Complete Graph Research Articles

Harnessing collective structure knowledge in data augmentation for graph neural networks

Graph neural networks (GNNs) have achieved state-of-the-art performance in graph representation learning. Message passing neural networks, which learn representations through recursively aggregating information from each node and its neighbors, are among the most commonly-used GNNs. However, a wealth of structural information of individual nodes and full graphs is often ignored in such process, which restricts the expressive power of GNNs. Various graph data augmentation methods that enable the message passing with richer structure knowledge have been introduced as one main way to tackle this issue, but they are often focused on individual structure features and difficult to scale up with more structure features. In this work we propose a novel approach, namely collective structure knowledge-augmented graph neural network (CoS-GNN), in which a new message passing method is introduced to allow GNNs to harness a diverse set of node- and graph-level structure features, together with original node features/attributes, in augmented graphs. In doing so, our approach largely improves the structural knowledge modeling of GNNs in both node and graph levels, resulting in substantially improved graph representations. This is justified by extensive empirical results where CoS-GNN outperforms state-of-the-art models in various graph-level learning tasks, including graph classification, anomaly detection, and out-of-distribution generalization.

Funnel graph neural networks with multi-granularity cascaded fusing for protein–protein interaction prediction

The identification of potential protein–protein interactions (PPIs) between humans and viruses is crucial for comprehending viral infection and disease mechanisms at the molecular level. Recently, graph neural networks (GNNs) have emerged as a promising approach to expedite PPI identification. However, GNNs often suffer from over-smoothing when capturing high-order neighbor information. To tackle this issue and effectively capture implicit collaborative information from multi-hop neighbors, we propose FGNN, Funnel Graph Neural Networks with Multi-Granularity Cascaded Fusing, facilitating the distillation of information in a funnel-like manner. Specifically, it enables the mapping of information flow from the full graph to subgraphs and ultimately to nodes. By regarding subgraphs as bridges connecting higher-order neighbors, we ensure the projection of multi-hop neighbors into the same subspace, thereby achieving a comprehensive mapping of the full graph into subgraphs. Moreover, we employ an encoder equipped with a multi-head attention mechanism to effectively map subgraphs onto nodes, facilitating further refinement and compression of information derived from high-order neighbors. FGNN can effectively capture high-order neighbor information whilst relieving over-smoothing. Extensive experiments demonstrate FGNN is superior to the state-of-the-art methods in terms of AUC value. The achieved improvements in the four cardiovascular disease datasets are 7.96 %, 2.3 %, 2.49 %, and 0.82 %, respectively.

Machine learning assisted prediction of organic salt structure properties

We demonstrate a machine learning-based approach which predicts the properties of crystal structures following relaxation based on the unrelaxed structure. Use of crystal graph singular values reduces the number of features required to describe a crystal by more than an order of magnitude compared to the full crystal graph representation. We construct machine learning models using the crystal graph singular value representations in order to predict the volume, enthalpy per atom, and metal versus semiconductor/insulator phase of DFT-relaxed organic salt crystals based on randomly generated unrelaxed crystal structures. Initial base models are trained to relate 89,949 randomly generated structures of salts formed by varying ratios of 1,3,5-triazine and HCl with the corresponding volumes, enthalpies per atom, and phase of the DFT-relaxed structures. We further demonstrate that the base model is able to be extended to related chemical systems (isomers, pyridine, thiophene and piperidine) with the inclusion of 2000 to 10,000 crystal structures from the additional system. After training a single model with a large number of data points, extension can be done at significantly lower cost. The constructed machine learning models can be used to rapidly screen large sets of randomly generated organic salt crystal structures and efficiently downselect the structures most likely to be experimentally realizable. The models can be used as a stand-alone crystal structure predictor, but may serve CSP efforts best as a filtering step in more sophisticated workflows.

Separable Spatial-Temporal Residual Graph for Cloth-Changing Group Re-Identification.

