Network alignment, which aims to find node correspondence across different networks, is the cornerstone of various downstream multi-network and Web mining tasks. Most of the embedding-based methods indirectly model cross-network node relationships by contrasting positive and negative node pairs sampled from hand-crafted strategies, which are vulnerable to graph noises and lead to potential misalignment of nodes. Another line of work based on the optimal transport (OT) theory directly models cross-network node relationships and generates noise-reduced alignments. However, OT methods heavily rely on fixed, pre-defined cost functions that prohibit end-to-end training and are hard to generalize. In this paper, we aim to unify the embedding and OT-based methods in a mutually beneficial manner and propose a joint optimal transport and embedding framework for network alignment named JOENA. For one thing (OT for embedding), through a simple yet effective transformation, the noise-reduced OT mapping serves as an adaptive sampling strategy directly modeling all cross-network node pairs for robust embedding learning. For another (embedding for OT), on top of the learned embeddings, the OT cost can be gradually trained in an end-to-end fashion, which further enhances the alignment quality. With a unified objective, the mutual benefits of both methods can be achieved by an alternating optimization schema with guaranteed convergence. Extensive experiments on real-world networks validate the effectiveness and scalability of JOENA, achieving up to 16% improvement in MRR and 20 times speedup compared with the state-of-the-art alignment methods.

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.

Multi-sourced networks naturally appear in many application domains, ranging from bioinformatics, social networks, neuroscience to management. Although state-of-the-art offers rich models and algorithms to find various patterns when input networks are given, it has largely remained nascent on how vulnerable the mining results are due to the adversarial attacks. In this paper, we address the problem of attacking multi-network mining through the way of deliberately perturbing the networks to alter the mining results. The key idea of the proposed method admiring is effective and efficient influence functions on the Sylvester equation defined over the input networks, which plays a central and unifying role in various multi-network mining tasks. The proposed algorithms bear three main advantages, including (1) effectiveness, being able to accurately quantify the rate of change of the mining results in response to attacks; (2) efficiency, scaling linearly with more than 100 times speed-up over the straight-forward implementation without any quality loss; and (3) generality, being applicable to a variety of multi-network mining tasks (e.g., graph kernel, network alignment, cross-network node similarity) with different attacking strategies (e.g., edge/node removal, attribute alteration).

Recent years have witnessed the superior performance of heterogeneous graph neural networks (HGNNs) in dealing with heterogeneous information networks (HINs). Nonetheless, the success of HGNNs often depends on the availability of sufficient labeled training data, which can be very expensive to obtain in real scenarios. Active learning provides an effective solution to tackle the data scarcity challenge. For the vast majority of the existing work regarding active learning on graphs, they mainly focus on homogeneous graphs, and thus fall in short or even become inapplicable on HINs. In this paper, we study the active learning problem with HGNNs and propose a novel meta-reinforced active learning framework MetRA. Previous reinforced active learning algorithms train the policy network on labeled source graphs and directly transfer the policy to the target graph without any adaptation. To better exploit the information from the target graph in the adaptation phase, we propose a novel policy transfer algorithm based on meta-Q-learning termed per-step MQL. Empirical evaluations on HINs demonstrate the effectiveness of our proposed framework. The improvement over the best baseline is up to 7% in Micro-F1.

Network alignment finds node correspondences across multiple networks, where the alignment accuracy is of crucial importance because of its profound impact on downstream applications. The vast majority of existing works focus on how to best utilize the topology and attribute information of the input networks as well as the anchor links when available. Nonetheless, it has not been well studied on how to boost the alignment performance through actively obtaining high-quality and informative anchor links, with a few exceptions. The sparse literature on active network alignment introduces the human in the loop to label some seed node correspondence (i.e., anchor links), which are informative from the perspective of querying the most uncertain node given few potential matchings. However, the direct influence of the intrinsic network attribute information on the alignment results has largely remained unknown. In this paper, we tackle this challenge and propose an active network alignment method (Attent) to identify the best nodes to query. The key idea of the proposed method is to leverage effective and efficient influence functions defined over the alignment solution to evaluate the goodness of the candidate nodes for query. Our proposed query strategy bears three distinct advantages, including (1) effectiveness, being able to accurately quantify the influence of the candidate nodes on the alignment results; (2) efficiency, scaling linearly with 15 − 17 × speed-up over the straight-forward implementation without any quality loss; (3) generality, consistently improving alignment performance of a variety of network alignment algorithms.

