First-order Neighbors Research Articles

PerCNet: Periodic complete representation for crystal graphs

Crystal molecules are considered as graph structures in different representation methods. A reasonable crystal representation method should capture the local and global information. However, existing methods only consider the local information of crystal molecules by modeling the bond distance and bond angle of first-order neighbors of atoms, which leads to the issue that different crystals will have the same representation. To solve this many-to-one issue, we consider the global information by further considering dihedral angles. We propose a periodic complete representation of graph modeling and a calculation algorithm for infinite extended crystal materials. A theoretical proof for the representation that satisfies the periodic completeness is provided. Based on the proposed representation, we then propose a network for predicting crystal material properties, PerCNet, with a specially designed message-passing mechanism. To our best known, we are the first work that ensures the representation corresponds one-to-one with the crystal material based on graph modeling. Extensive experiments are conducted on two large-scale real-world material benchmark datasets. The PerCNet achieves the best performance among baseline methods in terms of MAE. Our code is available at https://github.com/JiaoHuang111/PerCNet.

Explicitly Exploiting Implicit User and Item Relations in Graph Convolutional Network (GCN) for Recommendation

Most existing collaborative filtering-based recommender systems rely solely on available user–item interactions for user and item representation learning. Their performance often suffers significantly when interactions are sparse, as limited user and item interactions are insufficient for learning robust representations. To address this issue, recent research has explored additional information between users and items by leveraging the user–item bipartite graph. However, these methods have not fully exploited high-order neighborhood information, primarily using sampled interactions to enrich training data rather than integrating this information directly into representation learning. In this paper, we propose a novel model, EIR-GCN (Embedding Integration with Relational Graph Convolutional Network), which directly incorporates various types of collaborative relations, such as user–user and item–item interactions, into the embedding function for user preference modeling. Specifically, our model employs advanced graph convolutional network (GCN) techniques to integrate user–item, user–user, and item–item relations for comprehensive representation learning. EIR-GCN initially selects the most influential second-order neighbors from the user–item bipartite graph to form user–user and item–item connections. With these enriched connections, a message-passing method is adopted to learn node representations by aggregating messages from directly linked nodes, including first-order item neighbors and selected second-order user neighbors. Extensive experiments on several public datasets demonstrate that EIR-GCN outperforms strong baselines, including recent GCN-based models and those exploiting high-order information. Our results show that EIR-GCN achieves state-of-the-art performance and effectively addresses the sparsity issue, highlighting its robustness and efficacy in recommendation tasks.

Networks and their degree distribution, leading to a new concept of small worlds

The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order.Next, we introduce a new class of small worlds, namely those based on the degrees of nodes in a network. Similar to a previous study, small worlds are defined as sequences of networks with certain limiting properties. We distinguish between three types of small worlds: those based on the highest degree, those based on the average degree, and those based on the median degree. We show that these new classes of small worlds are different from those introduced previously based on the diameter of the network or the average and median distance between nodes. However, there exist sequences of networks that qualify as small worlds in both senses of the word, with stars being an example. Our approach enables the comparison of two networks with an equal number of nodes in terms of their “small-worldliness”.Finally, we introduced neighboring arrays based on the degrees of the zeroth and first-order neighbors.

A Generalized Neural Diffusion Framework on Graphs

Recent studies reveal the connection between GNNs and the diffusion process, which motivates many diffusion based GNNs to be proposed. However, since these two mechanisms are closely related, one fundamental question naturally arises: Is there a general diffusion framework that can formally unify these GNNs? The answer to this question can not only deepen our understanding of the learning process of GNNs, but also may open a new door to design a broad new class of GNNs. In this paper, we propose a general diffusion equation framework with the fidelity term, which formally establishes the relationship between the diffusion process with more GNNs. Meanwhile, with this framework, we identify one characteristic of graph diffusion networks, i.e., the current neural diffusion process only corresponds to the first-order diffusion equation. However, by an experimental investigation, we show that the labels of high-order neighbors actually appear monophily property, which induces the similarity based on labels among high-order neighbors without requiring the similarity among first-order neighbors. This discovery motives to design a new high-order neighbor-aware diffusion equation, and derive a new type of graph diffusion network (HiD-Net) based on the framework. With the high-order diffusion equation, HiD-Net is more robust against attacks and works on both homophily and heterophily graphs. We not only theoretically analyze the relation between HiD-Net with high-order random walk, but also provide a theoretical convergence guarantee. Extensive experimental results well demonstrate the effectiveness of HiD-Net over state-of-the-art graph diffusion networks.

