Anomaly detection on attributed networks has received an increasing amount of attention in recent years. Despite the success, most of the existing methods only focus on detecting the abnormal nodes while fail to detect the abnormal subgraphs. In this paper, we define a new problem of hybrid-order anomaly detection on attributed networks, which aims to detect both of the abnormal nodes and subgraphs. To this end, a new deep learning model called Hybrid-Order Graph Attention Network (HO-GAT) is developed, which is able to simultaneously detect the abnormal nodes and motif instances in an attributed network. In order to model the mutual influence between nodes and motif instances, the learning procedures of the node representation and the motif instance representation are integrated into a unified graph attention network with a novel hybrid-order self-attention mechanism. After learning the node representation and the motif instance representation, two decoders are respectively designed to reconstruct the attribute information of the nodes and motif instances, and the hybrid-order topological structure among nodes and motif instances. And finally, the reconstruction errors are utilized as the abnormal score of nodes and motif instances respectively. Extensive experiments conducted on real-world datasets have confirmed the effectiveness of the HO-GAT method.

Recently, hybrid-order community detection has been proposed for addressing the hypergraph fragmentation issue suffered by the motif-based higher-order community detection. However, the existing attempts of hybrid-order community detection inadvertently damage the lower-order connectivity pattern and the higher-order connectivity pattern when constructing the fusion model. Additionally, like the higher-order community detection approaches, they also adopt a two-phase strategy that separately applies the existing graph node clustering methods to the proximity matrix derived from the lower-order connectivity pattern and the higher-order connectivity pattern. Therefore, the higher-order connectivity pattern is only utilized for constructing proximity matrix and hence has no direct effect on the final community results. In this paper, to address the above issues, we propose a Generative model for Hybrid-Order Community detection (GHOC). The main idea lies in defining a likelihood function of a generative model that finds the optimal community membership strength vectors of nodes, based on which the original lower-order connectivity pattern and the higher-order connectivity pattern can be directly reconstructed simultaneously. From the community membership strength vectors, the final community structure can be derived. Extensive experiments have been conducted on several data sets, and the results have confirmed the superiority of the proposed GHOC method.

Most proximity-based multi-view clustering methods are sensitive to the initial proximity matrix, where the clustering performance is quite unstable when using different initial proximity matrixes. This problem is defined as the initial value sensitivity problem. Since clustering is an unsupervised learning task, it is unrealistic to tune the initial proximity matrix. Thus, how to overcome the initial value sensitivity problem is a significant but unsolved issue in the proximity-based multi-view clustering. To this end, this paper proposes a novel multi-view proximity learning method, named multi-view consensus proximity learning (MCPL). On the one hand, by integrating the information of all views in a self-weighted manner and giving a rank constraint on the Laplacian matrix, the MCPL method learns the consensus proximity matrix to directly reflect the clustering result. On the other hand, different from most multi-view proximity learning methods, in the proposed MCPL method, the data representatives rather than the original data objects are adopted to learn the consensus proximity matrix. The data representatives will be updated in the process of the proximity learning so as to weaken the impact of the initial value on the clustering performance. Extensive experiments are conducted to demonstrate the effectiveness of the proposed method.

Recently, some attempts have been made in introducing deep neural networks (DNNs) to recommender systems for generating more accurate prediction due to the nonlinear representation learning capability of DNNs. However, they inevitably result in high computational and storage costs. Worse still, due to the relatively small number of ratings that can be fed into DNNs, they may easily suffer from the overfitting issue. To tackle these issues, we propose a novel recommendation framework based on Back Propagation (BP) neural network with attention mechanism, namely BPAM++. In particular, the BP neural network is utilized to learn the complex relationship between the target user and his/her neighbors and the complex relationship between the target item and its neighbors. Compared with DNNs, the shallow neural network, i.e., BP neural network, can not only reduce the computational and storage costs, but also alleviate the overfitting issues in DNNs caused by a relatively small number of ratings. In addition, an attention mechanism is designed to capture the global impact of the nearest users of the target user on their nearest target user sets. Extensive experiments conducted on eight benchmark datasets confirm the effectiveness of the proposed model.

Many real-world graphs can be viewed as Heterogeneous Networks or Heterogeneous Information Networks (HINs) for that they comprise a diversity of node types and relation types. Due to the efficient representation ability of Graph Neural Network and the idea of random walk, many recent studies apply graph representation learning to HINs and achieve satisfactory results. However, these works either treat different node types in a metapath equally, which is inconsistent with the original graph semantic information for that different node types should have different statuses, or only consider the first-order (node-level) and second-order (metapath-level, a.k.a. link-level) information aggregation while ignoring the higher-order relations. To tackle these two problems, we propose a novel Star-Shaped Hierarchical Graph Attentional Network (StarGAT) model to boost representation learning in HINs. Specifically, we assume nodes in HINs can be categorized into a star-shaped structure including one center node type and a bunch of auxiliary node types in a specific task; and we encode node-level, link-level and motif-level attentions in a hierarchical manner to capture richer semantic information. Extensive experiments on three datasets illustrate the model effectiveness.

