism under the framework of autoencoder. Specifically, we use the mutual information between node attributes and embedding as a reasonable alternative of this encoding mechanism (which is much easier to track). Additionally, we introduce another mapping mechanism (which is based on GAN) as a competitor into the adversarial learning system. A range of empirical results demonstrate the effectiveness of the proposed approach.

The allocation of epidemic-control resources has been an increasingly active topic in the physical world. Most existing studies focus on the allocation of abstract and continuous epidemic control resources, and then formulate differentiable convex programming problems. However, real-world resources are usually discrete materials, goods, or services, so that resource allocation problems become non-convex. As a complementary study, this paper builds three discrete resource allocation problems based on an improved Susceptible-Exposed-Infectious- Vigilant (SEIV) spread model: the cost-constraint optimization problem (CCOP), rate-constraint optimization problem (RCOP), and eradication optimization problem (EOP). Then, existing swarm-based metaheuristic algorithms are adapted to effectively solve the problems. Thereinto, the Heuristic Majority-Voting Binary Particle Swarm Optimizer (HMV-BPSO) is present, which introduces a heuristic factor which concerns the probability distribution of resources to guide the evolution of particles and helps improve the performance of original MV-BPSO. Numerical experiments are developed to verify the effectiveness of swarm- based metaheuristic algorithms on epidemic control. Results show that HMV-BPSO can produce higher-quality solutions than other algorithms.

Existing topic modeling approaches possess several issues, including the overfitting issue of Probablistic Latent Semantic Indexing (pLSI), the failure of capturing the rich topical correlations among topics in Latent Dirichlet Allocation (LDA), and high inference complexity. In this paper, we provide a new method to overcome the overfitting issue of pLSI by using the amortized inference with word embedding as input, instead of the Dirichlet prior in LDA. For generative topic model, the large number of free latent variables is the root of overfitting. To reduce the number of parameters, the amortized inference replaces the inference of latent variable with a function which possesses the shared (amortized) learnable parameters. The number of the shared parameters is fixed and independent of the scale of the corpus. To overcome the limited application of amortized inference to independent and identically distributed (i.i.d) data, a novel graph neural network, Graph Attention TOpic Network (GATON), is proposed to model the topic structure of non-i.i.d documents according to the following two observations. First, pLSI can be interpreted as stochastic block model (SBM) on a specific bi-partite graph. Second, graph attention network (GAT) can be explained as the semi-amortized inference of SBM, which relaxes the i.i.d data assumption of vanilla amortized inference. GATON provides a novel scheme, i.e. graph convolution operation based scheme, to integrate word similarity and word co-occurrence structure. Specifically, the bag-of-words document representation is modeled as a bi-partite graph topology. Meanwhile, word embedding, which captures the word similarity, is modeled as attribute of the word node and the term frequency vector is adopted as the attribute of the document node. Based on the weighted (attention) graph convolution operation, the word co-occurrence structure and word similarity patterns are seamlessly integrated for topic identification. Extensive experiments demonstrate that the effectiveness of GATON on topic identification not only benefits the document classification, but also significantly refines the input word embedding.

Multi-view scene analysis has been widely explored in computer vision, including numerous practical applications. The texts in multi-view scenes are often detected by following the existing text detection method in a single image, which however ignores the multi-view corresponding constraint. The multi-view correspondences may contain structure, location information and assist difficulties induced by factors like occlusion and perspective distortion, which are deficient in the single image scene. In this paper, we address the corresponding text detection task and propose a novel text co-detection method to identify the cooccurring texts among multi-view scene images with compositions of detection and correspondence under large environmental variations. In our text co-detection method, the visual and geometrical correspondences are designed to explore texts holding high pairwise representation similarity and guide the exploitation of texts with geometrical correspondences, simultaneously. To guarantee the pairwise consistency among multiple images, we additionally incorporate the cycle consistency constraint, which guarantees alignments of text correspondences in the image set. Finally, text correspondence is represented by a permutation matrix and solved via positive semidefinite and low-rank constraints. Moreover, we also collect a new text co-detection dataset consisting of multi-view image groups obtained from the same scene with different photographing conditions. The experiments show that our text co-detection obtains satisfactory performance and outperforms the related state-of-the-art text detection methods.

