Graph Diffusion Research Articles

Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap

We derive several upper bounds on the spectral gap of the Laplacian on compact metric graphs with standard or Dirichlet vertex conditions. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total length of the graph, as well as further metric quantities introduced here for the first time, such as the avoidance diameter. Using known results about Ramanujan graphs, a class of expander graphs, we also prove that some of these metric quantities, or combinations thereof, do not to deliver any spectral bounds with the correct scaling.

A novel heterophilic graph diffusion convolutional network for identifying cancer driver genes.

Identifying cancer driver genes plays a curial role in the development of precision oncology and cancer therapeutics. Although a plethora of methods have been developed to tackle this problem, the complex cancer mechanisms and intricate interactions between genes still make the identification of cancer driver genes challenging. In this work, we propose a novel machine learning method of heterophilic graph diffusion convolutional networks (called HGDCs) to boost cancer-driver gene identification. Specifically, HGDC first introduces graph diffusion to generate an auxiliary network for capturing the structurally similar nodes in a biomolecular network. Then, HGDC designs an improved message aggregation and propagation scheme to adapt to the heterophilic setting of biomolecular networks, alleviating the problem of driver gene features being smoothed by its neighboring dissimilar genes. Finally, HGDC uses a layer-wise attention classifier to predict the probability of one gene being a cancer driver gene. In the comparison experiments with other existing state-of-the-art methods, our HGDC achieves outstanding performance in identifying cancer driver genes. The experimental results demonstrate that HGDC not only effectively identifies well-known driver genes on different networks but also novel candidate cancer genes. Moreover, HGDC can effectively prioritize cancer driver genes for individual patients. Particularly, HGDC can identify patient-specific additional driver genes, which work together with the well-known driver genes to cooperatively promote tumorigenesis.

DHSEGATs: distance and hop-wise structures encoding enhanced graph attention networks

Numerous works prove that existing neighbor-averaging graph neural networks (GNNs) cannot efficiently catch structure features, and many works show that injecting structure, distance, position, or spatial features can significantly improve the performance of GNNs, however, injecting high-level structure and distance into GNNs is an intuitive but untouched idea. This work sheds light on this issue and proposes a scheme to enhance graph attention networks (GATs) by encoding distance and hop-wise structure statistics. Firstly, the hop-wise structure and distributional distance information are extracted based on several hop-wise ego-nets of every target node. Secondly, the derived structure information, distance information, and intrinsic features are encoded into the same vector space and then added together to get initial embedding vectors. Thirdly, the derived embedding vectors are fed into GATs, such as GAT and adaptive graph diffusion network (AGDN) to get the soft labels. Fourthly, the soft labels are fed into correct and smooth (C&S) to conduct label propagation and get final predictions. Experiments show that the distance and hop-wise structures encoding enhanced graph attention networks (DHSEGATs) achieve a competitive result.

Local-Sample-Weighted Clustering Ensemble with High-Order Graph Diffusion

The clustering ensemble method has attracted much attention because it can improve the stability and robustness of single clustering methods. Among them, similarity-matrix-based methods or graph-based methods have had a wide range of applications in recent years. Most similarity-matrix-based methods calculate fully connected pairwise similarities by treating a base cluster as a whole and ignoring the importance of the relevance ranking of samples within the same base cluster. Since unreliable similarity estimates degrade clustering performance, constructing accurate similarity matrices is of great importance in applications. Higher-order graph diffusion based on reliable similarity matrices can further uncover potential connections between data. In this paper, we propose a more substantial graph-learning-based ensemble algorithm for local-sample-weighted clustering, which implicitly optimizes the adaptive weights of different neighborhoods based on the ranking importance of different neighbors. By further diffusion on the consensus matrix, we obtained an optimal consistency matrix with more substantial discriminative power, revealing the potential similarity relationship between samples. The experimental results showed that, compared with the second-best DREC algorithm, the accuracy of the proposed algorithm improved by 17.7%, and that of the normalized mutual information (NMI) algorithm improved by 15.88%. All empirical results showed that our clustering model consistently outperformed the related clustering methods.