Group re-identification (GReID) aims to correctly associate group images belonging to the same group identity, which is a crucial task for video surveillance. Existing methods only model the member feature representations inside each image (regarded as spatial members), which leads to potential failures in long-term video surveillance due to cloth-changing behaviors. Therefore, we focus on a new task called cloth-changing group re-identification (CCGReID), which needs to consider group relationship modeling in GReID and robust group representation against cloth-changing members. In this paper, we propose the separable spatial-temporal residual graph (SSRG) for CCGReID. Unlike existing GReID methods, SSRG considers both spatial members inside each group image and temporal members among multiple group images with the same identity. Specifically, SSRG constructs full graphs for each group identity within the batched data, which will be completely and non-redundantly separated into the spatial member graph (SMG) and temporal member graph (TMG). SMG aims to extract group features from spatial members, and TMG improves the robustness of the cloth-changing members by feature propagation. The separability enables SSRG to be available in the inference rather than only assisting supervised training. The residual guarantees efficient SSRG learning for SMG and TMG. To expedite research in CCGReID, we develop two datasets, including GroupPRCC and GroupVC, based on the existing CCReID datasets. The experimental results show that SSRG achieves state-of-the-art performance, including the best accuracy and low degradation (only 2.15% on GroupVC). Moreover, SSRG can be well generalized to the GReID task. As a weakly supervised method, SSRG surpasses the performance of some supervised methods and even approaches the best performance on the CSG dataset.

Composite Neighbor-Aware Convolutional Metric Networks for Hyperspectral Image Classification.

Supervised classification of hyperspectral image (HSI) is generally required to obtain better performance in spectral-spatial feature learning by fully using complex pixel- and superpixel-level interdependencies with small labeled samples. Limited by the local regular convolutions, convolutional neural networks (CNNs) can only exploit information from the short-range Euclidean neighbors of a target, hindering the effectiveness of feature representation. In contrast, graph convolutional networks (GCNs) can learn long-range dependencies between non-Euclidean neighbors but usually require the input of a full graph constructed from a whole HSI, making GCNs must be trained in a full-batch manner with tremendous computational consumption. In this work, we propose a composite neighbor-aware convolutional metric network (CNCMN), aiming to learn each target's representation from its composite neighbors (i.e., both Euclidean and non-Euclidean neighbors) in a batchwise manner. Specifically, for each target in an HSI, its Euclidean neighbors are the pixels in the local square region centered on itself, and its non-Euclidean neighbors are several related nodes selected from the constructed full graph. Correspondingly, a composite convolution (CoConv) is proposed by coupling an image convolution and a graph convolution, which can perform flexible convolutions on those composite neighbors and extract adaptively fused features from them. Besides, to further boost classification, we also propose a mini-batch metric classifier to dynamically optimize interclass and intraclass distances of samples batch by batch, which is then combined with the CoConv to form the mini-batch CNCMN. Extensive experiments on three real-world HSIs demonstrate the advantages of the proposed method over mini-batch deep learning algorithms and have obtained the state-of-the-art performance in these fields. The code is available at: https://github.com/qichaoliu/HSI-CNCMN.

Interval colourable orientations of graphs

A graph is interval colourable if it admits a proper edge colouring in which for each vertex the set of colours of edges that are incident with the vertex is an interval of integers. An oriented graph is interval colourable if it admits a proper arc colouring in which for each vertex the set of colours of in-arcs and the set of colours of out-arcs that are incident with the vertex are both intervals of integers. In this paper we apply a classical approach and a new special trail technique to confirm the existence of interval colourable orientations of graphs from three classes: i) all k-trees with Δ(G)≤2k and k∈{2,3,4} and all k-paths with arbitrary k∈N; ii) graphs in which the length of every even closed trail is at least 2s and each such a trail has common edges with no more than d other even closed trails and 21−2se(d+1)≤1; iii) graphs that are decomposable into a bipartite interval colourable graph and a graph whose each connected component has at most one cycle that, if it exists, has odd length. Consequently, cactus graphs, graphs that are homeomorphic to Halin graphs, full subdivision graphs and others have interval colourable orientations.

