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This paper proposes a spherical evolution algorithm with two-stage search. Spherical search and hypercube search are combined to achieve individuals' evolution. A self-adaptive Gaussian scale factor and a variable scale factor are designed to adaptively control individuals' spherical and hypercube search area according to their search situations. Two search stages frequently switch with four search cases to enhance the balance between exploration and exploitation processes. A directed adjacency matrix is devised to analyze the relationship among individuals from the perspective of graph theory. Experiments compare the proposed algorithm with five algorithms with distinctive search patterns on twenty nine CEC2017 benchmark functions. The diversity analysis and graph theory analysis show the good population diversity and effective information spreading of the proposed algorithm. Twenty two real-world problems evaluate the practicality and optimization ability of the proposed algorithm. Finally, the computational time complexity demonstrates that the proposed algorithm is more efficient than the original spherical evolution algorithm. • A spherical evolution algorithm with two-stage search is proposed. • Spherical search and hypercube search are combined to adaptively guide individuals' evolution. • A directed adjacency matrix is firstly introduced to analyze the relationship among individuals. • Functions and real-world problems verify the superior search performance of the proposed algorithm. • The computational efficiency of the proposed algorithm is enhanced. [ABSTRACT FROM AUTHOR]

The intrinsic dimension (ID) of a data set is crucial for data processing, especially for high-dimensional data sets. In order to obtain an accurate ID estimate, two neighborhoods of sample points with a radius ratio of k are considered. The ratio of the number of sample points contained in the two neighborhoods is denoted as q ∊ . When the data set is located on a d -dimensional submanifold in R D , the expected value of q ∊ is k d . Based on this consideration, we redefine the adjacency matrix by using the local adjacency information of sample points and propose a new ID estimation method known as ID(k). The ID(k) algorithm contains only one parameter, the scaling ratio k , and we outline the criterion through which the user can select an appropriate k value. We demonstrate the convergence of the new method both theoretically and experimentally. Experimental results from artificial and real data sets show that the estimates obtained by this new ID(k) method are closer to the true intrinsic dimension than those derived using similar methods. [ABSTRACT FROM AUTHOR]

• We use three different features to calculate the dynamic adjacency matrix correlated with the dynamic correlation matrix. • We design a novel deep learning-based framework to learn dynamic spatio-temporal dependencies. • We conduct experiments on two real-world datasets in predicting urban traffic flow and traffic speed, respectively. • We collect two cities' traffic data, and make predictions for traffic flow and speed, respectively. Moreover, we conduct ablation study to prove the effectiveness of each module. Accurate urban traffic prediction is a critical issue in Intelligent Transportation Systems (ITS). It is challenging since urban traffic usually indicates high dynamic spatio-temporal correlations, leading to uncertainty and complexity of traffic status. Since the transportation network is a graph structure practically, existing works have applied Graph Convolutional Network (GCN) on urban traffic prediction with a pre-defined adjacency matrix based on node distance or connectivity. However, in many urban traffic scenarios, spatio-temporal dependencies among traffic data usually change over time, so using a fixed adjacency matrix cannot describe the dynamic dependencies. To track the dynamic spatio-temporal dependencies among traffic data, we propose a novel deep learning framework, Dynamic Traffic Correlation-based Spatio-Temporal Graph Convolutional network (DTC-STGCN), to forecast traffic flow and speed accurately. DTC-STGCN extracts a dynamic adjacency matrix from different traffic characters to describe dynamic spatio-temporal correlations. Moreover, an attention and dynamic adjacency matrix-based GCNs framework is proposed to capture urban traffic dynamic spatial features, while a long-short-term memory network (LSTM) is used to capture urban traffic temporal features, respectively. Finally, we feed the spatio-temporal features generated by GCN and LSTM, with real road segments into a hybrid graph convolution framework to simultaneously model the dynamic spatial and temporal dependencies for traffic predictions. The experiments on two real-world datasets demonstrate that the proposed DTC-STGCN model consistently outperforms the state-of-the-art traffic prediction baselines on MAE and RMSE over 10%, and achieve a stable performance for two specific tasks (long-term traffic prediction and peak time prediction). And ablation study validates the effectiveness of dynamic adjacency matrix, attention mechanism, respectively. [ABSTRACT FROM AUTHOR]