As a critical task in intelligent traffic systems, traffic prediction has received a large amount of attention in the past few decades. The early efforts mainly model traffic prediction as the time-series mining problem, in which the spatial dependence has been largely ignored. As the rapid development of deep learning, some attempts have been made in modeling traffic prediction as the spatio-temporal data mining problem in a road network, in which deep learning techniques can be adopted for modeling the spatial and temporal dependencies simultaneously. Despite the success, the spatial and temporal dependencies are only modeled in a regionless network without considering the underlying hierarchical regional structure of the spatial nodes, which is an important structure naturally existing in the real-world road network. Apart from the challenge of modeling the spatial and temporal dependencies like the existing studies, the extra challenge caused by considering the hierarchical regional structure of the road network lies in simultaneously modeling the spatial and temporal dependencies between nodes and regions and the spatial and temporal dependencies between regions. To this end, this article proposes a new Temporal Hierarchical Graph Attention Network (TH-GAT). The main idea lies in augmenting the original road network into a region-augmented network, in which the hierarchical regional structure can be modeled. Based on the region-augmented network, the region-aware spatial dependence model and the region-aware temporal dependence model can be constructed, which are two main components of the proposed TH-GAT model. In addition, in the region-aware spatial dependence model, the graph attention network is adopted, in which the importance of a node to another node, of a node to a region, of a region to a node, and of a region to another region, can be captured automatically by means of the attention coefficients. Extensive experiments are conducted on two real-world traffic datasets, and the results have confirmed the superiority of the proposed TH-GAT model.

Recently, network embedding has received a large amount of attention in network analysis. Although some network embedding methods have been developed from different perspectives, on one hand, most of the existing methods only focus on leveraging the plain network structure, ignoring the abundant attribute information of nodes. On the other hand, for some methods integrating the attribute information, only the lower-order proximities (e.g., microscopic proximity structure) are taken into account, which may suffer if there exists the sparsity issue and the attribute information is noisy. To overcome this problem, the attribute information and mesoscopic community structure are utilized. In this article, we propose a novel network embedding method termed Attributed Network Embedding with Micro-Meso structure, which is capable of preserving both the attribute information and the structural information including the microscopic proximity structure and mesoscopic community structure. In particular, both the microscopic proximity structure and node attributes are factorized by Nonnegative Matrix Factorization (NMF), from which the low-dimensional node representations can be obtained. For the mesoscopic community structure, a community membership strength matrix is inferred by a generative model (i.e., BigCLAM) or modularity from the linkage structure, which is then factorized by NMF to obtain the low-dimensional node representations. The three components are jointly correlated by the low-dimensional node representations, from which two objective functions (i.e., ANEM_B and ANEM_M) can be defined. Two efficient alternating optimization schemes are proposed to solve the optimization problems. Extensive experiments have been conducted to confirm the superior performance of the proposed models over the state-of-the-art network embedding methods.

Multi-layer network community detection has drawn an increasing amount of attention recently. Despite success, the existing methods mainly focus on the lower-order connectivity structure at the level of individual nodes and edges. And the higher-order connectivity structure has been largely ignored, which contains better signature of community compared with edges. The main challenges in utilizing higher-order structure for multi-layer network community detection are that the most representative higher-order structure may vary from one layer to another and the connectivity structure formed by the same node subset may exhibit different higher-order connectivity patterns in different layers. To this end, this paper proposes a novel higher-order structure, termed harmonic motif, which is a dense subgraph having on average the largest statistical significance in each layer. Based on the harmonic motif, a primary layer is constructed by integrating higher-order structural information from all layers. Additionally, the higher-order structural information of each individual layer is taken as the auxiliary information. A coupling is established between the primary layer and each auxiliary layer. Accordingly, a harmonic motif modularity is designed to generate the community structure. Extensive experiments on eleven real-world multi-layer network datasets have been conducted to confirm the effectiveness of the proposed method.

Community detection (or graph clustering) is crucial for unraveling the structural properties of complex networks. As an important technique in community detection, label propagation has shown the advantage of finding a good community structure with nearly linear time complexity. However, despite the progress that has been made, there are still several important issues that have not been properly addressed. First, the label propagation typically proceeds over the lower order structure of the network and only the direct one-hop connections between nodes are taken into consideration. Unfortunately, the higher order structure that may encode design principle of the network and be crucial for community detection is neglected under this regime. Second, the stability of the identified community structure may also be seriously affected by the inherent randomness in the label propagation process. To tackle the above issues, this article proposes a Motif-Aware Weighted Label Propagation method for community detection. We focus on triangles within the network, but our technique extends to other kinds of motifs as well. Specifically, the motif-based higher order structure mining is conducted to capture structural characteristics of the network. First, the motif of interest (locally meaningful pattern) is identified, and then, the motif-based hypergraph can be constructed to encode the higher order connections. To further utilize the structural information of the network, a re-weighted network is designed, which unifies both the higher order structure and the original lower order structure. Accordingly, a novel voting strategy termed NaS (considering both Number and Strength of connections) is proposed to update node labels during the label propagation process. In this way, the random label selection can be effectively eliminated, yielding more stable community structures. Experimental results on multiple real-world datasets have shown the superiority of the proposed method.