The connectivity of networks has been widely studied in many high-impact applications, ranging from immunization, critical infrastructure analysis, social network mining, to bioinformatic system studies. Regardless of the end application domains, connectivity minimization has always been a fundamental task to effectively control the functioning of the underlying system. The combinatorial nature of the connectivity minimization problem imposes an exponential computational complexity to find the optimal solution, which is intractable in large systems. To tackle the computational barrier, greedy algorithm is extensively used to ensure a near-optimal solution by exploiting the diminishing returns property of the problem. Despite the empirical success, the theoretical and algorithmic challenges of the problems still remain wide open. On the theoretical side, the intrinsic hardness and the approximability of the general connectivity minimization problem are still unknown except for a few special cases. On the algorithmic side, existing algorithms are hard to balance between the optimization quality and computational efficiency. In this article, we address the two challenges by (1) proving that the general connectivity minimization problem is NP-hard and is the best approximation ratio for any polynomial algorithms, and (2) proposing the algorithm CONTAIN and its variant CONTAIN + that can well balance optimization effectiveness and computational efficiency for eigen-function based connectivity minimization problems in large networks.

Understanding diffusion processes in networks has emerged as an important research topic because of its wide range of applications. Analysis of diffusion traces can help us answer important questions such as the source(s) of diffusion and the role of each node during the diffusion process. However, in large-scale networks, due to the cost and privacy concerns, it is almost impossible to monitor the entire network and collect the complete diffusion trace. In this paper, we tackle the problem of reconstructing the diffusion history from a partial observation. We formulate the diffusion history reconstruction problem as a maximum a posteriori (MAP) problem and prove the problem is NP-hard. Then, we propose a step-by-step reconstruction algorithm, which can always produce a diffusion history that is consistent with the partial observation. Our experimental results based on synthetic and real networks show that the algorithm significantly outperforms some existing methods.

This paper presents a novel algorithm for recovering missing values of co-evolving time series with partial embedded network information. The idea is to connect two sources of data (time series data and embedded network data) through a shared low dimensional latent space. The proposed algorithm, named NetDyna, is an Expectation-Maximization (EM) algorithm, and uses the Kalman filter and matrix factorization approaches to infer the missing values both in the time series and embedded network. Our experimental results on real datasets, including a Motes dataset and a Motion Capture dataset, show that (1) NetDyna outperforms other state-of-the-art algorithms, especially with partially observed network information; (2) its computational complexity scales linearly with the time duration of time series; and (3) the algorithm recovers the embedded network in addition to missing time series values.

Multi-sourced networks naturally appear in many application domains, ranging from bioinformatics, social networks, neuroscience to management. Although state-of-the-art offers rich models and algorithms to find various patterns when input networks are given, it has largely remained nascent on how vulnerable the mining results are due to the adversarial attacks. In this paper, we address the problem of attacking multi-network mining through the way of deliberately perturbing the networks to alter the mining results. The key idea of the proposed method (Admiring) is effective influence functions on the Sylvester equation defined over the input networks, which plays a central and unifying role in various multi-network mining tasks. The proposed algorithms bear two main advantages, including (1) effectiveness, being able to accurately quantify the rate of change of the mining results in response to attacks; and (2) generality, being applicable to a variety of multi-network mining tasks ( e.g., graph kernel, network alignment, cross-network node similarity) with different attacking strategies (e.g., edge/node removal, attribute alteration).

The unprecedented amounts of data have catalyzed the trend of combining human insights with machine learning techniques, which facilitate the use of crowdsourcing to enlist label information both effectively and efficiently. One crucial challenge in crowdsourcing is the diverse worker quality, which determines the accuracy of the label information provided by such workers. Motivated by the observations that same set of tasks are typically labeled by the same set of workers, we studied their behaviors across multiple related tasks and proposed an optimization framework for learning from task and worker dual heterogeneity. The proposed method uses a weight tensor to represent the workers’ behaviors across multiple tasks, and seeks to find the optimal solution of the tensor by exploiting its structured information. Then, we propose an iterative algorithm to solve the optimization problem and analyze its computational complexity. To infer the true label of an example, we construct a worker ensemble based on the estimated tensor, whose decisions will be weighted using a set of entropy weight. We also prove that the gradient of the most time-consuming updating block is separable with respect to the workers, which leads to a randomized algorithm with faster speed. Moreover, we extend the learning framework to accommodate to the multi-class setting. Finally, we test the performance of our framework on several datasets, and demonstrate its superiority over state-of-the-art techniques.

This paper studies the problem of robustifying an interdependent network by rewiring a small number of links in realtime during a cascading attack. Interdependent networks have been widely used to model interconnected complex systems such as a critical infrastructure network including both the power grid and the Internet. Realtime robustification of interdependent networks, therefore, has significant practical importance. This paper formulates the problem using the Markov decision process (MDP) framework. We first show the problem is NP-hard and then develop an effective and efficient greedy algorithm, named REALWIRE, to robustify the network in realtime. REALWIREscores each link (and each node) based on the expected number of links failures resulted from the failure of the link (or the node), and rewires the links greedily according to the scores. Extensive experimental results show that REALWIREoutperforms other algorithms on multiple trobustness metrics.