Fine-Grained Essential Tensor Learning for Robust Multi-View Spectral Clustering.

Multi-view subspace clustering (MVSC) has drawn significant attention in recent study. In this paper, we propose a novel approach to MVSC. First, the new method is capable of preserving high-order neighbor information of the data, which provides essential and complicated underlying relationships of the data that is not straightforwardly preserved by the first-order neighbors. Second, we design log-based nonconvex approximations to both tensor rank and tensor sparsity, which are effective and more accurate than the convex approximations. For the associated shrinkage problems, we provide elegant theoretical results for the closed-form solutions, for which the convergence is guaranteed by theoretical analysis. Moreover, the new approximations have some interesting properties of shrinkage effects, which are guaranteed by elegant theoretical results. Extensive experimental results confirm the effectiveness of the proposed method.

Contrastive Multiview Attribute Graph Clustering With Adaptive Encoders.

Multiview attribute graph clustering aims to cluster nodes into disjoint categories by taking advantage of the multiview topological structures and the node attribute values. However, the existing works fail to explicitly discover the inherent relationships in multiview topological graph matrices while considering different properties between the graphs. Besides, they cannot well handle the sparse structure of some graphs in the learning procedure of graph embeddings. Therefore, in this article, we propose a novel contrastive multiview attribute graph clustering (CMAGC) with adaptive encoders method. Within this framework, the adaptive encoders concerning different properties of distinct topological graphs are chosen to integrate multiview attribute graph information by checking whether there exists high-order neighbor information or not. Meanwhile, the number of layers of the GCN encoders is selected according to the prior knowledge related to the characteristics of different topological graphs. In particular, the feature-level and cluster-level contrastive learning are conducted on the multiview soft assignment representations, where the union of the first-order neighbors from the corresponding graph pairs is regarded as the positive pairs for data augmentation and the sparse neighbor information problem in some graphs can be well dealt with. To the best of our knowledge, it is the first time to explicitly deal with the inherent relationships from the interview and intraview perspectives. Extensive experiments are conducted on several datasets to verify the superiority of the proposed CMAGC method compared with the state-of-the-art methods.

Local structure-aware graph contrastive representation learning

Traditional Graph Neural Network (GNN), as a graph representation learning method, is constrained by label information. However, Graph Contrastive Learning (GCL) methods, which tackles the label problem effectively, mainly focus on the feature information of the global graph or small subgraph structure (e.g., the first-order neighborhood). In this paper, we propose a Local Structure-aware Graph Contrastive representation Learning method (LS-GCL) to model the structural information of nodes from multiple views. Specifically, we construct the semantic subgraphs that are not limited to the first-order neighbors. For the local view, the semantic subgraph of each target node is input into a shared GNN encoder to obtain the target node embeddings at the subgraph-level. Then, we use a pooling function to generate the subgraph-level graph embeddings. For the global view, considering the original graph preserves indispensable semantic information of nodes, we leverage the shared GNN encoder to learn the target node embeddings at the global graph-level. The proposed LS-GCL model is optimized to maximize the common information among similar instances at three various perspectives through a multi-level contrastive loss function. Experimental results on six datasets illustrate that our method outperforms state-of-the-art graph representation learning approaches for both node classification and link prediction tasks.