Temporal group-aware graph diffusion networks for dynamic link prediction

Dynamic link prediction is a critical task in network research that seeks to predict future network links based on the relative behavior of prior network changes. However, most existing methods overlook mutual interactions between neighbors and long-distance interactions and lack the interpretability of the model’s predictions. To tackle the above issues, in this paper, we propose a temporal group-aware graph diffusion network(TGGDN). First, we construct a group affinity matrix to describe mutual interactions between neighbors, i.e., group interactions. Then, we merge the group affinity matrix into the graph diffusion to form a group-aware graph diffusion, which simultaneously captures group interactions and long-distance interactions in dynamic networks. Additionally, we present a transformer block that models the temporal information of dynamic networks using self-attention, allowing the TGGDN to pay greater attention to task-related snapshots while also providing interpretability to better understand the network evolutionary patterns. We compare the proposed TGGDN with state-of-the-art methods on five different sizes of real-world datasets ranging from 1k to 20k nodes. Experimental results show that TGGDN achieves an average improvement of 8.3% and 3.8% in terms of ACC and AUC on all datasets, respectively, demonstrating the superiority of TGGDN in the dynamic link prediction task.

A Central Limit Theorem for Diffusion in Sparse Random Graphs

We consider bootstrap percolation and diffusion in sparse random graphs with fixed degrees, constructed by configuration model. Every vertex has two states: it is either active or inactive. We assume that to each vertex is assigned a nonnegative (integer) threshold. The diffusion process is initiated by a subset of vertices with threshold zero which consists of initially activated vertices, whereas every other vertex is inactive. Subsequently, in each round, if an inactive vertex with threshold $$\theta $$ has at least $$\theta $$ of its neighbours activated, then it also becomes active and remains so forever. This is repeated until no more vertices become activated. The main result of this paper provides a central limit theorem for the final size of activated vertices. Namely, under suitable assumptions on the degree and threshold distributions, we show that the final size of activated vertices has asymptotically Gaussian fluctuations.

Graph Diffusion Convolutional Network for Skeleton Based Semantic Recognition of Two-Person Actions.

Graph Convolutional Networks (GCNs) have successfully boosted skeleton-based human action recognition. However, existing GCN-based methods mostly cast the problem as separated person's action recognition while ignoring the interaction between the action initiator and the action responder, especially for the fundamental two-person interactive action recognition. It is still challenging to effectively take into account the intrinsic local-global clues of the two-person activity. Additionally, message passing in GCN depends on adjacency matrix, but skeleton-based human action recognition methods tend to calculate the adjacency matrix with the fixed natural skeleton connectivity. It means that messages can only travel along a fixed path at different layers of the network or in different actions, which greatly reduces the flexibility of the network. To this end, we propose a novel graph diffusion convolutional network for skeleton based semantic recognition of two-person actions by embedding the graph diffusion into GCNs. At technical fronts, we dynamically construct the adjacency matrix based on practical action information, so that we can guide the message propagation in a more meaningful way. Simultaneously, we introduce the frame importance calculation module to conduct dynamic convolution, so that we can avoid the negative effect caused by the traditional convolution, wherein the shared weights may fail to capture key frames or be affected by noisy frames. Besides, we comprehensively leverage the multidimensional features related to joints' local visual appearances, global spatial relationship and temporal coherency, and for different features, different metrics are designed to measure the similarity underlying the corresponding real physical law of the motions. Moreover, extensive experiments and comprehensive evaluations on four public large-scale datasets (NTU-RGB+D 60, NTU-RGB+D 120, Kinetics-Skeleton 400, and SBU-Interaction) demonstrate that our method outperforms the state-of-the-art methods.