Recently, multi-view outlier detection has emerged as a challenging research topic in outlier detection because of complex distributions of data across different views. There are mainly three types of outliers, i.e., attribute outliers, class outliers and class-attribute outliers. Most existing multi-view outlier detection approaches only detect part of the three types of outliers in a pairwise manner across different views, which is not able to accomplish the task of multi-view outlier detection comprehensively and uniformly. Outlier detection in a pairwise manner across different views also leads to time-consuming computation. We propose a new algorithm termed Multi-view Outlier Detection in Deep Intact Space (MODDIS) to find all the three types of outliers simultaneously and avoid comparing different views in a pairwise manner. Rather than leveraging subspace clustering, the performance of which is seriously affected by the dependence of subspaces on most real datasets, neural networks are employed in MODDIS in that neural networks have a stronger representation learning ability. Meanwhile, based on the view insufficiency assumption, a multi-view intact outlierness space assumption is proposed. Based on this assumption, a multi-view latent intact space is constructed to encode outlierness information of all views, where outlierness in any view is a snapshot from some perspective. Finally, an outlier detection measurement is defined in the latent intact space. Experiments are conducted on several UCI datasets and the empirical results demonstrate the effectiveness of our proposed method.

Recommender system is widely used in e-commercial platforms to recommend users suitable items according to users's preferences. In recent years, an increasing amount of attention has been paid to the application of recommender system in education. There are many online learning systems that can recommend students suitable courses according to students' learning performances. However, there are few universities using recommender system to recommend students suitable elective courses. It is generally known that students in higher grade take the courses earlier than those in lower grade. Therefore, the elective course scores of sophomores can be predicted by using the course score information from students of higher grades. However, the unbalanced distribution of course-enrollment data makes it hard to predict the scores of the courses that are in a low selection rate. Therefore, we propose a Constrained Matrix Factorization (ConMF) algorithm to predict sophomores' elective course scores, which integrates the course average score into the objective function so as to make up the prediction deviation caused by the unbalanced course selection rate and make more accurate prediction than the traditional Matrix Factorization (MF) approach. The experimental results show that our proposed model outperforms the state-of-the-art methods in the task of university students' course score prediction.

Network community detection is a hot research topic in network analysis. Although many methods have been proposed for community detection, most of them only take into consideration the lower-order structure of the network at the level of individual nodes and edges. Thus, they fail to capture the higher-order characteristics at the level of small dense subgraph patterns, e.g., motifs. Recently, some higher-order methods have been developed but they typically focus on the motif-based hypergraph which is assumed to be a connected graph. However, such assumption cannot be ensured in some real-world networks. In particular, the hypergraph may become fragmented. That is, it may consist of a large number of connected components and isolated nodes, despite the fact that the original network is a connected graph. Therefore, the existing higher-order methods would suffer seriously from the above fragmentation issue, since in these approaches, nodes without connection in hypergraph can't be grouped together even if they belong to the same community. To address the above fragmentation issue, we propose an Edge enhancement approach for Motif-aware community detection (EdMot ). The main idea is as follows. Firstly, a motif-based hypergraph is constructed and the top K largest connected components in the hypergraph are partitioned into modules. Afterwards, the connectivity structure within each module is strengthened by constructing an edge set to derive a clique from each module. Based on the new edge set, the original connectivity structure of the input network is enhanced to generate a rewired network, whereby the motif-based higher-order structure is leveraged and the hypergraph fragmentation issue is well addressed. Finally, the rewired network is partitioned to obtain the higher-order community structure. Extensive experiments have been conducted on eight real-world datasets and the results show the effectiveness of the proposed method in improving the community detection performance of state-of-the-art methods.

During the past several years, multi-layer network community detection has drawn an increasing amount of attention and many approaches have been developed from different perspectives. Despite the success, they mainly rely on the lower-order connectivity structure at the level of individual nodes and edges. However, the higher-order connectivity structure plays the essential role as the building block for multiplex networks, which may contain better signature of community than edge. The main challenge in utilizing higher-order structure for multi-layer network community detection is that the most representative higher-order structure may vary from one layer to another. In this paper, we propose a higher-order structural approach for multi-layer network community detection, termed harmonic motif modularity (HM-Modularity). The key idea is to design a novel higher-order structure, termed harmonic motif, which is able to integrate higher-order structural information from multiple layers to construct a primary layer. The higher-order structural information of each individual layer is also extracted, which is taken as the auxiliary information for discovering the multi-layer community structure. A coupling is established between the primary layer and each auxiliary layer. Finally, a harmonic motif modularity is designed to generate the community structure. By solving the optimization problem of the harmonic motif modularity, the community labels of the primary layer can be obtained to reveal the community structure of the original multi-layer network. Experiments have been conducted to show the effectiveness of the proposed method.