An effective heterogeneous information network representation learning framework

Given the heterogeneity of real-world networks and the low efficiency of directly mining networks, heterogeneous information network (HIN) representation learning, which learns low-dimensional embeddings of nodes to represent various structural and semantic information in HINs, becomes a very crucial topic. Existing HIN based representation learning methods either omit the global information of networks, or only consider the first-order neighbors of each node. The two problems reflect the insufficient extraction and exploitation of network information for HIN embedding. To address these problems, we propose a novel Heterogeneous Graph SAmple and aggreGatE framework, named HGSAGE, for learning low-dimensional similarity-preserved embeddings of nodes in HINs. This framework consists of three mechanisms, i.e., the gravity model based on the meta-path reachable graphs mechanism to capture the global information of HINs, the node-level sampling and aggregating mechanism to sample and incorporate features from immediate and mediate neighbors of nodes, and the semantic-level aggregating mechanism to combine embeddings with respect to different meta-paths. Extensive experiments on three real-world heterogeneous networks of different types and scales for multiple tasks show that the proposed framework significantly outperforms the baselines. Moreover, HGSAGE has important application values in this research field.

Hierarchical parallel multi-scale graph network for 3d human pose estimation

Graph convolutional network (GCN) is a widespread architecture for 2D-to-3D human pose estimation (HPE). Vanilla graph convolution is the key in GCN for body joints feature extraction by aggregating features from the first-order neighbors of each joint at single-scale. However, the nodes features updated in graph are gradually assimilated with the network deepens This makes it difficult to model the powerful feature representation for joints and has an adverse effect on resolving the uncertainty caused by occlusion or depth ambiguity. To address these problems, we propose a hierarchical parallel multi-scale graph convolutional network (HPM-GNet) for 3D HPE in this paper. The proposed network is composed by multi-scale sub-graph networks in parallel framework, guided by the geometric constraint of human body. Firstly, a well-designed weight masked graph convolutional (WMGConv) layer is used as a fundamental unit to construct the parallel multi-scale sub-graph convolutional network module (PMGCN) in HPM-GNet, which corporately captures the features of target nodes and neighbor nodes with weight assignment. Then, a cross-scale features exchange fusion block (CFEB) is designed to aggregate multi-scale features from local and global perspective with considering the geometric information from different parts of human body. Finally, we conduct experiments on two challenging 3D human pose benchmark datasets to evaluate the effectiveness of the proposed model. The experimental results demonstrate that our model achieves state-of-the-art performance.

Regular Splitting Graph Network for 3D Human Pose Estimation.

In human pose estimation methods based on graph convolutional architectures, the human skeleton is usually modeled as an undirected graph whose nodes are body joints and edges are connections between neighboring joints. However, most of these methods tend to focus on learning relationships between body joints of the skeleton using first-order neighbors, ignoring higher-order neighbors and hence limiting their ability to exploit relationships between distant joints. In this paper, we introduce a higher-order regular splitting graph network (RS-Net) for 2D-to-3D human pose estimation using matrix splitting in conjunction with weight and adjacency modulation. The core idea is to capture long-range dependencies between body joints using multi-hop neighborhoods and also to learn different modulation vectors for different body joints as well as a modulation matrix added to the adjacency matrix associated to the skeleton. This learnable modulation matrix helps adjust the graph structure by adding extra graph edges in an effort to learn additional connections between body joints. Instead of using a shared weight matrix for all neighboring body joints, the proposed RS-Net model applies weight unsharing before aggregating the feature vectors associated to the joints in order to capture the different relations between them. Experiments and ablations studies performed on two benchmark datasets demonstrate the effectiveness of our model, achieving superior performance over recent state-of-the-art methods for 3D human pose estimation.

Matrix reconstruction with reliable neighbors for predicting potential MiRNA-disease associations.