Semi-supervised representation-based subspace clustering is to partition data into their underlying subspaces by finding effective data representations with partial supervisions. Essentially, an effective and accurate representation should be able to uncover and preserve the true data structure. Meanwhile, a reliable and easy-to-obtain supervision is desirable for practical learning. To meet these two objectives, in this paper we make the first attempt towards utilizing the orderly relationship, such as the data a is closer to b than to c, as a novel supervision. We propose an orderly subspace clustering approach with a novel regularization term. OSC enforces the learned representations to simultaneously capture the intrinsic subspace structure and reveal orderly structure that is faithful to true data relationship. Experimental results with several benchmarks have demonstrated that aside from more accurate clustering against state-of-the-arts, OSC interprets orderly data structure which is beyond what current approaches can offer.

The purpose of network embedding is to learn a low-dimensional representation for each node in the network. One can then use this low-dimensional representation to solve some network analysis tasks, such as node classification and node clustering. At present, there are several network embedding learning methods based on GAN (Generative Adversarial Networks) to enhance the robustness of representations. However, these methods have two drawbacks. First, they are often too difficult to be trained stably. Second, they only learn the robust representations by matching the posterior distribution of the latent representations to the given priors. On the contrary, Capsule Networks can learn a more equivariant representation of images that is more robust to the changes in pose and spatial relationships of parts of objects in images. However, there is still no research using Capsule Network for network embedding since the social network is essentially different from images. For this problem, we propose a new approach of adversarial capsule learning (ACL) for network embedding, which is the first time to use Capsule Network in the network analysis tasks. To be specific, the new model consists of two parts, a generator and discriminator. We use Graph Convolutional Networks (GCN) as the generator to learn the embedding of nodes, and use Capsule Network as the discriminator to distinguish between the real and fake samples as accurately as possible. The experimental results demonstrate the effectiveness of the proposed new method.

The success of graph convolutional neural networks (GCNNs) based semi-supervised node classification is credited to the attribute smoothing (propagating) over the topology. However, the attributes may be interfered by the utilization of the topology information. This distortion will induce a certain amount of misclassifications of the nodes, which can be correctly predicted with only the attributes. By analyzing the impact of the edges in attribute propagations, the simple edges, which connect two nodes with similar attributes, should be given priority during the training process compared to the complex ones according to curriculum learning. To reduce the distortions induced by the topology while exploit more potentials of the attribute information, Dual Self-Paced Graph Convolutional Network (DSP-GCN) is proposed in this paper. Specifically, the unlabelled nodes with confidently predicted labels are gradually added into the training set in the node-level self-paced learning, while edges are gradually, from the simple edges to the complex ones, added into the graph during the training process in the edge-level self-paced learning. These two learning strategies are designed to mutually reinforce each other by coupling the selections of the edges and unlabelled nodes. Experimental results of transductive semi-supervised node classification on many real networks indicate that the proposed DSP-GCN has successfully reduced the attribute distortions induced by the topology while it gives superior performances with only one graph convolutional layer.

In the past few years, semi-supervised node classification in attributed network has been developed rapidly. Inspired by the success of deep learning, researchers adopt the convolutional neural network to develop the Graph Convolutional Networks (GCN), and they have achieved surprising classification accuracy by considering the topological information and employing the fully connected network (FCN). However, the given network topology may also induce a performance degradation if it is directly employed in classification, because it may possess high sparsity and certain noises. Besides, the lack of learnable filters in GCN also limits the performance. In this paper, we propose a novel Topology Optimization based Graph Convolutional Networks (TO-GCN) to fully utilize the potential information by jointly refining the network topology and learning the parameters of the FCN. According to our derivations, TO-GCN is more flexible than GCN, in which the filters are fixed and only the classifier can be updated during the learning process. Extensive experiments on real attributed networks demonstrate the superiority of the proposed TO-GCN against the state-of-the-art approaches.

Semi-supervised classification is a fundamental technology to process the structured and unstructured data in machine learning field. The traditional attribute-graph based semi-supervised classification methods propagate labels over the graph which is usually constructed from the data features, while the graph convolutional neural networks smooth the node attributes, i.e., propagate the attributes, over the real graph topology. In this paper, they are interpreted from the perspective of propagation, and accordingly categorized into symmetric and asymmetric propagation based methods. From the perspective of propagation, both the traditional and network based methods are propagating certain objects over the graph. However, different from the label propagation, the intuition ``the connected data samples tend to be similar in terms of the attributes", in attribute propagation is only partially valid. Therefore, a masked graph convolution network (Masked GCN) is proposed by only propagating a certain portion of the attributes to the neighbours according to a masking indicator, which is learned for each node by jointly considering the attribute distributions in local neighbourhoods and the impact on the classification results. Extensive experiments on transductive and inductive node classification tasks have demonstrated the superiority of the proposed method.