• Differential privacy protection based on community density aggregation and matrix perturbation. • Well-designed community detection algorithm to realize the node label aggregation. • Design the appropriate algorithms according to the different density of the divided regions. • Improve the efficiency of publishing social privacy data and enhance the data utility. With the development and popularity of social networks, the security issues of personal data await effective solution. We propose a differential privacy protection scheme for social network data based on community density aggregation and matrix perturbation (MPCD) and introduce the correlation coefficient k to preserve differential privacy and availability of edge-related data. We adopt a community structure rapid identification algorithm to identify social network structure labels, to realize the label aggregation of community nodes. Combined with the structure of a binary tree, we use the adaptive method to identify the dense regions for the generated upper triangular adjacency matrix. We perturb the edge connection probability of the identified dense regions and reconstruct a disturbed adjacency matrix by edge optimal allocation to publish the final network graph, which can improve the efficiency of the algorithm and data availability. In addition, we experimentally evaluate our approach on four social network datasets and show that the published network graph has better data availability and privacy protection, with higher execution efficiency than the four classical schemes. [ABSTRACT FROM AUTHOR]

As a fundamental problem in network science, link prediction is both theoretically significant and practically useful. Many existing link prediction algorithms rely on predefined assumptions about the link formation mechanism of the network, limiting their generalizability. The recently proposed Network Self-Representation (NSR) model avoids such predefined assumptions by representing the likelihood of link existence between two nodes as a linear transformation of their neighboring connections, resulting in a more generic link prediction approach. To further improve the self-learning capability, this study proposes an Extended Network Self-Representation (ENSR) model. Instead of leveraging a linear transformation as the NSR function, the ENSR model considers the likelihood of link existence as a general function of the adjacency matrix. This study further formulates the ENSR model as an optimization model and analytically derives a critical property of its optimal solution, based on which the optimal ENSR function is approximated by polynomial regression. Experiments on 15 real-world networks show that our proposed ENSR model achieves better link prediction performance than the NSR model as well as several other benchmark algorithms. Notably, the ENSR function's coefficients match the contributions of multi-hop paths to link prediction. In most cases, the self-learned coefficients by the ENSR model align with the predefined assumptions of the second-best link prediction algorithms, which implies that the ENSR model can adaptively discover the underlying link formation mechanisms of complex networks. • Link existence likelihood is modeled as a general function of the adjacency matrix. • The property of the optimal self-representation function is analytically derived. • Better link prediction performance is achieved. • The proposed model can adaptively discover the link formation mechanisms. [ABSTRACT FROM AUTHOR]

How to automatically mining the spatial association patterns in spatial data is a challenging task in spatial data mining. In this paper, we propose three indices that represent the per-class, inter-class, and overall spatial associations of a nominal variable, which are based on the conditional probabilities of surface object categories. These indices represent relative quantities and are normalized to the region [ − 1 , 1 ] , which more accord with the intuitive cognition of people. We present some algorithms for detecting spatial associations that are based on these indices. The proposed method can be regarded as an extension of join count statistics and Transiogram. Several constructive examples were used to illustrate the advantages of the new method. Using two real data sets, vegetation types in Qingxian, Shanxi, China and neural tube birth defects in Heshun, Shanxi, China, we ran comparative experiments with other commonly used methods, including join count statistics, co-location quotient, and Q ( m ) statistics. The experimental results show that the proposed method can detect more subtle spatial associations, and is not sensitive to the sequence of neighbors. [ABSTRACT FROM AUTHOR]