Network connectivity optimization, which aims to manipulate network connectivity by changing its underlying topology, is a fundamental task behind a wealth of high-impact data mining applications, ranging from immunization, critical infrastructure construction, social collaboration mining, bioinformatics analysis, to intelligent transportation system design. To tackle its exponential computation complexity, greedy algorithms have been extensively used for network connectivity optimization by exploiting its diminishing returns property. Despite the empirical success, two key challenges largely remain open. First, on the theoretic side, the hardness, as well as the approximability of the general network connectivity optimization problem are still nascent except for a few special instances. Second, on the algorithmic side, current algorithms are often hard to balance between the optimization quality and the computational efficiency. In this paper, we systematically address these two challenges for the network connectivity optimization problem. First, we reveal some fundamental limits by proving that, for a wide range of network connectivity optimization problems, (1) they are NP-hard and (2) (1-1/e) is the optimal approximation ratio for any polynomial algorithms. Second, we propose an effective, scalable and general algorithm (CONTAIN) to carefully balance the optimization quality and the computational efficiency.

Nowadays, crowdsourcing has been commonly used to enlist label information both effectively and efficiently. One major challenge in crowdsourcing is the diverse worker quality, which determines the accuracy of the label information provided by such workers. Motivated by the observation that in many crowdsourcing platforms, the same set of workers typically work on the same set of tasks, we propose to model the diverse worker quality by studying their behaviors across multiple related tasks. To this end, we propose an optimization framework named MultiC2 for learning from task and worker dual heterogeneity. It uses a weight tensor to represent the workers' behaviors across multiple tasks, and seeks to find the optimal solution of the tensor by exploiting its structured information. We then propose an iterative algorithm to solve the optimization framework and analyze its computational complexity. To infer the true label of an example, we construct a worker ensemble based on the estimated tensor, whose decisions will be weighted using a set of entropy weight. Finally, we test the performance of MultiC2 on various data sets, and demonstrate its superiority over state-of-the-art crowdsourcing techniques.

The increasingly connected world has catalyzed the fusion of networks from different domains, which facilitates the emergence of a new network model-multi-layered networks. Examples of such kind of network systems include critical infrastructure networks, biological systems, organization-level collaborations, cross-platform e-commerce, and so forth. One crucial structure that distances multi-layered network from other network models is its cross-layer dependency, which describes the associations between the nodes from different layers. Needless to say, the cross-layer dependency in the network plays an essential role in many data mining applications like system robustness analysis and complex network control. However, it remains a daunting task to know the exact dependency relationships due to noise, limited accessibility, and so forth. In this article, we tackle the cross-layer dependency inference problem by modeling it as a collective collaborative filtering problem. Based on this idea, we propose an effective algorithm Fascinate that can reveal unobserved dependencies with linear complexity. Moreover, we derive Fascinate-ZERO, an online variant of Fascinate that can respond to a newly added node timely by checking its neighborhood dependencies. We perform extensive evaluations on real datasets to substantiate the superiority of our proposed approaches.

Multi-layered networks have recently emerged as a new network model, which naturally finds itself in many high-impact application domains, ranging from critical inter-dependent infrastructure networks, biological systems, organization-level collaborations, to cross-platform e-commerce, etc. Cross-layer dependency, which describes the dependencies or the associations between nodes across different layers/networks, often plays a central role in many data mining tasks on such multi-layered networks. Yet, it remains a daunting task to accurately know the cross-layer dependency a prior. In this paper, we address the problem of inferring the missing cross-layer dependencies on multi-layered networks. The key idea behind our method is to view it as a collective collaborative filtering problem. By formulating the problem into a regularized optimization model, we propose an effective algorithm to find the local optima with linear complexity. Furthermore, we derive an online algorithm to accommodate newly arrived nodes, whose complexity is just linear wrt the size of the neighborhood of the new node. We perform extensive empirical evaluations to demonstrate the effectiveness and the efficiency of the proposed methods.

Diffusion processes in networks can be used to model many real-world processes. Analysis of diffusion traces can help us answer important questions such as the source of diffusion and the role of each node in the diffusion process. However, in large-scale networks, it is very expensive if not impossible to monitor the entire network to collect the complete diffusion trace. This paper considers diffusion history reconstruction from a partial observation and develops a greedy, step-by-step reconstruction algorithm. It is proved that the algorithm always produces a diffusion history that is consistent with the partial observation. Our experimental results based on real networks and real diffusion data show that the algorithm significantly outperforms some existing methods.