Edge Perturbation Research Articles

Parallel Sampling of Decomposable Graphs Using Markov Chains on Junction Trees

Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is straightforward in this setup, inferring the underlying graph is a challenge driven by the computational difficulty in exploring the space of decomposable graphs. This work makes two contributions to address this problem. First, we provide sufficient and necessary conditions for when multi-edge perturbations maintain decomposability of the graph. Using these, we characterize a simple class of partitions that efficiently classify all edge perturbations by whether they maintain decomposability. Second, we propose a novel parallel nonreversible Markov chain Monte Carlo sampler for distributions over junction tree representations of the graph. At every step, the parallel sampler executes simultaneously all edge perturbations within a partition. Through simulations, we demonstrate the efficiency of our new edge perturbation conditions and class of partitions. We find that our parallel sampler yields improved mixing properties in comparison to the single-move variate, and outperforms current state-of-the-art methods in terms of accuracy and computational efficiency. The implementation of our work is available in the Python package parallelDG. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Graph Contrastive Topic Model

Contrastive learning has recently been introduced into neural topic models (NTMs) to improve latent semantic discovery, but existing methods suffer from the sample bias problem owing to word frequency-based sampling strategy, which may result in false negative samples with similar semantics to the prototypes. We propose the novel graph contrastive neural topic model (GCTM), based on the graph-based sampling strategy, guided by the in-depth correlation and irrelevance information among documents and words. We model the input document as the document word bipartite graph (DWBG) and construct positive and negative word co-occurrence graphs (WCGs), to capture in-depth semantic correlation and irrelevance among words. Based on the DWBG and WCGs, we design the document-word information propagation (DWIP) process to perform the edge perturbation of DWBG, based on multi-hop correlations/irrelevance among documents and words. This yields the desired negative and positive samples, which are utilized for GCL together with the prototypes to improve learning document topic representations and latent topics. Experiments on several benchmark datasets demonstrate the effectiveness of our method for topic coherence and document representation learning compared with existing state-of-the-art methods.

Directed Network Comparison Using Motifs.

Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Most previous network comparison methods that rely on topological properties have been restricted to measuring differences between two undirected networks. However, many networks, such as biological networks, social networks, and transportation networks, exhibit inherent directionality and higher-order attributes that should not be ignored when comparing networks. Therefore, we propose a motif-based directed network comparison method that captures local, global, and higher-order differences between two directed networks. Specifically, we first construct a motif distribution vector for each node, which captures the information of a node's involvement in different directed motifs. Then, the dissimilarity between two directed networks is defined on the basis of a matrix, which is composed of the motif distribution vector of every node and the Jensen-Shannon divergence. The performance of our method is evaluated via the comparison of six real directed networks with their null models, as well as their perturbed networks based on edge perturbation. Our method is superior to the state-of-the-art baselines and is robust with different parameter settings.

DMMG: Dual Min-Max Games for Self-Supervised Skeleton-Based Action Recognition.

In this work, we propose a new Dual Min-Max Games (DMMG) based self-supervised skeleton action recognition method by augmenting unlabeled data in a contrastive learning framework. Our DMMG consists of a viewpoint variation min-max game and an edge perturbation min-max game. These two min-max games adopt an adversarial paradigm to perform data augmentation on the skeleton sequences and graph-structured body joints, respectively. Our viewpoint variation min-max game focuses on constructing various hard contrastive pairs by generating skeleton sequences from various viewpoints. These hard contrastive pairs help our model learn representative action features, thus facilitating model transfer to downstream tasks. Moreover, our edge perturbation min-max game specializes in building diverse hard contrastive samples through perturbing connectivity strength among graph-based body joints. The connectivity-strength varying contrastive pairs enable the model to capture minimal sufficient information of different actions, such as representative gestures for an action while preventing the model from overfitting. By fully exploiting the proposed DMMG, we can generate sufficient challenging contrastive pairs and thus achieve discriminative action feature representations from unlabeled skeleton data in a self-supervised manner. Extensive experiments demonstrate that our method achieves superior results under various evaluation protocols on widely-used NTU-RGB+D, NTU120-RGB+D and PKU-MMD datasets.