Numerous experimental studies have indicated that alteration and dysregulation in mircroRNAs (miRNAs) are associated with serious diseases. Identifying disease-related miRNAs is therefore an essential and challenging task in bioinformatics research. Computational methods are an efficient and economical alternative to conventional biomedical studies and can reveal underlying miRNA-disease associations for subsequent experimental confirmation with reasonable confidence. Despite the success of existing computational approaches, most of them only rely on the known miRNA-disease associations to predict associations without adding other data to increase the prediction accuracy, and they are affected by issues of data sparsity. In this paper, we present MRRN, a model that combines matrix reconstruction with node reliability to predict probable miRNA-disease associations. In MRRN, the most reliable neighbors of miRNA and disease are used to update the original miRNA-disease association matrix, which significantly reduces data sparsity. Unknown miRNA-disease associations are reconstructed by aggregating the most reliable first-order neighbors to increase prediction accuracy by representing the local and global structure of the heterogeneous network. Five-fold cross-validation of MRRN produced an area under the curve (AUC) of 0.9355 and area under the precision-recall curve (AUPR) of 0.2646, values that were greater than those produced by comparable models. Two different types of case studies using three diseases were conducted to demonstrate the accuracy of MRRN, and all top 30 predicted miRNAs were verified.

Long-distance dependency combined multi-hop graph neural networks for protein–protein interactions prediction

BackgroundProtein–protein interactions are widespread in biological systems and play an important role in cell biology. Since traditional laboratory-based methods have some drawbacks, such as time-consuming, money-consuming, etc., a large number of methods based on deep learning have emerged. However, these methods do not take into account the long-distance dependency information between each two amino acids in sequence. In addition, most existing models based on graph neural networks only aggregate the first-order neighbors in protein–protein interaction (PPI) network. Although multi-order neighbor information can be aggregated by increasing the number of layers of neural network, it is easy to cause over-fitting. So, it is necessary to design a network that can capture long distance dependency information between amino acids in the sequence and can directly capture multi-order neighbor information in protein–protein interaction network.ResultsIn this study, we propose a multi-hop neural network (LDMGNN) model combining long distance dependency information to predict the multi-label protein–protein interactions. In the LDMGNN model, we design the protein amino acid sequence encoding (PAASE) module with the multi-head self-attention Transformer block to extract the features of amino acid sequences by calculating the interdependence between every two amino acids. And expand the receptive field in space by constructing a two-hop protein–protein interaction (THPPI) network. We combine PPI network and THPPI network with amino acid sequence features respectively, then input them into two identical GIN blocks at the same time to obtain two embeddings. Next, the two embeddings are fused and input to the classifier for predict multi-label protein–protein interactions. Compared with other state-of-the-art methods, LDMGNN shows the best performance on both the SHS27K and SHS148k datasets. Ablation experiments show that the PAASE module and the construction of THPPI network are feasible and effective.ConclusionsIn general terms, our proposed LDMGNN model has achieved satisfactory results in the prediction of multi-label protein–protein interactions.

Risk perception and subsidy policy-based voluntary vaccination driven by multiple information sources.

Exploring vaccination behavior is fundamental to understand the role of vaccine in suppressing the epidemic. Motivated by the efficient role of the risk perception and the subsidy policy in promoting vaccination, we propose the Risk Perception and the Risk Perception with Subsidy Policy voluntary vaccination strategies with imperfect vaccine. The risk perception is driven by multiple information sources based on global information (released by Public Health Bureau) and local information (from first-order neighbors). In time-varying networks, we use the mean-field approach and the Monte Carlo simulations to analyze the epidemic dynamics under vaccination behavior with imperfect vaccine. We find that vaccination with the incorporation of risk perception and subsidy policy can effectively control the epidemic. Moreover, information from different sources plays different roles. Global information is more helpful in promoting vaccination than local information. In addition, to further understand the influence of vaccination strategies, we calculate the social cost as the cost for the vaccine and treatment, and find that excess vaccination cost results in a higher social cost after the herd immunity. Thus, for balancing the epidemic control and social cost, providing individuals with more global information as well as local information would be helpful in vaccination. These results are expected to provide insightful guidance for designing the policy to promote vaccination.