Existing person re-identification methods usually directly calculate the similarities of person pictures regardless of their viewpoints. However, matching persons under different viewpoints is difficult since it is intrinsically hard to directly learn a representation which is geometrically invariant to large viewpoint variations. In this paper, we explicitly take viewpoint information into account and propose a novel Deep Residual Equivariant Mapping and Fine-grained Features (DREMFF) approach for viewpoint-robust person re-identification. Specifically, DREMFF hypothesizes that there exists inherent mapping between different viewpoints of a person, and consequently, the global representation discrepancy of a person under different viewpoints will be bridged through equivariant mapping by adaptively adding residuals to original representation according corresponding angle deviation. What's more, based on attention mechanism, DREMFF extracts fine-grained features for each image from multiple salient regions as well as different scales. These captured information is capable of providing assistant decision-making at lower granularities. The mapped global features and the learned fine-grained features work collaboratively to enable viewpoint-robust person re-identification. Experiments on three challenging benchmarks consistently demonstrate the effectiveness of the proposed approach.

Topic models have many important applications in fields such as Natural Language Processing. Topic embedding modelling aims at introducing word and topic embeddings into topic models to describe correlations between topics. Existing topic embedding methods use documents alone, which suffer from the topical fuzziness problem brought by the introduction of embeddings of semantic fuzzy words, e.g. polysemous words or some misleading academic terms. Links often exist between documents which form document networks. The use of links may alleviate this semantic fuzziness, but they are sparse and noisy which may meanwhile mislead topics. In this paper, we utilize community structure to solve these problems. It can not only alleviate the topical fuzziness of topic embeddings since communities are often believed to be topic related, but also can overcome the drawbacks brought by the sparsity and noise of networks (because community is a high-order network information). We give a new generative topic embedding model which incorporates documents (with topics) and network (with communities) together, and uses probability transition to describe the relationship between topics and communities to make it robust when topics and communities do not match. An efficient variational inference algorithm is then proposed to learn the model. We validate the superiority of our new approach on two tasks, document classifications and visualization of topic embeddings, respectively.

In network analysis, community detection and network embedding are two important topics. Community detection tends to obtain the most noticeable partition, while network embedding aims at seeking node representations which contains as many diverse properties as possible. We observe that the current community detection and network embedding problems are being resolved by a general solution, i.e., "maximizing the consistency between similar nodes while maximizing the distance between the dissimilar nodes." This general solution only exploits the most noticeable structure (facet) of the network, which effectively satisfies the demands of the community detection. Unfortunately, most of the specific embedding algorithms, which are developed from the general solution, cannot achieve the goal of network embedding by exploring only one facet of the network. To improve the general solution for better modeling the real network, we propose a novel network embedding method, Multi-facet Network Embedding (MNE), to capture the multiple facets of the network. MNE learns multiple embeddings simultaneously, with the Hilbert Schmidt Independence Criterion (HSIC) being the a diversity constraint. To efficiently solve the optimization problem, we propose a Binary HSIC with linear complexity and solve the MNE objective function by adopting the Augmented Lagrange Multiplier (ALM) method. The overall complexity is linear with the scale of the network. Extensive results demonstrate that MNE gives efficient performances and outperforms the state-of-the-art network embedding methods.

Combinational network embedding, which learns the node representation by exploring both topological and non-topological information, becomes popular due to the fact that the two types of information are complementing each other. Most of the existing methods either consider the topological and non-topological information being aligned or possess predetermined preferences during the embedding process.Unfortunately, previous methods fail to either explicitly describe the correlations between topological and non-topological information or adaptively weight their impacts. To address the existing issues, three new assumptions are proposed to better describe the embedding space and its properties. With the proposed assumptions, nodes, communities and topics are mapped into one embedding space. A novel generative model is proposed to formulate the generation process of the network and content from the embeddings, with respect to the Bayesian framework. The proposed model automatically leans to the information which is more discriminative.The embedding result can be obtained by maximizing the posterior distribution by adopting the variational inference and reparameterization trick. Experimental results indicate that the proposed method gives superior performances compared to the state-of-the-art methods when a variety of real-world networks is analyzed.