Cluster-Guided Contrastive Graph Clustering Network

Benefiting from the intrinsic supervision information exploitation capability, contrastive learning has achieved promising performance in the field of deep graph clustering recently. However, we observe that two drawbacks of the positive and negative sample construction mechanisms limit the performance of existing algorithms from further improvement. 1) The quality of positive samples heavily depends on the carefully designed data augmentations, while inappropriate data augmentations would easily lead to the semantic drift and indiscriminative positive samples. 2) The constructed negative samples are not reliable for ignoring important clustering information. To solve these problems, we propose a Cluster-guided Contrastive deep Graph Clustering network (CCGC) by mining the intrinsic supervision information in the high-confidence clustering results. Specifically, instead of conducting complex node or edge perturbation, we construct two views of the graph by designing special Siamese encoders whose weights are not shared between the sibling sub-networks. Then, guided by the high-confidence clustering information, we carefully select and construct the positive samples from the same high-confidence cluster in two views. Moreover, to construct semantic meaningful negative sample pairs, we regard the centers of different high-confidence clusters as negative samples, thus improving the discriminative capability and reliability of the constructed sample pairs. Lastly, we design an objective function to pull close the samples from the same cluster while pushing away those from other clusters by maximizing and minimizing the cross-view cosine similarity between positive and negative samples. Extensive experimental results on six datasets demonstrate the effectiveness of CCGC compared with the existing state-of-the-art algorithms. The code of CCGC is available at https://github.com/xihongyang1999/CCGC on Github.

A data-driven optimization method for coarse-graining gene regulatory networks

One major challenge in systems biology is to understand how various genes in a gene regulatory network (GRN) collectively perform their functions and control network dynamics. This task becomes extremely hard to tackle in the case of large networks with hundreds of genes and edges, many of which have redundant regulatory roles and functions. The existing methods for model reduction usually require the detailed mathematical description of dynamical systems and their corresponding kinetic parameters, which are often not available. Here, we present a data-driven method for coarse-graining large GRNs, named SacoGraci, using ensemble-based mathematical modeling, dimensionality reduction, and gene circuit optimization by Markov Chain Monte Carlo methods. SacoGraci requires network topology as the only input and is robust against errors in GRNs. We benchmark and demonstrate its usage with synthetic, literature-based, and bioinformatics-derived GRNs. We hope SacoGraci will enhance our ability to model the gene regulation of complex biological systems.

Exploring the multidimensional heterogeneities of glioblastoma multiforme based on sample-specific edge perturbation in gene interaction network.

Glioblastoma multiforme (GBM) is the most malignant brain cancer with great heterogeneities in many aspects, such as prognosis, clinicopathological features, immune landscapes, and immunotherapeutic responses. Considering that gene interaction network is relatively stable in a healthy state but widely perturbed in cancers, we sought to explore the multidimensional heterogeneities of GBM through evaluating the degree of network perturbations. The gene interaction network perturbations of GBM samples (TCGA cohort) and normal samples (GTEx database) were characterized by edge perturbations, which were quantized through evaluating the change in relative gene expression value. An unsupervised consensus clustering analysis was performed to identify edge perturbation-based clusters of GBM samples. Results revealed that the edge perturbation of GBM samples was stronger than that of normal samples. Four edge perturbation-based clusters of GBM samples were identified and showed prominent heterogeneities in prognosis, clinicopathological features, somatic genomic alterations, immune landscapes, and immunotherapeutic responses. In addition, a sample-specific perturbation of gene interaction score (SPGIScore) was constructed based on the differently expressed genes (DEGs) among four clusters, and exhibited a robust ability to predict prognosis. In conclusion, the bioinformatics approach based on sample-specific edge perturbation in gene interaction network provided a new perspective to understanding the multidimensional heterogeneities of GBM.

AutoGCL: Automated Graph Contrastive Learning via Learnable View Generators

Contrastive learning has been widely applied to graph representation learning, where the view generators play a vital role in generating effective contrastive samples. Most of the existing contrastive learning methods employ pre-defined view generation methods, e.g., node drop or edge perturbation, which usually cannot adapt to input data or preserve the original semantic structures well. To address this issue, we propose a novel framework named Automated Graph Contrastive Learning (AutoGCL) in this paper. Specifically, AutoGCL employs a set of learnable graph view generators orchestrated by an auto augmentation strategy, where every graph view generator learns a probability distribution of graphs conditioned by the input. While the graph view generators in AutoGCL preserve the most representative structures of the original graph in generation of every contrastive sample, the auto augmentation learns policies to introduce adequate augmentation variances in the whole contrastive learning procedure. Furthermore, AutoGCL adopts a joint training strategy to train the learnable view generators, the graph encoder, and the classifier in an end-to-end manner, resulting in topological heterogeneity yet semantic similarity in the generation of contrastive samples. Extensive experiments on semi-supervised learning, unsupervised learning, and transfer learning demonstrate the superiority of our AutoGCL framework over the state-of-the-arts in graph contrastive learning. In addition, the visualization results further confirm that the learnable view generators can deliver more compact and semantically meaningful contrastive samples compared against the existing view generation methods. Our code is available at https://github.com/Somedaywilldo/AutoGCL.

