Network embedding is a commonly used technique in graph mining and plays an important role in a variety of applications. Most network embedding works can be categorized into positional node embedding methods and target at capturing the proximity/relative position of node pairs. Recently, structural node embedding has attracted tremendous research interest, which is intended to perceive the local structural information of node, i.e., nodes can share similar local structures in different positions of graphs. Although numerous structural node embedding methods are designed to encode such structural information, most, if not all, of these methods cannot simultaneously achieve the following three desired properties: (1) bijective mapping between embedding and local structure of node; (2) inductive capability; and (3) good interpretability of node embedding. To address this challenge, in this paper, we propose a novel structural node embedding algorithm named topological anonymous walk embedding (TAWE). Specifically, TAWE creatively integrates anonymous walk and breadth-first search (BFS) to construct the bijective mapping between node embedding and local structure of node. In addition, TAWE possesses inductive capability and good interpretability of node embedding. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of the proposed TAWE algorithm in both structural node classification task and structural node clustering task.

Graph neural networks (GNNs) have exhibited superb power in many graph related tasks. Existing GNNs can be categorized into spatial GNNs and spectral GNNs. The spatial GNNs primarily capture the local information around each node, while the spectral GNNs are able to operate on the frequency signals of the entire graph. However, most, if not all, existing spectral GNNs are faced with two limitations: (1) the polynomial limitation that for most spectral GNNs, the expressive power in the spectral domain is limited to polynomial filters; and (2) the transductive limitation that most spectral GNNs can only be applied to the transductive setting on relatively small-scale graphs. In this paper, we propose a novel spectral graph neural network named SLOG to solve the above two limitations. For the polynomial limitation, SLOG proposes a novel real-valued filter with geometric interpretability, mathematical feasibility and adaptive filtering ability to go beyond polynomial. For the transductive limitation, SLOG combines the subgraph sampling technique in spatial GNNs and the signal processing technique in spectral GNNs together to make itself tailored to the inductive setting on large-scale graphs. Extensive experimental results on 16 datasets demonstrate the superiority of SLOG in inductive homophilic and heterophilic node classification task.

Diffusion on graphs is ubiquitous with numerous high-impact applications, ranging from the study of residential segregation in socioeconomics and activation cascading in neuroscience, to the modeling of disease contagion in epidemiology and malware spreading in cybersecurity. In these applications, complete diffusion histories play an essential role in terms of identifying dynamical patterns, reflecting on precaution actions, and forecasting intervention effects. Despite their importance, complete diffusion histories are rarely available and are highly challenging to reconstruct due to ill-posedness, explosive search space, and scarcity of training data. To date, few methods exist for diffusion history reconstruction. They are exclusively based on the maximum likelihood estimation (MLE) formulation and require to know true diffusion parameters. In this paper, we study an even harder problem, namely reconstructing Diffusion history from A single SnapsHot (DASH), where we seek to reconstruct the history from only the final snapshot without knowing true diffusion parameters. We start with theoretical analyses that reveal a fundamental limitation of the MLE formulation. We prove: (a) estimation error of diffusion parameters is unavoidable due to NP-hardness of diffusion parameter estimation, and (b) the MLE formulation is sensitive to estimation error of diffusion parameters. To overcome the inherent limitation of the MLE formulation, we propose a novel barycenter formulation: finding the barycenter of the posterior distribution of histories, which is provably stable against the estimation error of diffusion parameters. We further develop an effective solver named DIffusion hiTting Times with Optimal proposal (DITTO) by reducing the problem to estimating posterior expected hitting times via the Metropolis-Hastings Markov chain Monte Carlo method (M-H MCMC) and employing an unsupervised graph neural network to learn an optimal proposal to accelerate the convergence of M-H MCMC. We conduct extensive experiments to demonstrate the efficacy of the proposed method. Our code is available at https://github.com/q-rz/KDD23-DITTO. The appendix can be found at https://arxiv.org/abs/2306.00488.

Multivariate time series (MTS) imputation is a widely studied problem in recent years. Existing methods can be divided into two main groups, including (1) deep recurrent or generative models that primarily focus on time series features, and (2) graph neural networks (GNNs) based models that utilize the topological information from the inherent graph structure of MTS as relational inductive bias for imputation. Nevertheless, these methods either neglect topological information or assume the graph structure is fixed and accurately known. Thus, they fail to fully utilize the graph dynamics for precise imputation in more challenging MTS data such as networked time series (NTS), where the underlying graph is constantly changing and might have missing edges. In this paper, we propose a novel approach to overcome these limitations. First, we define the problem of imputation over NTS which contains missing values in both node time series features and graph structures. Then, we design a new model named PoGeVon which leverages variational autoencoder (VAE) to predict missing values over both node time series features and graph structures. In particular, we propose a new node position embedding based on random walk with restart (RWR) in the encoder with provable higher expressive power compared with message-passing based graph neural networks (GNNs). We further design a decoder with 3-stage predictions from the perspective of multi-task learning to impute missing values in both time series and graph structures reciprocally. Experiment results demonstrate the effectiveness of our model over baselines.

This paper explicitly addresses the multi-modal traffic signal control problem in the shared space street (SSS), where there are multiple travel modes (e.g. passenger cars, buses, and light rails) competing for their spaces in the same lane. SSS widely exists in central business districts where the road space is limited and the multi-modal travel demand is high. An optimization framework with a multi-modal cell transmission model (M-CTM) is developed to model the multi-modal traffic in the network. Also, this study models the passenger’s choice of choosing among different travel modes based on travel costs. Regarding multi-modal signal coordination, a cycle-based traffic signal plan selection model is developed to choose the best offline optimized signal plan to minimize the total travel cost of all three modes. Therefore, the computation burden is significantly reduced in the optimization model. Moreover, a particle swarm optimization (PSO) method is implemented to solve the proposed optimization model. A case study in downtown Buffalo validates the proposed model with microscopic traffic simulation VISSIM.