Discovering the signal subgraph: An iterative screening approach on graphs

Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard Euclidean data and do not account for the structural information inherent in graphs. In this paper, we propose an iterative vertex screening method to achieve dimension reduction across multiple graph datasets with matched vertex sets and associated graph attributes. Our method aims to identify a signal subgraph to provide a more concise representation of the full graphs, potentially benefiting subsequent vertex classification tasks. The method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. We establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. Additionally, we establish the convergence rate of classification error under the Erdos-Renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. Our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. The results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.

On Single-Objective Sub-Graph-Based Mutation for Solving the Bi-Objective Minimum Spanning Tree Problem.

We contribute to the efficient approximation of the Pareto-set for the classical NP-hard multiobjective minimum spanning tree problem (moMST) adopting evolutionary computation. More precisely, by building upon preliminary work, we analyze the neighborhood structure of Pareto-optimal spanning trees and design several highly biased sub-graph-based mutation operators founded on the gained insights. In a nutshell, these operators replace (un)connected sub-trees of candidate solutions with locally optimal sub-trees. The latter (biased) step is realized by applying Kruskal's single-objective MST algorithm to a weighted sum scalarization of a sub-graph. We prove runtime complexity results for the introduced operators and investigate the desirable Pareto-beneficial property. This property states that mutants cannot be dominated by their parent. Moreover, we perform an extensive experimental benchmark study to showcase the operator's practical suitability. Our results confirm that the sub-graph-based operators beat baseline algorithms from the literature even with severely restricted computational budget in terms of function evaluations on four different classes of complete graphs with different shapes of the Pareto-front.

Fast Incomplete Multi-View Clustering With View-Independent Anchors.

Multi-view clustering (MVC) methods aim to exploit consistent and complementary information among each view and achieve encouraging performance improvement than single-view counterparts. In practical applications, it is common to obtain instances with partially available information, raising researches of incomplete multi-view clustering (IMC) issues. Recently, several fast IMC methods have been proposed to process the large-scale partial data. Though with considerable acceleration, these methods seek view-shared anchors and ignore specific information among single views. To tackle the above issue, we propose a fast IMC with view-independent anchors (FIMVC-VIA) method in this article. Specifically, we learn individual anchors based on the diversity of distribution among each incomplete view and construct a unified anchor graph following the principle of consistent clustering structure. By constructing an anchor graph instead of pairwise full graph, the time and space complexities of our proposed FIMVC-VIA are proven to be linearly related to the number of samples, which can efficiently solve the large-scale task. The experiment performed on benchmarks with different missing rate illustrates the improvement in complexity and effectiveness of our method compared with other IMC methods. Our code is publicly available at https://github.com/Tracesource/ FIMVC-VIA.

Incorporating non-local anyonic statistics into a graph decomposition

In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev’s toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.

Static graph approximations of dynamic contact networks for epidemic forecasting.

Epidemic modeling is essential in understanding the spread of infectious diseases like COVID-19 and devising effective intervention strategies to control them. Recently, network-based disease models have integrated traditional compartment-based modeling with real-world contact graphs and shown promising results. However, in an ongoing epidemic, future contact network patterns are not observed yet. To address this, we use aggregated static networks to approximate future contacts for disease modeling. The standard method in the literature concatenates all edges from a dynamic graph into one collapsed graph, called the full static graph. However, the full static graph often leads to severe overestimation of key epidemic characteristics. Therefore, we propose two novel static network approximation methods, DegMST and EdgeMST, designed to preserve the sparsity of real world contact network while remaining connected. DegMST and EdgeMST use the frequency of temporal edges and the node degrees respectively to preserve sparsity. Our analysis show that our models more closely resemble the network characteristics of the dynamic graph compared to the full static ones. Moreover, our analysis on seven real-world contact networks suggests EdgeMST yield more accurate estimations of disease dynamics for epidemic forecasting when compared to the standard full static method.