MVGCNMDA: Multi-view Graph Augmentation Convolutional Network for Uncovering Disease-Related Microbes.

Exploring the interrelationships between microbes and disease can help microbiologists make decisions and plan treatments. Predicting new microbe-disease associations currently relies on biological experiments and domain knowledge, which is time-consuming and inefficient. Automated algorithms are used to uncover the intrinsic link between microbes and disease. However, due to data noise and inadequate understanding of relevant biology, the efficient prediction of microbe-disease associations is still crucial. This study develops a multi-view graph augmentation convolutional network (MVGCNMDA) to predict potential disease-associated microbes. First, we use two data augmentation methods, edge perturbation and node dropping, to remove the data noise in the preprocessing stage. Second, we calculate Gaussian interaction profile kernel similarity and cosine similarity. Therefore, the Graph Convolutional Network(GCN) can fully use multi-view features. Then, the multi-view features are fed into the multi-attention block to learn the weights of different features adaptively. Finally, the embedding results are obtained using a Convolutional Neural Network (CNN) combiner, and the matrix completion is used to predict the relationship between potential microbes and diseases. We test our model on the Human microbe-disease Association Database (HMDAD), Disbiome, and the Combined Dataset (Peryton and MicroPhenoDB). The area under PR curve (AUPR), area under ROC curve (AUC), F1 score, and RECALL value are calculated to evaluate the performance of the developed MVGCNMDA. The AUPR is 0.9440, AUC is 0.9428, F1 score is 0.9383, and RECALL value is 0.8858. The experiments show that our model can accurately predict potential microbe-disease associations compared with the state-of-the-art works on the global Leave-One-Out-Cross-Validation (LOOCV) and the fivefold Cross-Validation (fivefold CV). To further verify the effectiveness of the proposed graph data augmentation, we designed five different settings in the ablation study. Furthermore, we present two case studies that validate the prediction of the potential association between microbes and diseases by MVGCNMDA.

A novel classification method for NSCLC based on the background interaction network and the edge-perturbation matrix.

The biological functional network of tumor tissues is relatively stable for a period of time and under different conditions, so the impact of tumor heterogeneity is effectively avoided. Based on edge perturbation, functional gene interaction networks were used to reveal the pathological environment of patients with non-small cell carcinoma at the individual level, and to identify cancer subtypes with the same or similar status, and then a multi-dimensional and multi-omics comprehensive analysis was put into practice. Two edge perturbation subtypes were identified through the construction of the background interaction network and the edge-perturbation matrix (EPM). Further analyses revealed clear differences between those two clusters in terms of prognostic survival, stemness indices, immune cell infiltration, immune checkpoint molecular expression, copy number alterations, mutation load, homologous recombination defects (HRD), neoantigen load, and chromosomal instability. Additionally, a risk prediction model based on TCGA for lung adenocarcinoma (LUAD) and lung squamous cell carcinoma (LUSC) was successfully constructed and validated using the independent data set (GSE50081).

Laplacian state transfer on graphs with an edge perturbation between twin vertices

We consider quantum state transfer relative to the Laplacian matrix of a graph. Let N(u) denote the set of all neighbors of a vertex u in a graph G. A pair of vertices u and v are called twin vertices of G provided N(u)∖{v}=N(v)∖{u}. We investigate the existence of quantum state transfer between a pair of twin vertices in a graph when the edge between the vertices is perturbed. We find that removal of any set of pairwise non-adjacent edges from a complete graph with a number of vertices divisible by 4 results Laplacian perfect state transfer (or LPST) at π2 between the end vertices of every edge removed. Further, we show that all Laplacian integral graphs with a pair of twin vertices exhibit LPST when the edge between the vertices is perturbed. In contrast, we conclude that LPST can be achieved in every complete graph between the end vertices of any number of suitably perturbed non-adjacent edges. The results are further generalized to obtain a family of edge perturbed circulant graphs exhibiting Laplacian pretty good state transfer (or LPGST) between twin vertices. A subfamily of which is also identified to admit LPST at π2.