Spectral clustering aims to minimise inter-cluster similarity by constructing graph model, which possesses a significant effect in data of arbitrary shape. Nonetheless, there are still two limitations in the existing algorithms. First, spectral methods perform poorly if the densities of instances vary greatly. Second, they are challenging to handle the complex distribution that different objects of densities are mixed. To address the two limitations, in this paper, a novel spectral clustering algorithm is constructed to accommodate more complex multi-density data. The idea of density stratification is proposed through the probability density of Gaussian mixture model, and the number of layers can be automatically determined by the defined scatter index. Then, a new density ratio is established to effectively reduce the density imbalance of diverse instances based on mutual nearest-neighbour and density stratification, which is more advantageous in the clusters with less clear boundaries. Finally, the optimised adjacency matrix and multi-density spectral clustering algorithm are induced to improve the effect of multi-density data. As per experimental results, the proposed algorithm generally outperforms the popular representative algorithms for both synthetic and benchmark datasets, and works more effectively on multi-density as well as single-density data, which illustrates the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Graph Neural Networks are effective in learning representations of graph-structured data. Some recent works are devoted to addressing heterophily, which exists ubiquitously in real-world networks, breaking the homophily assumption that nodes belonging to the same class are more likely to be connected and restricting the generalization of traditional methods in tasks such as node classification. However, these heterophily-oriented methods still lose efficacy in some typical heterophilic datasets. Moreover, issues on leveraging the knowledge from both node features and graph structure and investigating inherent properties of the datasets still need further consideration. In this work, we first provide insights based on similarity metrics to interpret the long-existing confusion that simple models sometimes perform better than models dedicated to heterophilic networks. Then, sticking to these insights and the classification principle of narrowing the intra-class distance and enlarging the inter-class distance of the sample's embeddings, we propose a Similarity-Navigated Graph Neural Network (SNGNN) which uses Node Similarity matrix coupled with mean aggregation operation instead of the normalized adjacency matrix in the neighborhood aggregation process. Moreover, based on SNGNN, a novel explicitly aggregating mechanism for selecting similar neighbors, named SNGNN+, is devised to preserve distinguishable features and handle the heterophilic problem. Additionally, a variant, SNGNN++, is further designed to adaptively integrate the knowledge from both node features and graph structure for improvement. Extensive experiments are conducted and demonstrate that our proposed framework outperforms the state-of-the-art methods for both small-scale and large-scale graphs regardless of their heterophilic extent. Our implementation is available online. [ABSTRACT FROM AUTHOR]

Graph representation learning is a hot topic in non-Euclidean data in various domains, such as social networks, biological networks, etc. When some data labels are missing, graph autoencoder and graph variational autoencoder can perform outstanding abilities on node clustering or link prediction tasks. However, most existing graph representation learning ignores data's multi-modal features and takes the node features and graph structure features as one view. Besides, most graph autoencoders only reconstruct the node feature matrix or adjacency matrix, which does not fully use the hidden representation information. In this paper, we propose a multi-view representation model based on graph autoencoder, which can employ the global structure topology, latent local topology, and feature relative information. Meanwhile, we add another decoder to reconstruct the node feature matrix as an auxiliary task. In this way, the proposed framework can utilize the learned representation sufficiently. We validate the effectiveness of our framework on four datasets, and the experimental results demonstrate superior performance compared with other advanced frameworks. [ABSTRACT FROM AUTHOR]

GCN is a widely-used representation learning method for capturing hidden features in graph data. However, traditional GCNs suffer from the over-smoothing problem, hindering their ability to extract high-order information and obtain robust data representation. To overcome this limitation, we propose a novel graph model, the high-order graph attention network. Compared to other existing graph attention networks, our model can adaptively aggregate node features from multi-hop neighbors through an attention mechanism. Moreover, the edges in the original graph may not accurately represent the relationships between nodes. We implement a new approach to update the graph by using the aggregated node representation to adjust the edges with small step sizes. Additionally, we perform a theoretical analysis to demonstrate the relationships between our proposed model and other GCN models. Finally, we evaluate our proposed model against eight variants of GCN models on multiple widely-used benchmark datasets. The experimental results show the superiority of our proposed model over other models. We propose a novel model that integrates low- and high-order information from node neighborhoods. First, we perform feature mapping and propagation to create a feature tensor that stores diverse-order node representations. Then, we use an attention mechanism to aggregate the node features across different orders. Finally, we can update the edges of the original adjacency matrix using obtained with the newly obtained node features. • Propose a high-order graph attention model to alleviate the over-smoothing problem. • Implement a new strategy that incrementally updates the edge weights using a small step size. • Explore relations between the new model and other models. • Show that the new model is very effective in the experiments. [ABSTRACT FROM AUTHOR]

With the continuous development of intelligent transportation, an increasing number of smart devices and sensors are being used to record traffic information. Recently, researchers have relied on machine learning and differential privacy to achieve privacy protection during the continuous release of statistics. However, mechanisms based on differential privacy and prediction are limited by two key issues: the lack of attention given to the spatial-temporal correlations among the input data leads to poor prediction accuracy, and unreasonable privacy budget allocations cause reduced data utility. A traffic statistics publication mechanism with differential privacy and a spatial-temporal graph attention network (DP-STGAT) is proposed to address these problems. The key components include an adjacency matrix based on equivalent distance, a multistep prediction model based on an STGAT, and a combination of pre-allocation and adaptive allocation method for privacy budget allocation. These three components are tightly integrated to improve the accuracy of forecasting and solve the problem regarding poorly allocated privacy budgets. We evaluate the proposed mechanism with two real-world datasets and compare it with four representative methods with a w-event privacy guarantee. The experimental results show that the proposed scheme outperforms the existing methods. [ABSTRACT FROM AUTHOR]

