Graph neural networks (GNNs) have been extensively utilized in various fields due to their efficient and strong capability in processing graph-structured data. However, as the scale of real-world graphs continues to grow, processing large-scale graphs with GNNs has become increasingly storage-intensive and time-consuming. Graph condensation, which aims to synthesize a smaller yet informative substitute graph, has emerged as a promising solution. Most existing approaches, however, primarily focus on feature condensation while paying less attention to faithfully reconstructing structural information. Moreover, the condensed representations are typically dense, which not only limits storage and computational efficiency but also risks retaining noise and redundancy. To address these limitations, we propose DGC, a Discrete Graph Condensation framework, where numerous nodes in the original graph can be represented by the discrete codes in the codebook while maintaining the original structure information. Specifically, we leverage high-order proximity between nodes to capture the original graph's structure and transfer it to the condensed graph via low-rank approximation. Meanwhile, node features are discretized and compressed through a vector quantized variational autoencoder, effectively reducing redundancy and enhancing storage efficiency while retaining critical information. Extensive experiments on multiple real-world graphs demonstrate the effectiveness of our proposed model against nine competitive baseline methods across different condensation ratios.

In recent years, Message Passing Neural Networks (MPNNs) have emerged as a leading paradigm for learning over graph-structured data, owing to their simple architecture and excellent scalability. However, their expressive power is strictly limited by the one-dimensional Weisfeiler–Leman (1-WL) test. A common approach to enhance expressivity is designing models based on higher-order k -WL and k -Folklore WL ( k -FWL) tests, collectively referred to as tuple-based GNNs. Despite their greater expressive power, these methods face two major challenges: (1) The neighboring tuples in k -WL/FWL are generated by replacing any node in the graph, disregarding adjacency relationships and thus failing to capture structural dependencies between tuples. (2) The design of k -WL/FWL lacks flexibility, while increasing k enhances expressivity, it also results in an exponential surge in time and space complexity. To overcome these limitations, we propose Trail-WL, a more expressive variant of the WL test, along with its neural network counterpart, Trail-based Tuple Neural Network (TTNN). We redefine node tuples as collections of trail structures, providing a more intuitive representation of graph connectivity compared to prior tuple-based methods. By incorporating variable trail lengths and node distance constraints, our model adaptively balances expressivity and scalability while preserving essential structural features. Furthermore, we propose and formally prove three theoretical expressivity theorems for Trail-WL. Finally, we conduct comprehensive experiments on both synthetic and real-world datasets, demonstrating that our approach consistently matches or outperforms baseline methods, thereby substantiating its effectiveness.

Sequential interaction networks (SIN) have been commonly adopted in many applications such as recommendation systems, search engines and social networks to describe the mutual influence between users and items/products. Efforts on representing SIN are mainly focused on capturing the dynamics of networks in Euclidean space, and recently plenty of work has extended to hyperbolic geometry for implicit hierarchical learning. Previous approaches which learn the embedding trajectories of users and items achieve promising results. However, there are still a range of fundamental issues remaining open. For example, is it appropriate to place user and item nodes in one identical space regardless of their inherent discrepancy? Instead of residing in a single fixed curvature space, how will the representation spaces evolve when new interaction occurs?

Social network alignment, identifying social accounts of the same individual across different social networks, shows fundamental importance in a wide spectrum of applications, such as link prediction and information diffusion. Individuals more often than not join in multiple social networks, and it is in fact much too expensive or even impossible to acquiring supervision for guiding the alignment. To the best of our knowledge, few method in the literature can align multiple social networks without supervision. In this article, we propose to study the problem of unsupervised multiple social network alignment. To address this problem, we propose a novel unsupervised model of joint Matrix factorization with a diagonal Cone under orthogonal Constraint, referred to as MC 2 . Its core idea is to embed and align multiple social networks in the common subspace via an unsupervised approach. Specifically, in MC 2 model, we first design a matrix optimization to infer the common subspace from different social networks. To address the nonconvex optimization, we then design an efficient alternating algorithm by leveraging its inherent functional property. Through extensive experiments on real-world datasets, we demonstrate that the proposed MC 2 model significantly outperforms the state-of-the-art methods.