The effect on A α -eigenvalues of mixed graphs and unit gain graphs by adding edges in clusters

Given a simple graph G, a -cluster of G is a pair of vertex subsets , where size of C is and every vertex in C shares the same set S of s neighbours. Let be a mixed graph whose underlying graph G contains a -cluster and let be a mixed graph on c vertices. Then is a graph obtained from by adding edges between some vertices in C such that . Let and be the adjacency matrix and the degree diagonal matrix of a graph G, respectively. Then the -matrix is defined to be , where . Assume that is a mixed graph containing a cognate -cluster , and for any two mixed graphs on c vertices satisfying each row sum of is equal to that of . We show that and share part of their -eigenvalues. Similarly, we consider the above problem on the unit gain graph. All of these results extend those of Cardoso and Rojo [Edge perturbation on graphs with clusters: adjacency, Laplacian and signless Laplacian eigenvalues. Linear Algebra Appl. 2017;512:113–128.] and those of Belardo, Brunetti and Ciampella [Edge perturbation on signed graphs with clusters: adjacency and Laplacian eigenvalues. Discrete Appl Math. 2019;269:130–138]. Based on our obtained results, we construct some pairs of -cospectral mixed graphs (with respect to two kinds of matrices for mixed graphs) which may not be switching equivalent.

An elementary proof and detailed investigation of the bulk-boundary correspondence in the generic two-band model of Chern insulators

With the inclusion of arbitrary long-range hopping and (pseudo)spin–orbit coupling amplitudes, we formulate a generic model that can describe any two-dimensional two-band bulk insulators, thus providing a simple framework to investigate arbitrary adiabatic deformations upon the systems of any arbitrary Chern numbers. Without appealing to advanced techniques beyond the standard methods of solving linear difference equations and applying Cauchy’s integral formula, we obtain a mathematically elementary yet rigorous proof of the bulk-boundary correspondence on a strip, which is robust against any adiabatic deformations upon the bulk Hamiltonian and any uniform edge perturbation along the edges. The elementary approach not only is more transparent about the underlying physics but also reveals various intriguing nontopological features of Chern insulators that have remained unnoticed or unclear so far. Particularly, if a certain condition is satisfied (as in most renowned models), the loci of edge bands in the energy spectrum and their (pseudo)spin polarizations can be largely inferred from the bulk Hamiltonian alone without invoking any numerical computation for the energy spectrum of a strip.

EPMDA: Edge Perturbation Based Method for miRNA-Disease Association Prediction.

In the recent few years, plenty of research has shown that microRNA (miRNA) is likely to be involved in the formation of many human diseases. So effectively predicting potential associations between miRNAs and diseases helps to understand the development and treatment of diseases. In this study, an edge perturbation based method is proposed for predicting potential miRNA-disease association (EPMDA). Different from the previous studies, we design an feature vector to describe each edge of a graph by structural Hamiltonian information. Moreover, the extracted features are used to train a multi-layer perception model to predict the candidate disease-miRNA associations. The experimental results on the HMDD dataset show that EPMDA achieves the AUC value of 0.9818 through 5-fold cross-validation, which improves the AUC values by approximately 3.5 percent compared to the latest method DeepMDA. For the leave-one-disease-out cross-validation, EPMDA achieves the AUC value of 0.9371, which improves the AUC values by approximately 7.4 percent compared to DeepMDA. In the case study, we verify the prediction performance of EPMDA on three human diseases. As a result, there are 42, 46, and 41 of the top 50 predicted miRNAs for these three diseases which are confirmed by the published experimental discoveries, respectively.

Achieving spectral localization of network using betweenness-based edge perturbation

Graph is a simple but effective way to represent a complex system, where a node represents a component of the system and edge represents connection between the components. Several insights can be inferred by analyzing such graphs. In this field, optimization of spread and localization are relatively a new research domain. The objective of the spread problem is to maximize the influence, whereas localization controls the diffusion. In this paper, our focus is on the eigenvector localization of the network adjacency matrix using inverse participation ratio (IPR). In this context, we propose betweenness centrality-based perturbation (BP) to localize the network. The results show that the BP approach achieves a better localization than the existing random perturbation (RP) approach. It shows maximum IPR than RP. The performance of the approaches is evaluated using threshold rate of diffusion (τ), number of modifications and IPR. Susceptible–infected–susceptible model is used to investigate the τ value.

Bayesian Adversarial Attack on Graph Neural Networks (Student Abstract)

Adversarial attack on graph neural network (GNN) is distinctive as it often jointly trains the available nodes to generate a graph as an adversarial example. Existing attacking approaches usually consider the case that all the training set is available which may be impractical. In this paper, we propose a novel Bayesian adversarial attack approach based on projected gradient descent optimization, called Bayesian PGD attack, which gets more general attack examples than deterministic attack approaches. The generated adversarial examples by our approach using the same partial dataset as deterministic attack approaches would make the GNN have higher misclassification rate on graph node classification. Specifically, in our approach, the edge perturbation Z is used for generating adversarial examples, which is viewed as a random variable with scale constraint, and the optimization target of the edge perturbation is to maximize the KL divergence between its true posterior distribution p(Z|D) and its approximate variational distribution qθ(Z). We experimentally find that the attack performance will decrease with the reduction of available nodes, and the effect of attack using different nodes varies greatly especially when the number of nodes is small. Through experimental comparison with the state-of-the-art attack approaches on GNNs, our approach is demonstrated to have better and robust attack performance.