• A new unsupervised method of initializing the Expectation*Maximization algorithm is proposed. • Time series are mapped to complex networks using Markov Transition Fields. • This technique is useful to estimate Mixture Models on financial time series. An efficient initialization of the Expectation-Maximization algorithm to estimate mixture models via maximum likelihood is proposed. A fully unsupervised network-based initialization technique is provided by mapping time series to complex networks using as adjacency matrix the Markov Transition Field associated to the time series. In this way, the optimal number of mixture model components and the vector of initial parameters can be directly obtained. An experiment conducted on financial times series with very different characteristics shows that our approach produces significantly better results if compared to conventional methods of initialization, such as K -means and Random, thus demonstrating the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization and spectral clustering are widely recognized techniques in data analysis due to their distinctive geometric interpretation and proven effectiveness across various applications. However, despite their popularity, these methods are not without their limitations. Specifically, they are susceptible to noise (outliers), which can significantly impact their clustering performance. Furthermore, their ability to learn spatial information heavily relies on the quality of the initial adjacency matrix. To mitigate the mentioned limitations, this paper proposes a novel clustering approach that integrates non-negative matrix factorization with spectral clustering. The proposed method utilizes a novel robust loss function to quantify the reconstruction error of samples, thereby improving the model's capacity to handle noise (outliers) and enhance clustering performance. Additionally, our method incorporates an adaptive-order graph learning strategy that enhances the model's adaptability to initial adjacency matrices. To optimize the proposed model, we have devised a highly efficient algorithm and conducted a analysis of its convergence properties. Experimental results on diverse datasets substantiate the effectiveness of our method in robust clustering and spatial learning tasks. • A novel general loss function is presented. It exhibits strong robustness and can be applied to other machine learning methods. • An adaptive-order adjacency matrix learning strategy is introduced. It has a strong spatial learning ability. • A novel robust clustering method is proposed. It has remarkable robustness and strong spatial learning ability. [ABSTRACT FROM AUTHOR]

• The notion of scored kNN (SkNN) is proposed to guide the propagation of neighborhoods from fine granularity to coarse. • The existence of a solution to multi-granularity sparse subspace representation is proved. • The consistency of sparse subspace representation at all multi-granularity levels is captured effectively by the proposed AMGSSC. • The smoothness of learned sparse representation by using AMGLSSC increases the intra-class connectivity of adjacency graph. Sparse subspace clustering (SSC) focuses on revealing data distribution from algebraic perspectives and has been widely applied to high-dimensional data. The key to SSC is to learn the sparsest representation and derive an adjacency graph. Theoretically, the adjacency matrix with proper block diagonal structure leads to a desired clustering result. Various generalizations have been made through imposing Laplacian regularization or locally linear embedding to describe the manifold structure based on the nearest neighborhoods of samples. However, a single set of nearest neighborhoods cannot effectively characterize local information. From the perspective of granular computing, the notion of scored nearest neighborhoods is introduced to develop multi-granularity neighborhoods of samples. The multi-granularity representation of samples is integrated with SSC to collaboratively learn the sparse representation, and an adaptive multi-granularity sparse subspace clustering model (AMGSSC) is proposed. The learned adjacency matrix has a consistent block diagonal structure at all granularity levels. Furthermore, the locally linear relationship between samples is embedded in AMGSSC, and an enhanced AMGLSSC is developed to eliminate the over-sparsity of the learned adjacency graph. Experimental results show the superior performance of both models on several clustering criteria compared with state-of-the-art subspace clustering methods. [ABSTRACT FROM AUTHOR]