An improved recommendation based on graph convolutional network

Graph convolutional network is a recently developed artificial neural network method commonly used in recommendation system research. This paper points out three shortcomings of existing recommendation systems based on the graph convolutional network. 1. Existing models that take the one-hot encoding based on node ordinal numbers in the graph or encoding based on original entity attributes as input may not fully utilize the information carried by the attribute interactions. 2. Previous models update the node embeddings only by the first-order neighbors in the graph convolution layer, which is easily affected by noise. 3. Existing models do not take into account differences in user opinions. We propose an improved graph convolutional network-based collaborative filtering model to address these drawbacks. We identify inner and cross interaction between user attributes and item attributes, and then we take the vector representations of aggregated attributes graph as input. In the convolutional layer, we aggregate the second-order collaborative signals and incorporate the different user opinions. The experiments on three public datasets show that our model outperforms state-of-the-art models.

Graph convolutional networks fusing motif-structure information

With the advent of the wave of big data, the generation of more and more graph data brings great pressure to the traditional deep learning model. The birth of graph neural network fill the gap of deep learning in graph data. At present, graph convolutional networks (GCN) have surpassed traditional methods such as network embedding in node classification. However, The existing graph convolutional networks only consider the edge structure information of first-order neighbors as the bridge of information aggregation in a convolution operation, which undoubtedly loses the higher-order structure information in complex networks. In order to capture more abundant information of the graph topology and mine the higher-order information in complex networks, we put forward our own graph convolutional networks model fusing motif-structure information. By identifying the motif-structure in the network, our model fuses the motif-structure information of nodes to study the aggregation feature weights, which enables nodes to aggregate higher-order network information, thus improving the capability of GCN model. Finally, we conduct node classification experiments in several real networks, and the experimental results show that the GCN model fusing motif-structure information can improve the accuracy of node classification.

Persistent destructive quantum interference in the inverted graph method

We formulate a general criterion that underlies the persistence of conductance zeros induced by destructive quantum interference under the application of external perturbations in physical systems described by a discrete nonsingular Hamiltonian $H$. Our approach uses nonzero matrix elements of ${H}^{\ensuremath{-}1}$ between two lattice points as edges of a graph to indicate the existence of a nonzero conductance between the same points. A given conductance zero, or a missing edge in the inverted graph, is preserved when the perturbation, in the form of on-site or additional interpoint hopping energies, is applied only to points outside the set of first-order graph neighbors of either the entry lead or the exit lead. We discuss the application of these results to a study of the robustness of the conductance zeros in the fulvene and benzene molecules.

ALDPI: adaptively learning importance of multi-scale topologies and multi-modality similarities for drug-protein interaction prediction.

Effective computational methods to predict drug-protein interactions (DPIs) are vital for drug discovery in reducing the time and cost of drug development. Recent DPI prediction methods mainly exploit graph data composed of multiple kinds of connections among drugs and proteins. Each node in the graph usually has topological structures with multiple scales formed by its first-order neighbors and multi-order neighbors. However, most of the previous methods do not consider the topological structures of multi-order neighbors. In addition, deep integration of the multi-modality similarities of drugs and proteins is also a challenging task. We propose a model called ALDPI to adaptively learn the multi-scale topologies and multi-modality similarities with various significance levels. We first construct a drug-protein heterogeneous graph, which is composed of the interactions and the similarities with multiple modalities among drugs and proteins. An adaptive graph learning module is then designed to learn important kinds of connections in heterogeneous graph and generate new topology graphs. A module based on graph convolutional autoencoders is established to learn multiple representations, which imply the node attributes and multiple-scale topologies composed of one-order and multi-order neighbors, respectively. We also design an attention mechanism at neighbor topology level to distinguish the importance of these representations. Finally, since each similarity modality has its specific features, we construct a multi-layer convolutional neural network-based module to learn and fuse multi-modality features to obtain the attribute representation of each drug-protein node pair. Comprehensive experimental results show ALDPI's superior performance over six state-of-the-art methods. The results of recall rates of top-ranked candidates and case studies on five drugs further demonstrate the ability of ALDPI to discover potential drug-related protein candidates. zhang@hlju.edu.cn.