Computing The Energy of Certain Graphs based on Vertex Status.

The concept of Hückel molecular orbital theory is used to compute the graph energy numerically as well asnd graphically, on the base of the status of a vertex. Our aim is to explore the graph energy of various graph families on the base of the status adjacency matirx matrix and its Laplacian version. We opt for the technique of finding eigenvalues of adjacency and Laplacian matrices constructed on the base of the status of vertices. We explore the exact status sum and Laplacian status sum energies of a complete graph, complete bipartite graph, star graphs, bistar graphs, barbell graphs and graphs of two thorny rings. We also compared the obtained results of energy numerically and graphically. In this article, we extended the study of graph spectrum and energy by introducing the new concept of the status sum adjacency matrix and the Laplacian status sum adjacency matrix of a graph. We investigated and visualized these newly defined spectrums and energies of well-known graphs, such as complete graphs, complete bi-graphs, star graphs, friendship graphs, bistar graphs, barbell graphs, and thorny graphs with 3 and 4 cycles.

An Automated Analysis Framework for Epidemiological Survey on COVID-19.

For a long time, the prevention and control of COVID-19 has received significant attention. A crucial aspect of controlling the disease's spread is the epidemiological survey of patients and the subsequent analysis of epidemiological survey reports (case reports). However, current mainstream analysis approaches are all made manually. This manual method is time-consuming and manpower-intensive. This paper designs an automated visual epidemiological survey analysis (AVESA) framework for the epidemiological survey on COVID-19. AVESA designs a deep neural network for information extraction from case reports and automatically constructs an epidemiological knowledge graph based on predefined pattern. Moreover, a multi-dimensional knowledge reasoning model is developed for conducting knowledge reasoning in the complete COVID-19 epidemiological knowledge graph. In the entity extraction sub-task and multi-task extraction sub-task, AVESA achieved F1 scores of 85.12% and 92.29% respectively on the constructed dataset, significantly outperforming the standalone information extraction models. In full-graph computing, all three experiments align closely with manual analysis standards. In the risk analysis experiment, the weighted PageRank algorithm showed an average improvement of 11.21% in Top_Recall_n% over the standard PageRank algorithm. In the community detection experiment, the weighted Louvain algorithm showed a mere 4.34% community difference rate compared to manual analysis.

Communication topology for AUV formation consensus based on optimal cost control under time-varying communication and input delays

This study investigates the optimal communication topology for consensus in autonomous underwater vehicle (AUV) formations, considering both leader-following and leaderless scenarios. Initially, a second-order dynamic model of the AUV is established using the feedback linearization method. To address time-varying delays, a universal predictor-based consensus protocol is introduced, capable of operation with or without a designated leader. Subsequently, two global quadratic cost functions are formulated based on distinct consensus errors. Utilizing linear quadratic regulator (LQR) theory and matrix theory, the optimal communication topologies and associated gain matrices are deduced. Specifically, for leader-following AUV formations, the optimal communication topology is identified as an unevenly weighted star-shaped directed spanning tree. Conversely, for leaderless formations, the optimal topology adopts a complete digraph, which indicates high interaction requirements. To accommodate practical constraints, a suboptimal topology is devised, featuring a directed spanning tree. These findings offer a theoretical framework for selecting communication topologies in AUV formations, with numerical examples provided to validate the proposed approaches.

Causality-Aware Predictions in Static Anticausal Machine Learning Tasks.

We propose a counterfactual approach to train "causality-aware" predictive models that are able to leverage causal information in static anticausal machine learning tasks (i.e., prediction tasks where the outcome influences the inputs). In applications plagued by confounding, the approach can be used to generate predictions that are free from the influence of observed confounders. In applications involving observed mediators, the approach can be used to generate predictions that only capture the direct or the indirect causal influences. Mechanistically, we train supervised learners on (counterfactually) simulated inputs that retain only the associations generated by the causal relations of interest. We focus on linear models, where analytical results connecting covariances, causal effects, and prediction mean square errors are readily available. Quite importantly, we show that our approach does not require knowledge of the full causal graph. It suffices to know which variables represent potential confounders and/or mediators. We investigate the stability of the method with respect to dataset shifts generated by selection biases and also relax the linearity assumption by extending the approach to additive models better able to account for nonlinearities in the data. We validate our approach in a series of synthetic data experiments and illustrate its application to a real dataset.