Graph metric learning quantifies morphological differences between two genotypes of shoot apical meristem cells inArabidopsis

AbstractWe present a method for learning ‘spectrally descriptive’ edge weights for graphs. We generalize a previously known distance measure on graphs (graph diffusion distance [GDD]), thereby allowing it to be tuned to minimize an arbitrary loss function. Because all steps involved in calculating this modified GDD are differentiable, we demonstrate that it is possible for a small neural network model to learn edge weights which minimize loss. We apply this method to discriminate between graphs constructed from shoot apical meristem images of two genotypes of Arabidopsis thaliana specimens: wild-type and trm678 triple mutants with cell division phenotype. Training edge weights and kernel parameters with contrastive loss produce a learned distance metric with large margins between these graph categories. We demonstrate this by showing improved performance of a simple k-nearest-neighbour classifier on the learned distance matrix. We also demonstrate a further application of this method to biological image analysis. Once trained, we use our model to compute the distance between the biological graphs and a set of graphs output by a cell division simulator. Comparing simulated cell division graphs to biological ones allows us to identify simulation parameter regimes which characterize mutant versus wild-type Arabidopsis cells. We find that trm678 mutant cells are characterized by increased randomness of division planes and decreased ability to avoid previous vertices between cell walls.

Streaming feature selection via graph diffusion

Streaming feature selection for unlabeled data aims to remove redundant and irrelevant features from the continuously arriving features without label information. Most existing methods usually focus on selecting a small set of features that approximately reconstruct each sample in the raw data. However, the real-world streaming data may contain irrelevant features which the current reconstruction strategy cannot effectively exclude. These irrelevant features significantly impair the reliability of the selected feature subset. To address this problem, we introduce a dynamic similarity graph to learn the pairwise sample correlations for adaptively evaluating irrelevant features. By virtue of similarity graph diffusion, the unreliable similarities caused by irrelevant features can be gradually eliminated. The past and current diffused graphs are then used to guide feature selection, thus successfully removing redundant and irrelevant features, respectively. The proposed method consists of two stages: 1) minimum redundancy: accepting only features containing new information based on the past diffused graph; 2) maximum relevance: selecting the most relevant features based on the current diffused graph. Additionally, a compound threshold operator is derived to solve the graph-based learning objective. Extensive experiments on real-world data demonstrate that the proposed method outperforms state-of-the-art unsupervised feature selection methods.

A graph neural network framework based on preference-aware graph diffusion for recommendation.

Transforming user check-in data into graph structure data is a popular and powerful way to analyze users' behaviors in the field of recommendation. Graph-based deep learning methods such as graph embeddings and graph neural networks have shown promising performance on the task of point-of-interest recommendation in recent years. Despite effectiveness, existing methods fail to capture deep graph structural information, leading the suboptimal representations. In addition, they lack the ability of learning the influences of both global preference and user preference on the check-in behavior. To address the aforementioned issues, we propose a general framework based on preference-aware graph diffusion, named PGD. We first construct two types of graphs to represent the global preference and user preference. Then, we apply a graph diffusion process to capture the structural information of the generated graphs, resulting in weighted adjacency matrices. Finally, graph neural network-based backbones are introduced to learn the representations of users and POIs on weighted adjacency matrices. A learnable aggregation module is developed to learn the final representations from global preference and user preference adaptively. Extensive experiments on four real-world datasets demonstrate the superiority of PGD on POI recommendation, compared with the mainstream graph-based deep learning methods.