In this paper, the swarm control for large-scale omnidirectional mobile robots (OMRs) within incremental behavior is proposed to imitate the confluence behavior of animals during migration. In previous work, the number of OMRs in the swarm system was small and immutable. As such, the system lacked flexibility for swarm systems in practical applications. To solve these problems, we make several innovations. Firstly, OMRs within incremental behavior are proposed. Based on this, the incremental system of OMRs within incremental behavior is designed when the original swarm system needs assistance to form an incremental swarm system, which allows the incremental behavior happens among different swarm systems and the formation of each incremental system unchanged. Notably, incremental updating method based on second-order communication topology is proposed to update the adjacency matrix and the state matrix instead of creating a new swarm system. Then, to solve the pressure caused by the increasing number of OMRs in incremental swarm systems on calculating and storage, the incremental swarm system of large-scale OMRs based on second-order communication topology is introduced to rank the system and weaken the strong coupling relationship. In this case, the swarm control for a large-scale incremental swarm system is proposed through the backstepping method. The Lyapunov function is designed to prove the stability of the proposed controller. The simulation results verify the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Short-term traffic flow prediction is a core branch of intelligent traffic systems (ITS) and plays an important role in traffic management. The graph convolution network (GCN) is widely used in traffic prediction models to efficiently handle the graphical structural data of road networks. However, the influence weights among different road sections are usually distinct in real life and are difficult to analyze manually. The traditional GCN mechanism, which relies on a manually set adjacency matrix, is unable to dynamically learn such spatial patterns during training. To address this drawback, this study proposes a novel location graph convolutional network (location-GCN). The location-GCN solves this problem by adding a new learnable matrix to the GCN mechanism, using the absolute value of this matrix to represent the distinct influence levels among different nodes. Subsequently, long short-term memory (LSTM) is employed in the proposed traffic prediction model. Moreover, trigonometric function encoding was used in this study to enable the short-term input sequence to convey long-term periodic information. Finally, the proposed model was compared with the baseline models and evaluated on two real-world traffic flow datasets. The results show that our model is more accurate and robust than the other representative traffic prediction models. [ABSTRACT FROM AUTHOR]

Traffic flow forecasting is a crucial task in transportation management and planning. The main challenges for traffic flow forecasting are that (1) as the length of prediction time increases, the accuracy of prediction will decrease; (2) the predicted results greatly rely on the extraction of temporal and spatial dependencies from the road networks. To overcome the challenges mentioned above, we propose a multi-channel spatial-temporal transformer model for traffic flow forecasting, which improves the accuracy of the prediction by fusing results from different channels of traffic data. Our approach leverages graph convolutional network to extract spatial features from each channel while using a transformer-based architecture to capture temporal dependencies across channels. We introduce an adaptive adjacency matrix to overcome limitations in feature extraction from fixed topological structures. Experimental results on six real-world datasets demonstrate that introducing a multi-channel mechanism into the temporal model enhances performance and our proposed model outperforms state-of-the-art models in terms of accuracy. [ABSTRACT FROM AUTHOR]

• Introduce a deep random walk to obtain a more accurate sample affinity matrix. • Propose a graph learning method to output sparse and low-rank graph structure. • Develop a joint learning of deep random walk and sparse low-rank embedding. Multi-view clustering aims to improve the learning performance by exploiting discriminative information from heterogeneous data sources. It has been capturing growing research attention due to its wide utilization in the areas of data mining and computer vision. However, the full use of complementarity and consistency from multi-view data is still a challenging task. Here, we propose a novel multi-view fuzzy clustering, which adopts the joint learning of deep random walk and sparse low-rank embedding. First, a deep random walk is employed to acquire a robust similarity matrix of data points and convert fuzzy membership matrix learning to adaptive graph learning. Second, the adaptive graph is restricted with sparse low-rank constraints, which ensures its strong discriminative ability and effective cluster assignments. Third, by exploiting the sparse low-rank property, the multi-view fuzzy clustering problem is formulated as optimizing a regularized graph adjacency matrix with distance metric learning and spectral norm minimization simultaneously. The distance metric learning is embedded to scatter all data points so that any two samples are projected onto a low-dimensional subspace with a large margin. Finally, an efficient algorithm is developed for the formulated problem and its convergence is also guaranteed. In order to demonstrate the superiority of the proposed method, extensive experiments are conducted by comparing state-of-the-arts on real-world databases. [ABSTRACT FROM AUTHOR]