Social network alignment, aligning different social networks on their common users, is receiving dramatic attentions from both academic and industry. All existing studies consider the social network to be static and neglect its inherent dynamics. In fact, the dynamics of social networks contain the discriminative pattern of an individual, which can be leveraged to facilitate social network alignment. Hence, we for the first time propose to study the problem of aligning dynamic social networks. Towards this end, we propose a novel Dynamic Graph autoencoder based dynamic social network Alignment approach, referred to as DGA, unfolding the fruitful dynamics of social networks for user alignment. However, it faces challenges in both modeling and optimization: (1) To model the intra-network dynamics, we design a novel dynamic graph autoencoder to learn user embeddings with complex network dynamics. (2) To model the inter-network alignment, we design a unified optimization framework over proposed dynamic graph autoencoders, constructing a common subspace for user alignment across different networks. (3) To address this optimization problem, we design an effective alternating algorithm with solid theoretical guarantees. We conduct extensive experiments on real-world datasets and show that the proposed approach substantially outperforms the state-of-the-art methods.

Network alignment aims to discover nodes in different networks belonging to the same identity. In recent years, the network alignment problem has aroused significant attentions in both industry and academia. However, the continuous exploding of network data brings two challenges in solving the network alignment problem, i.e., large network scale and scarce labeled data. To bridge this gap, in this paper we propose a novel approach termed asMulti-granularItyNetwork alIgnment based on coNtrastive learninG(MINING). Specifically, in MINING, we first design multi-granularity alignment framework to solve the issue of large network scale. Then, we design intra- and inter-network contrastive learning to solve the issue of scarce labeled data. Moreover, we provide theoretical proofs to demonstrate the effectiveness of MINING. Finally, we conduct extensive experiments on the benchmark datasets of Facebook-Twitter, AMiner-LinkedIn and DBpedia$_{\text{ZH}}$-DBpedia$_{\text{EN}}$, and results show that MINING can averagely achieve 15.93% higher$\operatorname{Hits@}k$and 14.82% higher$\operatorname{MRR@}k$compared with the state-of-the-art methods.

Recently, aligning users among different social networks has received significant attention. However, most of the existing studies do not consider users' behavior information during the aligning procedure and thus still suffer from poor learning performance. In fact, we observe that social network alignment and user behavior analysis can benefit from each other. Motivated by such an observation, we propose to jointly study the social network alignment and user behavior analysis problem in this paper. We design a novel framework named BANANA-RGB. In this framework, to capture users' multi-scale behavior information in each social network, we train a variant of the hierarchical periodic memory network with personalized memorization. To leverage behavior analysis for social network alignment, we design a tensor fusion network-based alignment component to improve the performance. To further leverage social network alignment for behavior analysis, we design a gating-based cross-network behavior fusion component to integrate users' behavior information in different social networks based on the alignment result. We iteratively train the above two components to make the two tasks benefit from each other. Extensive experiments on real-world datasets demonstrate that our proposed approach outperforms the state-of-the-art methods.

Knowledge graph embedding aims to learn representations of entities and relations in low-dimensional space. Recently, extensive studies combine the characteristics of knowledge graphs with different geometric spaces, including Euclidean space, complex space, hyperbolic space and others, which achieves significant progress in representation learning. However, existing methods are subject to at least one of the following limitations: 1) ignoring the uncertainty, 2) incapability of complex relation patterns. To address the above issues simultaneously, we propose a novel model named DiriE, which embeds entities as Dirichlet distributions and relations as multinomial distributions. DiriE employs Bayesian inference to measure the relations between entities and learns binary embeddings of knowledge graphs for modeling complex relation patterns. Additionally, we propose a two-step negative triple generation method that generates negative triples of both entities and relations. We conduct a solid theoretical analysis to demonstrate the effectiveness and robustness of our method, including the expressiveness of complex relation patterns and the ability to model uncertainty. Furthermore, extensive experiments show that our method outperforms state-of-the-art methods in link prediction on benchmark datasets.

In social networks, one of the most significant challenges is how to estimate the tweet popularity. Prior studies focus on leveraging different aspects of just a single tweet, while ignoring the impact of historical tweets. In this article, we propose to leverage such historical information and rethink the problem of tweet popularity estimation. From historical information, there are two important factors that can be extracted: (1) user reputation feature, which can represent coarse-grained level of tweet popularity and (2) tweet related features, which can represent fine-grained level of tweet popularity. To incorporate these two factors from historical information, we design a novel deep neural architecture, a Bi-layered LSTM for tweet popUlarity Estimation, called DeepBlue. Specifically, we first propose a user-reputation aware mechanism to combine coarse-grained and fine-grained level estimation into a united LSTM model. We also design a content attention mechanism to consider different impacts of historical tweets in terms of content similarity. We then propose a time aware mechanism to address the time interval irregularity issue. Finally, we apply the Poisson regression model to obtain the overall loss for tweet popularity estimation. Extensive experiments demonstrate the superiority of our proposed approach to other state-of-the-arts in terms of MAE and SRC.