State transfer in strongly regular graphs with an edge perturbation

Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state transfer in continuous-time quantum walks, which is understood to be a rare and interesting phenomenon. We consider a perturbation on an edge uv of a graph where we add a weight β to the edge and a loop of weight γ to each of u and v. We characterize when this perturbation results in strongly cospectral vertices u and v. Applying this to strongly regular graphs, we give infinite families of strongly regular graphs where some perturbation results in perfect state transfer. Further, we show that, for every strongly regular graph, there is some perturbation which results in pretty good state transfer. We also show for any strongly regular graph X and edge e∈E(X), that ϕ(X\\e) does not depend on the choice of e.

Helical plasma-wall interaction in the RFX-mod: effects of high-n mode locking

The purpose of this paper is to analyse higher toroidal harmonics m = 1 with 7 < n < 23 (secondary modes) in the quasi single helicity, reversed field pinch plasma in the RFX-mod device. The quasi single helicity is an improved confinement state characterized by a dominant mode m/n = 1/7, rotating along the toroidal direction. The spectroscopic measurements in the boundary plasma show footprints of a localized plasma deformation called ‘phase locking’, which can be described as an interferential pattern of toroidal Fourier harmonics. In the locking region the magnetic field lines are deformed in large poloidal lobes hitting the plasma facing components, a mechanism similar to the ‘homoclinic lobes’ observed in the Tokamak divertor with RMP application. Correspondingly, the magnetic connection length to the wall presents a strong decrease (‘hole’) with increased plasma-wall interaction, which fortunately is not stationary, but jumps in the toroidal direction thanks to the effective action of the RFX-mod feedback system. The global plasma wall interaction is the superposition of a rotating helix and of the localized toroidal deformation due to the secondary modes, which mirrors the local emission and particle influx from the wall. The local edge perturbation impacts also on the global plasma performance: a threshold to obtain an electron transport barrier has been identified. An improvement in plasma performance is expected in the upgraded device RFX-mod2, where the magnetic boundary will be modified to decrease the edge field deformation by a factor about 2.

Edge perturbation on signed graphs with clusters: Adjacency and Laplacian eigenvalues

Let Γ=(G,σΓ) be a signed graph, where G is the underlying simple graph and σΓ:E(G)⟶{+1,−1} is the sign function on the edges of G. A (c,s)-cluster in Γ is a pair of vertex subsets (C,S), where C is a set of cardinality |C|=c≥2 of pairwise co-neighbour vertices sharing the same set S of s neighbours. For each signed graph Λ of order c we consider the graph Γ(Λ) obtained by adding the edges of Λ, after suitably identifying C and V(Λ). It turns out that Γ(Λ) and Γ(Λ′) share part of their adjacency (resp. Laplacian) spectrum if Λ and Λ′ both show the sign-based regularity known as net-regularity (resp. negative regularity). Our results offer a generalization to signed graph of some theorems by Domingos Cardoso and Oscar Rojo concerning edge perturbations on (unsigned) graphs with clusters.

Helically localized ballooning instabilities in three-dimensional tokamak pedestals

Recent experimental observations have found toroidally localized MHD instabilities in the plasma edge during operation with applied magnetic perturbations on ASDEX Upgrade in H-mode with low collisionality . Large edge plasma displacements are induced by a stable kink response to the 3D magnetic perturbations. This kink response results in localized changes of geometric quantities, which in turn leads to the localization of MHD instabilities in the plasma edge. Infinite-n ideal MHD ballooning theory is shown to predict the existence of these instabilities, as well as the observed toroidal localization. Utilizing 3D VMEC equilibria, the local geometric parameters determining ideal stability, include the local magnetic shear, normal curvature, and geodesic curvature, are calculated for experimentally relevant conditions. It is found that these shaping parameters have significant levels of 3D variation, with the local magnetic shear being the dominant factor behind changes in the local geometry. This behavior leads to a significant decrease in the stabilizing line-bending energy for certain field lines, resulting in the localization of the ballooning instability. Furthermore, it is observed that a finite amount of magnetic perturbation (and subsequent edge perturbation) is necessary to modify the local geometry and excite the localized instability, leading to a threshold behavior.