Deep graph clustering approaches employ deep graph neural networks to encode node embeddings and subsequently partition nodes based on these representations. Recent one-step methods have demonstrated progress; however, they often encounter issues during the representation learning phase. A primary challenge is that the encoding networks fail to capture the high-order structural information of the graph for effective clustering. We believe that combining the two distributions comprehensively characterizes the real node distribution in terms of neighborhood proximity and community aggregation to achieve better clustering. Additionally, the prevalent representation learning paradigms based on adjacency matrix reconstruction are computationally intensive and increase optimization challenges. This paper presents a novel deep graph clustering model, termed Deep Integration of Community structure and Neighborhood information (DICN). The model incorporates a graph self-attention mechanism to aggregate neighborhood-level node information, and utilizes a probabilistic generative model for edge community detection to captain community-level node information. These two-level embeddings are employed to compute explicit node membership distributions for the clustering loss. This ensures that the clustering objective effectively integrates both low-order and high-order node characteristics. The comprehensive learning process of DICN optimizes not only the node embeddings but also the clustering results by integrating the two-level losses from representation learning and the clustering loss with a weak guidance loss for clustering. Experiments on some benchmark datasets illustrate that DICN model has superior performance over existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The quality of graphs directly affects the result of graph embedding since most existing models are vulnerable and highly sensitive to harmful/missing edges and imperceptible attacks. In this study, we propose a new robust graph embedding approach from a different point of view: Attack-aid Graph Denoising (AGD). AGD mitigates the impact of harmful and missing edges by leveraging adversarial attacks. Initially, AGD generates some auxiliary attacks on the topology by investigating their harm to classification accuracy. Subsequently, we derive a denoised adjacency matrix by removing these similar harmful edges and supplementing missing edges with flipping operations. Finally, we further extract the knowledge of topology to eliminate the influence of remaining harmful edges on the final embedding with Kullback-Leibler divergence. Extensive experiments have demonstrated that AGD not only shows its superiority over many state-of-the-art algorithms on the classification tasks but is also robust to various attacks. • Proposed Attack-aid Graph Denoising improves the graph quality and robustness. • AGD enhances robustness by leveraging auxiliary attacks for edge manipulation. • Proposed Topology Knowledge Extraction adapts message-passing to isolate attacks. [ABSTRACT FROM AUTHOR]

Community detection has been a significant and long-standing task in network analysis. While existing methods tend to focus on the assortative structure where communities are densely connected internally, in reality other kinds of network structure (e.g., disassortative) also exist. In addition, previous methods often have difficulties in dealing with noise and redundant information in the network topology. To address these problems, we develop a novel Bayesian probabilistic model for identifying the generalized communities, regardless of whether the network structure is assortative, disassortative, or otherwise. Specifically, the model combines the original adjacency matrix representation with the network embedding (the dense and continuous vector representations of nodes in a low-dimensional space). The two parts are connected and generated jointly via the community memberships of nodes learned from the model. Finally, we take a Bayesian treatment for model parameters and develop an efficient variational inference algorithm to detect communities. Experimental results demonstrate the outstanding performance of the new approach both on synthetic networks and on real-world networks, while case studies validate the ability of the proposed approach to describe generalized communities meaningfully. [ABSTRACT FROM AUTHOR]

We propose a new paradigm for describing complex networks in terms of the spectrum of the adjacency matrix and its submatrices. We show that a variety of basic node information, such as degree, clique, and subgraph centrality, can be calculated analytically. Moreover, we find that energy of spectrum series can uncover randomness and complexity of network structure. Interestingly, it presents an universal linear growth pattern with the growth of networks. Furthermore, the spectrum series of synthetic and real networks present clearly self-similarity characteristics for which the associated scaling exponents remain constant. Our work reveals that spectrum series representation will provide an alternative perspective for studying and understanding structure and function of complex networks rather than connectivity. [ABSTRACT FROM AUTHOR]

The domain of multi-view semi-supervised classification is an appealing topic in real-world applications. Due to the powerful capability of gathering information from neighbors, Graph Convolutional Network (GCN) has become a hotspot in the classification task. However, most of multi-view classification works based on GCN only assign weights for feature fusion, and directly consider the weighted sum of the adjacency matrices, ignoring the interaction and correlation among features. These may be problematic since aggregating the matrices from less relevant views may destroy the original topology space, leading to undesired performance. To tackle the aforementioned challenges, this paper presents an Adaptive Multi-Channel Graph Convolutional Network (AMC-GCN). To extract the interactive information, AMC-GCN designs a deep interactive feature integration network to incorporate consensus and complementary information. To fuse the graph structures, AMC-GCN exploits the relevance between views and imposes an adjacency matrix fusion network on constructing multiple GCN channels, thereby delivering discriminative information on graphs. To enhance the homogeneity of the framework, AMC-GCN applies a contrastive loss to joint learning during the optimization for classification. With these considerations, AMC-GCN exploits relevant and interactive information between views to promote graph and feature fusion. Substantial experimental results on real-world datasets verify the superiority of AMC-GCN. [ABSTRACT FROM AUTHOR]