Efficient information diffusion in time-varying graphs through deep reinforcement learning

Network seeding for efficient information diffusion over time-varying graphs (TVGs) is a challenging task with many real-world applications. There are several ways to model this spatio-temporal influence maximization problem, but the ultimate goal is to determine the best moment for a node to start the diffusion process. In this context, we propose Spatio-Temporal Influence Maximization (STIM), a model trained with Reinforcement Learning and Graph Embedding over a set of artificial TVGs that is capable of learning the temporal behavior and connectivity pattern of each node, allowing it to predict the best moment to start a diffusion through the TVG. We focus on the scenario where some nodes in the TVG present periodic connectivity patterns, an aspect that received little attention in previous approaches. We also develop a special set of artificial TVGs used for training that simulate a stochastic diffusion process in TVGs, showing that the STIM network can learn an efficient policy even over a non-deterministic environment. After trained, STIM can be used in TVGs of any size, since the number of parameters of the model is independent to the size of the TVG being processed. STIM is also evaluated in two real-world TVGs, where it also manages to efficiently propagate information through the nodes. Finally, we also show that the STIM model has a time complexity of O(|E|). STIM is also highly versatile, where one can change the goal of the model by simply changing the adopted reward function.

Stochastic modelling of fractal diffusion and dimension estimation

The revision of classical methods for spectral and walk dimension estimates is the main aim of the paper. Being focused on the unbiased estimation of the walk and spectral dimensions, we aim to construct the estimates with the minimal mean square error. Accompanied simulation experiments are performed on finite substrates, spacial structures serving as a good model of both continuum and fractal sets. We compare the classical approach based on the log–log transform of asymptotic models of returning probabilities and the second moments, and we also develop a weighted approach to improve the statistical properties of dimension estimates. The other discussed aspect is whether to simulate diffusion using the classical graph diffusion model with zero probability of staying in the same vertex or to prefer the physically motivated model of diffusion over edges with the optimal value of jump probability. Finally, we present the results of simulation experiments on two-dimensional finite substrates which approximate the continuum and selected Sierpinski gaskets and carpets. The paper also summarises general suggestions based on the obtained results from the simulation experiments.

Spatial-Temporal Diffusion Convolutional Network: A Novel Framework for Taxi Demand Forecasting

Taxi demand forecasting plays an important role in ride-hailing services. Accurate taxi demand forecasting can assist taxi companies in pre-allocating taxis, improving vehicle utilization, reducing waiting time, and alleviating traffic congestion. It is a challenging task due to the highly non-linear and complicated spatial-temporal patterns of the taxi data. Most of the existing taxi demand forecasting methods lack the ability to capture the dynamic spatial-temporal dependencies among regions. They either fail to consider the limitations of Graph Neural Networks or do not efficiently capture the long-term temporal dependencies. In this paper, we propose a Spatial-Temporal Diffusion Convolutional Network (ST-DCN) for taxi demand forecasting. The dynamic spatial dependencies are efficiently captured through a two-phase graph diffusion convolutional network where the attention mechanism is introduced. Moreover, a novel temporal convolution module is designed to learn various ranges of temporal dependencies, including recent, daily, and weekly periods. Inside the module, convolution layers are stacked to handle very long sequences. Experimental results on two large-scale real-world taxi datasets from New York City (NYC) and Chengdu demonstrate that our method significantly outperforms seven state-of-the-art baseline methods.

CCGL: Contrastive Cascade Graph Learning

Supervised learning, while prevalent for information cascade modeling, often requires abundant labeled data in training, and the trained model is not easy to generalize across tasks and datasets. It often learns task-specific representations, which can easily result in overfitting for downstream tasks. Recently, self-supervised learning is designed to alleviate these two fundamental issues in linguistic and visual tasks. However, its direct applicability for information cascade modeling, especially graph cascade related tasks, remains underexplored. In this work, we present Contrastive Cascade Graph Learning (CCGL), a novel framework for information cascade graph learning in a contrastive, self-supervised, and task-agnostic way. In particular, CCGL first designs an effective data augmentation strategy to capture variation and uncertainty by simulating the information diffusion in graphs. Second, it learns a generic model for graph cascade tasks via self-supervised contrastive pre-training using both unlabeled and labeled data. Third, CCGL learns a task-specific cascade model via fine-tuning using labeled data. Finally, to make the model transferable across datasets and cascade applications, CCGL further enhances the model via distillation using a teacher-student architecture. We demonstrate that CCGL significantly outperforms its supervised and semi-supervised counterparts for several downstream tasks.