Academic Collaborator Recommendation Based on Attributed Network Embedding

Abstract Purpose Based on real-world academic data, this study aims to use network embedding technology to mining academic relationships, and investigate the effectiveness of the proposed embedding model on academic collaborator recommendation tasks. Design/methodology/approach We propose an academic collaborator recommendation model based on attributed network embedding (ACR-ANE), which can get enhanced scholar embedding and take full advantage of the topological structure of the network and multi-type scholar attributes. The non-local neighbors for scholars are defined to capture strong relationships among scholars. A deep auto-encoder is adopted to encode the academic collaboration network structure and scholar attributes into a low-dimensional representation space. Findings 1. The proposed non-local neighbors can better describe the relationships among scholars in the real world than the first-order neighbors. 2. It is important to consider the structure of the academic collaboration network and scholar attributes when recommending collaborators for scholars simultaneously. Research limitations The designed method works for static networks, without taking account of the network dynamics. Practical implications The designed model is embedded in academic collaboration network structure and scholarly attributes, which can be used to help scholars recommend potential collaborators. Originality/value Experiments on two real-world scholarly datasets, Aminer and APS, show that our proposed method performs better than other baselines.

Definition of alternative tourist availability and its mapping

The purpose of the article is to justify approaches to assessing alternative tourist availability (using the example of Cherkasy region and its first-order neighbors) according to the authors’ indicators and their cartographic support. The main material. The article analyses prevailing approaches to the assessment of tourist destinations, their tourist potential. The authors have found that it is not enough to evaluate the territory itself as it functions and develops in constant competition with neighbours and territories that provide similar tourist services. The need for a traveller to choose a tourist destination between several mutually exclusive possibilities gives rise to the definition of an alternative place of rest. The article proposes to evaluate a comprehensive indicator - alternative tourist accessibility, based on the system of indicators of geographical location, infrastructural, natural-recreational, historical-cultural factors in accordance with territorial, practical, price, and informational accessibility, which is understood as a comparative assessment of territories according to specified criteria using a rating approach, geo-informational - the cartographic method and the sum of places method. Approbation of the methodology was carried out on the example of Cherkasy region and its neighbours of the first order, as they can pull off potential tourist flows most often or, conversely, act as a donor of potential tourists. Conclusions and further research. Based on the results of the study, the tourist leader is Kyiv region. Cherkasy region ranks second, losing in terms of territorial, informational and practical accessibility. The third place takes the territory of Poltava region, which is the main competitor for Cherkasy region, especially taking into account the similarity of tourist products. The main advantage of Cherkasy region in determining an alternative place of rest is affordability as the strongest competitive factor. Thus, the evaluation results confirm the present -day depiction of tourism development. We believe that such an indicator must be taken into account while developing tourism strategies and SWOT-analyses, because it allows us to identify prospects and threats, weaknesses and strengths. In the future, this method should be tested on the example of regions that are competitors for a certain type of tourist offer.

Efficient Graph Collaborative Filtering via Contrastive Learning.

Collaborative filtering (CF) aims to make recommendations for users by detecting user’s preference from the historical user–item interactions. Existing graph neural networks (GNN) based methods achieve satisfactory performance by exploiting the high-order connectivity between users and items, however they suffer from the poor training efficiency problem and easily introduce bias for information propagation. Moreover, the widely applied Bayesian personalized ranking (BPR) loss is insufficient to provide supervision signals for training due to the extremely sparse observed interactions. To deal with the above issues, we propose the Efficient Graph Collaborative Filtering (EGCF) method. Specifically, EGCF adopts merely one-layer graph convolution to model the collaborative signal for users and items from the first-order neighbors in the user–item interactions. Moreover, we introduce contrastive learning to enhance the representation learning of users and items by deriving the self-supervisions, which is jointly trained with the supervised learning. Extensive experiments are conducted on two benchmark datasets, i.e., Yelp2018 and Amazon-book, and the experimental results demonstrate that EGCF can achieve the state-of-the-art performance in terms of Recall and normalized discounted cumulative gain (NDCG), especially on ranking the target items at right positions. In addition, EGCF shows obvious advantages in the training efficiency compared with the competitive baselines, making it practicable for potential applications.