Traffic prediction is an important part of smart city management. Accurate traffic prediction can be deployed in urban applications such as congestion alerting and route planning, thus providing sustainable services to the public or relevant departments. Although some improvements have been made in existing traffic prediction methods, there are challenges due to the following: (1) Time series has multi-scale nature, that is, from different scale time ranges, traffic flow changes show different trends; (2) Spatial heterogeneity, meaning that traffic conditions in similar functional areas are usually similar. This task remains difficult. To address the above challenges, we propose a new spatial-temporal prediction method, namely Multi-Scale Spatial-Temporal Aware Transformer (MSSTAT), which is a Transformer architecture with multi-scale characteristics. Specifically, compared to the input of encoder, the input of different decoder layers has different scale information, MSSTAT synchronizes model the connection between time steps and scale information by a kind of Parallel Cross Multi-Head Attention, which gives each time step several times the perceived field while also being able to weaken the impact brought by anomaly point. In addition, to add connections between regions with similar functions, we map the traffic data of each node as a probability distribution and then measure the similarity between the nodes by the Wasserstein Distance, which leads to our proposed spatial-temporal aware adjacency matrix. Experimental results on four traffic flow datasets show that MSSTAT outperforms the state-of-the-art baseline. [ABSTRACT FROM AUTHOR]

In the face of complex and changeable group decision-making problems, making satisfactory decisions is always difficult, which is deeply affected by information such as different stages, criteria, experts and alternatives. Thus, this study aims to develop an effective multi-stage multi-criteria group decision making (MSMCGDM) method to solve the multi-stage group decision making problems with various information. Firstly, through the introduction of trust rejection threshold, a Cross Calibration method is proposed to calculate experts' weights, considering the social influence of experts in the same stage as well as different stages. Then, based on the extend DEMATEL and Shapley approaches, the DE-Shapley method is constructed to obtain criteria weights considering the hierarchical criteria interaction according to the evaluation information on criteria. Furthermore, inspired by the adjacency matrix, the relationship matrix on alternatives and the concept of alternative sets are proposed to consider the acceptability of alternatives in different stages. Afterwards, elastic mechanism in proposed framework is put forward to deal with the unexpected situations when implementing the optimal alternative set. Finally, two scenarios on snowmelt flood are presented to demonstrate the application of the proposed method, sensitive analysis and comparative analyses are conducted to highlight the advantages of our proposed method. • The Cross Calibration method is proposed to calculate experts' weights. • DE-Shapley method is formulated to calculate criteria weights. • Social influence of experts and hierarchical criteria interaction are studied. • Alternative set considering the acceptability of alternatives is introduced. • An elastic mechanism is put forward to deal with the unexpected situations. [ABSTRACT FROM AUTHOR]

Graph Neural Networks (GNNs) have shown expressive modeling ability on graphs. An inherent assumption is that those connected graph nodes exhibit strong homophily, passing consistent label information into the associated central node representation. However, heterophilic graphs may hold inconsistent labels for those connected nodes, degenerating the performance of the typical message passing and exacerbating its over-smoothing issue. In this paper, to tame heterophilic graphs for GNNs, a novel label estimation-based message passing scheme is presented, which can further relieve the over-smoothing and lead the learned representations to be more distinguishable on graphs with either homophily or heterophily. Specifically, we optimize the edge weights of the graph by invoking the label estimation with the goal of returning a more effective adjacency matrix. With this matrix, a novel message passing scheme is presented, aggregating neighbor information with consistent labels to their central nodes. Meanwhile, a symmetric cross entropy is also employed to mitigate negative effects from noisy labels. With such guarantees in our new message passing, a uniform framework termed Label Estimation-based GNN (LE-GNN) is finally established. Extensive experiments demonstrate the ability of our model to prevent over-smoothing and show its effectiveness for node classification on both homophilic and heterophilic graphs. [ABSTRACT FROM AUTHOR]