P2pGNN: A Decentralized Graph Neural Network for Node Classification in Peer-to-Peer Networks

In this work, we aim to classify nodes of unstructured peer-to-peer networks with communication uncertainty, such as users of decentralized social networks. Graph Neural Networks (GNNs) are known to improve the accuracy of simple classifiers in centralized settings by leveraging naturally occurring network links, but graph convolutional layers are challenging to implement in decentralized settings when node neighbors are not constantly available. We address this problem by employing decoupled GNNs, where base classifier predictions and errors are diffused through graphs after training. For these, we deploy pre-trained and gossip-trained base classifiers and implement peer-to-peer graph diffusion under communication uncertainty. In particular, we develop an asynchronous decentralized formulation of diffusion that converges to centralized predictions in distribution and linearly with respect to communication rates. We experiment on three real-world graphs with node features and labels and simulate peer-to-peer networks with uniformly random communication frequencies; given a portion of known labels, our decentralized graph diffusion achieves comparable accuracy to centralized GNNs with minimal communication overhead (less than 3% of what gossip training already adds).

A Model-Based Approach to Assess Epidemic Risk.

We study how international flights can facilitate the spread of an epidemic to a worldwide scale. We combine an infrastructure network of flight connections with a population density dataset to derive the mobility network, and then we define an epidemic framework to model the spread of the disease. Our approach combines a compartmental SEIRS model with a graph diffusion model to capture the clusteredness of the distribution of the population. The resulting model is characterised by the dynamics of a metapopulation SEIRS, with amplification or reduction of the infection rate which is determined also by the mobility of individuals. We use simulations to characterise and study a variety of realistic scenarios that resemble the recent spread of COVID-19. Crucially, we define a formal framework that can be used to design epidemic mitigation strategies: we propose an optimisation approach based on genetic algorithms that can be used to identify an optimal airport closure strategy, and that can be employed to aid decision making for the mitigation of the epidemic, in a timely manner.

GraphXCOVID: Explainable deep graph diffusion pseudo-Labelling for identifying COVID-19 on chest X-rays

Can one learn to diagnose COVID-19 under extreme minimal supervision? Since the outbreak of the novel COVID-19 there has been a rush for developing automatic techniques for expert-level disease identification on Chest X-ray data. In particular, the use of deep supervised learning has become the go-to paradigm. However, the performance of such models is heavily dependent on the availability of a large and representative labelled dataset. The creation of which is a heavily expensive and time consuming task, and especially imposes a great challenge for a novel disease. Semi-supervised learning has shown the ability to match the incredible performance of supervised models whilst requiring a small fraction of the labelled examples. This makes the semi supervised paradigm an attractive option for identifying COVID-19. In this work, we introduce a graph based deep semi-supervised framework for classifying COVID-19 from chest X-rays. Our framework introduces an optimisation model for graph diffusion that reinforces the natural relation among the tiny labelled set and the vast unlabelled data. We then connect the diffusion prediction output as pseudo-labels that are used in an iterative scheme in a deep net. We demonstrate, through our experiments, that our model is able to outperform the current leading supervised model with a tiny fraction of the labelled examples. Finally, we provide attention maps to accommodate the radiologist’s mental model, better fitting their perceptual and cognitive abilities. These visualisation aims to assist the radiologist in judging whether the diagnostic is correct or not, and in consequence to accelerate the decision.

MWISE: An Algorithm for Context-Based Annotation of Liquid Chromatography-Mass Spectrometry Features through Diffusion in Graphs.