Causal Incremental Graph Convolution for Recommender System Retraining.

The real-world recommender system needs to be regularly retrained to keep with the new data. In this work, we consider how to efficiently retrain graph convolution network (GCN)-based recommender models that are state-of-the-art techniques for the collaborative recommendation. To pursue high efficiency, we set the target as using only new data for model updating, meanwhile not sacrificing the recommendation accuracy compared with full model retraining. This is nontrivial to achieve since the interaction data participates in both the graph structure for model construction and the loss function for model learning, whereas the old graph structure is not allowed to use in model updating. Toward the goal, we propose a causal incremental graph convolution (IGC) approach, which consists of two new operators named IGC and colliding effect distillation (CED) to estimate the output of full graph convolution. In particular, we devise simple and effective modules for IGC to ingeniously combine the old representations and the incremental graph and effectively fuse the long- and short-term preference signals. CED aims to avoid the out-of-date issue of inactive nodes that are not in the incremental graph, which connects the new data with inactive nodes through causal inference. In particular, CED estimates the causal effect of new data on the representation of inactive nodes through the control of their collider. Extensive experiments on three real-world datasets demonstrate both accuracy gains and significant speed-ups over the existing retraining mechanism.

Operations on Complex Intuitionistic Fuzzy Graph

Abstract: This study introduces the complex intuitionistic fuzzy graphs and analyzes certain fundamental theorem and applications. Further, new ideas in CIFG such as complete complex intuitionistic fuzzy graphs with example. Also, we defined operations on the Direct product, Semi strong product and Strong product of CIFG. Additionally, we presented the density of CIFG and balanced complex intuitionistic fuzzy graph.

Extremal values for the spectral radius of the normalized distance Laplacian

The normalized distance Laplacian of a graph G is defined as DL(G)=T(G)−1/2(T(G)−D(G))T(G)−1/2 where D(G) is the matrix with pairwise distances between vertices and T(G) is the diagonal transmission matrix. In this project, we study the minimum and maximum spectral radii associated with this matrix, and the structures of the graphs that achieve these values. In particular, we prove a conjecture of Reinhart that the complete graph is the unique graph with minimum spectral radius, and we give several partial results towards a second conjecture of Reinhart regarding which graph has the maximum spectral radius.

On cover times of Markov chains

. We consider the cover time of a discrete-time homogenous Markov chain, which is the time needed by the Markov chain to visit all its states. We analyze both the distribution and the moments of the cover time, and we are interested in exact results instead of asymptotic values of the mean cover time, which are generally considered in the literature. We first obtain several general results on the hitting time and the cover time of a subset of the state space, both in terms of distribution and moments. These results are then applied to particular graphs, namely the generalized cycle graph, the complete graph, and the generalized path graph. They lead to recurrence or analytic relations for the distribution and the mean value of their cover times.

Integer k-matching preclusion of graphs

As a generalization of matching preclusion number of a graph, we provide the (strong) integer $k$-matching preclusion number, abbreviated as $MP^{k}$ number ($SMP^{k}$ number), which is the minimum number of edges (vertices and edges) whose deletion results in a graph that has neither perfect integer $k$-matching nor almost perfect integer $k$-matching. In this paper, we obtain a necessary condition of graphs with an almost-perfect integer $k$-matching and a relational expression between the matching number and the integer $k$-matching number of bipartite graphs. And then the $MP^{k}$ number and the $SMP^{k}$ number of complete graphs, bipartite graphs and arrangement graphs are obtained, respectively.