Community structure is an important characteristic of complex networks. It determines where important functions of a network are located. Recently, discovering community structure in complex networks has become a hot topic of research. However, the continuous increase in network size has made network structure more complex, and community detection has become extremely difficult in real applications. In particular, the detection results are usually not accurate enough when classical clustering methods are applied to high-dimensional data matrices. In this paper, inspired by the relationship between vertices, we design a novel and effective network adjacency matrix transformation method to describe vertices' similarity in the network topology. On this basis, we propose a framework to extract nonlinear features: community detection with deep transitive autoencoder (CDDTA). This framework can obtain powerful nonlinear features of a real network to make community detection algorithms perform excellently in practice. We further incorporate unsupervised transfer learning into the CDDTA (Transfer-CDDTA) by minimizing the Kullback–Leibler divergence of embedded instances, to discover powerful low-dimensional representations. Finally, we propose a new training strategy and optimization method for our algorithm. Extensive experimental results indicate that our new framework can ensure good performance on both real-world networks and artificial benchmark networks, which outperforms most of the state-of-the-art methods for community detection in social networks. [ABSTRACT FROM AUTHOR]

Given a graph, we interpret its adjacency matrix as an information table. We study this correspondence in two directions. Firstly, on the side of graphs by applying to it standard techniques from granular computing. In this way, we are able to connect automorphisms on graphs to the so-called indiscernibility relation and a particular hypergraph built from the starting graph to core and reducts. On the other hand, new concepts are introduced on graphs that have an interesting correspondence on information tables. In particular, some new topological interpretations of the graph and the concept of extended core are given. [ABSTRACT FROM AUTHOR]

An algorithm for matching the weighted sub-graphs based on gradient flows is proposed in this paper. First, the smaller and larger graphs for matching are represented by means of their weighted adjacency matrices. Then, an objective function is introduced to measure the differences between two weighted adjacency matrices. Because the permutation matrix for graph matching is usually relaxed to an orthogonal matrix with non-negative elements, an optimization-based approach is adopted to “navigate” the solution toward an appropriate permutation matrix. To accomplish this goal, two gradient flows in the space of orthogonal matrices are defined in such a way that they minimize the objective functions. One minimizes the objective function in the space of orthogonal matrices, and the other minimizes the distance of an orthogonal matrix from the set of permutations. In addition, two cost functions are introduced to force satisfaction (approximately) of the constraint that a translation matrix must have integer entries of different values. The experimental results show that the proposed sub-graph matching is feasible. [ABSTRACT FROM AUTHOR]

In this paper, the problems of group consensus for linearly coupled multi-agent networks including first-order and second-order are investigated, respectively. Based on the Laplacian matrix associated with the weighted adjacency matrix of the system, we present two novel linear protocols which can exactly reflect the interactive influence between the agents of the multi-agent network. Instead of relying on other conservative assumptions presented by the majority of the relevant research works, some promising criteria which can guarantee the reaching of group consensus of the multi-agent network are also obtained analytically. In addition, we also extend our work to study the group consensus for the multi-agent network with generally connected topology which neither needs to be strongly connected nor needs to contain a directed spanning tree. The conclusion that we have obtained should be more representative. Finally, the validity and correctness of our theoretical results are verified by several numerical simulated examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the testing bipartiteness of simple undirected graphs based on generalized rough sets. A new binary relation induced from a simple undirected graph is first defined. The concept of quasi-outer definable sets is then introduced, and some of its important properties are investigated. Finally, based on the quasi-outer definable set, a new algorithm is designed for testing bipartiteness of a simple undirected graph. Experiments show that the proposed algorithm is more efficient than the traditional one when the graph is represented by an adjacency matrix. [Copyright &y& Elsevier]

Abstract: In order to maintain load balancing in a distributed network, each node should obtain workload information from all the nodes in the network. To accomplish this, this processing requires O(v 2) communication complexity, where v is the number of nodes. First, we present a new synchronous dynamic distributed load balancing algorithm on a (v, k +1,1)-configured network applying a symmetric balanced incomplete block design, where v = k 2 + k +1. Our algorithm designs a special adjacency matrix and then transforms it to (v, k +1,1)-configured network for an efficient communication. It requires only communication complexity and each node receives workload information from all the nodes without redundancy since each link has the same amount of traffic for transferring workload information. Later, this algorithm is revised for distributed networks and is analyzed in terms of efficiency of load balancing. [Copyright &y& Elsevier]