Untargeted metabolomics using liquid chromatography coupled to mass spectrometry (LC-MS) allows the detection of thousands of metabolites in biological samples. However, LC-MS data annotation is still considered a major bottleneck in the metabolomics pipeline since only a small fraction of the metabolites present in the sample can be annotated with the required confidence level. Here, we introduce mWISE (metabolomics wise inference of speck entities), an R package for context-based annotation of LC-MS data. The algorithm consists of three main steps aimed at (i) matching mass-to-charge ratio values to the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, (ii) clustering and filtering the potential KEGG candidates, and (iii) building a final prioritized list using diffusion in graphs. The algorithm performance is evaluated with three publicly available studies using both positive and negative ionization modes. We have also compared mWISE to other available annotation algorithms in terms of their performance and computation time. In particular, we explored four different configurations for mWISE, and all four of them outperform xMSannotator (a state-of-the-art annotator) in terms of both performance and computation time. Using a diffusion configuration that combines the biological network obtained from the FELLA R package and raw scores, mWISE shows a sensitivity mean (standard deviation) across data sets of 0.63 (0.07), while xMSannotator achieves a sensitivity of 0.55 (0.19). We have also shown that the chemical structures of the compounds proposed by mWISE are closer to the original compounds than those proposed by xMSannotator. Finally, we explore the diffusion prioritization separately, showing its key role in the annotation process. mWISE is freely available on GitHub (https://github.com/b2slab/mWISE) under a GPL license.

Traffic Flow Forecasting with Spatial-Temporal Graph Diffusion Network

Accurate forecasting of citywide traffic flow has been playing critical role in a variety of spatial-temporal mining applications, such as intelligent traffic control and public risk assessment. While previous work has made significant efforts to learn traffic temporal dynamics and spatial dependencies, two key limitations exist in current models. First, only the neighboring spatial correlations among adjacent regions are considered in most existing methods, and the global interregion dependency is ignored. Additionally, these methods fail to encode the complex traffic transition regularities exhibited with time-dependent and multi-resolution in nature. To tackle these challenges, we develop a new traffic prediction framework–Spatial-Temporal Graph Diffusion Network (ST-GDN). In particular, ST-GDN is a hierarchically structured graph neural architecture which learns not only the local region-wise geographical dependencies, but also the spatial semantics from a global perspective. Furthermore, a multi-scale attention network is developed to empower ST-GDN with the capability of capturing multi-level temporal dynamics. Experiments on four real-life traffic datasets demonstrate that ST-GDN outperforms different types of state-of-the-art baselines.

Longitudinal predictive modeling of tau progression along the structural connectome

Tau neurofibrillary tangles, a pathophysiological hallmark of Alzheimer’s disease (AD), exhibit a stereotypical spatiotemporal trajectory that is strongly correlated with disease progression and cognitive decline. Personalized prediction of tau progression is, therefore, vital for the early diagnosis and prognosis of AD. Evidence from both animal and human studies is suggestive of tau transmission along the brains preexisting neural connectivity conduits. We present here an analytic graph diffusion framework for individualized predictive modeling of tau progression along the structural connectome. To account for physiological processes that lead to active generation and clearance of tau alongside passive diffusion, our model uses an inhomogenous graph diffusion equation with a source term and provides closed-form solutions to this equation for linear and exponential source functionals. Longitudinal imaging data from two cohorts, the Harvard Aging Brain Study (HABS) and the Alzheimer’s Disease Neuroimaging Initiative (ADNI), were used to validate the model. The clinical data used for developing and validating the model include regional tau measures extracted from longitudinal positron emission tomography (PET) scans based on the 18F-Flortaucipir radiotracer and individual structural connectivity maps computed from diffusion tensor imaging (DTI) by means of tractography and streamline counting. Two-timepoint tau PET scans were used to assess the goodness of model fit. Three-timepoint tau PET scans were used to assess predictive accuracy via comparison of predicted and observed tau measures at the third timepoint. Our results show high consistency between predicted and observed tau and differential tau from region-based analysis. While the prognostic value of this approach needs to be validated in a larger cohort, our preliminary results suggest that our longitudinal predictive model, which offers an in vivo macroscopic perspective on tau progression in the brain, is potentially promising as a personalizable predictive framework for AD.