Network embedding is to learn a low-dimensional representation for a network in order to capture intrinsic features of the network. It has been applied to many applications, e.g., network community detection and user recommendation. One of the recent research topics for network embedding has been focusing on exploitation of diverse information, including network topology and semantic information on nodes of networks. However, such diverse information has not been fully utilized nor adequately integrated in the existing methods, so that the resulting network embedding is far from satisfactory. In this paper, we develop a weight-free multi-component network embedding approach by network reconstruction via a deep Autoencoder. Three key components make our new approach effective, i.e., a uniformed graph representation of network topology and semantic information, enhancement to the graph representation using local network structure (i.e., pairwise relationship on nodes) by sampling with latent space regularization, and integration of the diverse information in graph forms in a deep Autoencoder. Extensive experimental results on seven real-world networks demonstrate a superior performance of our method over nine state-of-the-art methods for embedding.

Video-based person re-identification (re-id) has attracted a lot of research interest. When facing dramatic growth in new pedestrian videos, existing video-based person re-id methods usually need large quantities of labeled pedestrian videos to train a discriminative model. In practice, labeling large quantities of pedestrian videos is a costly and time-consuming task, which will limit the application of these methods in the real environment. Therefore, it is valuable and necessary to investigate how to learn a discriminative re-id model by using limited labeled training pedestrian videos. In this paper, we propose a semi-supervised cross-view projection-based dictionary learning (SCPDL) approach for video-based person re-id. Specifically, SCPDL jointly learns a pair of feature projection matrices and a pair of dictionaries by integrating the information contained in labeled and unlabeled pedestrian videos. With the learned feature projection matrices, the influence of variations within each video to the re-id can be reduced. With the learned dictionary pair, pedestrian videos from two different cameras can be converted into coding coefficients in a common representation space, such that the differences between different cameras can be bridged. In the learning process, the labeled pedestrian videos are used to ensure that the learned dictionaries have favorable discriminability; the large quantities of unlabeled pedestrian videos are used to ensure that SCPDL can better capture the variations between pedestrian videos, such that the learned dictionaries can own stronger representative capability. Experiments on two public pedestrian sequence data sets (iLIDS-VID and PRID 2011) demonstrate the effectiveness of the proposed approach.

Real data are usually complex and contain various components. For example, face images have expressions and genders. Each component mainly reflects one aspect of data and provides information others do not have. Therefore, exploring the semantic information of multiple components as well as the diversity among them is of great benefit to understand data comprehensively and in-depth. However, this cannot be achieved by current nonnegative matrix factorization (NMF)-based methods, despite that NMF has shown remarkable competitiveness in learning parts-based representation of data. To overcome this limitation, we propose a novel multi-component nonnegative matrix factorization (MCNMF). Instead of seeking for only one representation of data, MCNMF learns multiple representations simultaneously, with the help of the Hilbert Schmidt Independence Criterion (HSIC) as a diversity term. HSIC explores the diverse information among the representations, where each representation corresponds to a component. By integrating the multiple representations, a more comprehensive representation is then established. A new iterative updating optimization scheme is derived to solve the objective function of MCNMF, along with its correctness and convergence guarantees. Extensive experimental results on real-world datasets have shown that MCNMF not only achieves more accurate performance over the state-of-the-arts using the aggregated representation, but also interprets data from different aspects with the multiple representations, which is beyond what current NMFs can offer.

Recent methods for object co-segmentation focus on discovering single co-occurring relation of candidate regions representing the foreground of multiple images. However, region extraction based only on low and middle level information often occupies a large area of background without the help of semantic context. In addition, seeking single matching solution very likely leads to discover local parts of common objects. To cope with these deficiencies, we present a new object co-segmentation framework, which takes advantages of semantic information and globally explores multiple co-occurring matching cliques based on an N-partite graph structure. To this end, we first propose to incorporate candidate generation with semantic context. Based on the regions extracted from semantic segmentation of each image, we design a merging mechanism to hierarchically generate candidates with high semantic responses. Second, all candidates are taken into consideration to globally formulate multiple maximum weighted matching cliques, which complement the discovery of part of the common objects induced by a single clique. To facilitate the discovery of multiple matching cliques, an N-partite graph, which inherently excludes intralinks between candidates from the same image, is constructed to separate multiple cliques without additional constraints. Further, we augment the graph with an additional virtual node in each part to handle irrelevant matches when the similarity between the two candidates is too small. Finally, with the explored multiple cliques, we statistically compute pixel-wise co-occurrence map for each image. Experimental results on two benchmark data sets, i.e., iCoseg and MSRC data sets achieve desirable performance and demonstrate the effectiveness of our proposed framework.

Identification of modular or community structures of a network is a key to understanding the semantics and functions of the network. While many network community detection methods have been developed, which primarily explore network topologies, they provide little semantic information of the communities discovered. Although structures and semantics are closely related, little effort has been made to discover and analyze these two essential network properties together. By integrating network topology and semantic information on nodes, e.g., node attributes, we study the problems of detection of communities and inference of their semantics simultaneously. We propose a novel nonnegative matrix factorization (NMF) model with two sets of parameters, the community membership matrix and community attribute matrix, and present efficient updating rules to evaluate the parameters with a convergence guarantee. The use of node attributes improves upon community detection and provides a semantic interpretation to the resultant network communities. Extensive experimental results on synthetic and real-world networks not only show the superior performance of the new method over the state-of-the-art approaches, but also demonstrate its ability to semantically annotate the communities.

Moving object detection is one of the most fundamental tasks in computer vision. Many classic and contemporary algorithms work well under the assumption that backgrounds are stationary and movements are continuous, but degrade sharply when they are used in a real detection system, mainly due to: 1) the dynamic background (e.g., swaying trees, water ripples and fountains in real scenarios, as well as raindrops and snowflakes in bad weather) and 2) the irregular object movement (like lingering objects). This paper presents a unified framework for addressing the difficulties mentioned above, especially the one caused by irregular object movement. This framework separates dynamic background from moving objects using the spatial continuity of foreground, and detects lingering objects using the temporal continuity of foreground. The proposed framework assumes that the dynamic background is sparser than the moving foreground that has smooth boundary and trajectory. We regard the observed video as being made up of the sum of a low-rank static background, a sparse and smooth foreground, and a sparser dynamic background. To deal with this decomposition, i.e., a constrained minimization problem, the augmented Lagrangian multiplier method is employed with the help of the alternating direction minimizing strategy. Extensive experiments on both simulated and real data demonstrate that our method significantly outperforms the state-of-the-art approaches, especially for the cases with dynamic backgrounds and discontinuous movements.

People counting in extremely dense crowds is an important step for video surveillance and anomaly warning. The problem becomes especially more challenging due to the lack of training samples, severe occlusions, cluttered scenes and variation of perspective. Existing methods either resort to auxiliary human and face detectors or surrogate by estimating the density of crowds. Most of them rely on hand-crafted features, such as SIFT, HOG etc, and thus are prone to fail when density grows or the training sample is scarce. In this paper we propose an end-to-end deep convolutional neural networks (CNN) regression model for counting people of images in extremely dense crowds. Our method has following characteristics. Firstly, it is a deep model built on CNN to automatically learn effective features for counting. Besides, to weaken influence of background like buildings and trees, we purposely enrich the training data with expanded negative samples whose ground truth counting is set as zero. With these negative samples, the robustness can be enhanced. Extensive experimental results show that our method achieves superior performance than the state-of-the-arts in term of the mean and variance of absolute difference.

Community structure is one of the most important properties of complex networks and is a foundational concept in exploring and understanding networks. In real world, topology information alone is often inadequate to accurately find community structure due to its sparsity and noises. However, potential useful prior information can be obtained from domain knowledge in many applications. Thus, how to improve the community detection performance by combining network topology with prior information becomes an interesting and challenging problem. Previous efforts on utilizing such priors are either dedicated or insufficient. In this paper, we firstly present a unified interpretation to a group of existing community detection methods. And then based on this interpretation, we propose a unified semi-supervised framework to integrate network topology with prior information for community detection. If the prior information indicates that some nodes belong to the same community, we encode it by adding a graph regularization term to penalize the latent space dissimilarity of these nodes. This framework can be applied to many widely-used matrix-based community detection methods satisfying our interpretation, such as nonnegative matrix factorization, spectral clustering, and their variants. Extensive experiments on both synthetic and real networks show that the proposed framework significantly improves the accuracy of community detection, especially on networks with unclear structures.