User profiling is playing an increasingly important role in real-world applications. Previous works have shown that integrating user information from multiple social networks helps to significantly improve the performance of user profiling. However, these studies either ignore the different contributions of various features in different profiling tasks or need to train one model for each task. What’s more, the assumption of the strong relatedness between user profiling tasks limits their application. These phenomena make inferring comprehensive user attributes still an open problem. In this paper, we propose a novel method, called Hierarchical Attention-based Model with sparse-sharing-based muLti-task sElf-Training algorithm (HAMLET), for comprehensive user profiling. More specifically, we first employ a hierarchical attention-based network as our base network to represent users. It assigns various features from different social networks with different weights for different users during the fusing procedure. Then, we propose a multi-task self-training algorithm that takes advantage of both task correlations and self-training to obtain better performance. We conduct extensive experiments on two real-world datasets and verify the superiority of HAMLET for user profiling.

Recently, reconciling social networks, identifying the accounts belonging to the same individual across social networks, receives significant attention from both academic and industry. Most of the existing studies have limitations in the following three aspects: multiplicity, comprehensiveness and robustness. To address these limitations, we rethink this problem and, for the first time, robustly and comprehensively reconcile multiple social networks. In this paper, we propose two frameworks, MASTER and MASTER+, i.e., across Multiple social networks, integrate Attribute and STructure Embedding for Reconciliation. In MASTER, we first design a novel Constrained Dual Embedding model, simultaneously embedding and reconciling multiple social networks, to formulate this problem into a unified optimization. To address this optimization, we then design an effective NS-Alternating algorithm and prove it converges to KKT points. To further speed up MASTER, we propose a scalable framework, namely MASTER+. The core idea is to group accounts into clusters and then perform MASTER in each cluster in parallel. Specifically, we design an efficient Augmented Pre-Embedding model and Balance-aware Fuzzy Clustering algorithm for the high efficiency and the high accuracy. Extensive experiments demonstrate that both MASTER and MASTER+ outperform the state-of-the-art approaches. Moreover, MASTER+ inherits the effectiveness of MASTER and enjoys higher efficiency.

User profiling has very important applications for many downstream tasks, such as recommender system, behavior prediction and market strategy. Most existing methods only focus on modeling user profiles of one social network with plenty of data. However, user profiles are difficult to acquire, especially when the data is scarce. Modeling user profiles under such conditions often leads to poor performance. Fortunately, we observed that not only user attributes but also user relationships are useful for user profiling and benefit the results. Meanwhile, similar users have similar behavior in different social networks. Finding user dependencies between social networks will help to infer user profiles. Motivated by such observations, in this paper, we for the first time propose to study the user profiling problem from the transfer learning perspective. We design an efficient User Profile transferring acrOss Networks (UPON) framework, which transfers knowledge of user relationship from one social network with plenty of data to facilitate the user profiling on the other social network with scarce data. In UPON, we first design a novel graph convolutional networks based characteristic-aware domain attention model (GCN-CDAM) to find user dependencies within and between domains (referring to social networks). We then design a dual-domain weighted adversarial learning method to solve the domain shift problem existing in the transferring procedure. Experimental results on Twitter-Foursquare dataset demonstrate that UPON outperforms the state-of-the-art models.

Social network alignment shows fundamental importance in a wide spectrum of applications. To the best of our knowledge, existing studies mainly focus on network alignment at the individual user level, requiring abundant common information between shared individual users. For the networks that cannot meet such requirements, social community structures actually provide complementary and critical information at a slightly coarse-grained level, alignment of which will provide additional information for user alignment. In turn, user alignment also reveals more clues for community alignment. Hence, in this paper, we introduce the problem of joint social network alignment, which aims to align users and communities across social networks simultaneously. Key challenges lie in that (1) how to learn the representations of both users and communities, and (2) how to make user alignment and community alignment benefit from each other. To address these challenges, we first elaborate on the characteristics of real-world networks with the notion of δ-hyperbolicity, and show the superiority of hyperbolic space for representing social networks. Then, we present a novel hyperbolic embedding approach for the joint social network alignment, referred to as Perfect, in a unified optimization. Extensive experiments on real-world datasets show the superiority of Perfect in both user alignment and community alignment.

Social network alignment, identifying social accounts of the same individual across different social networks, shows fundamental importance across a wide spectrum of applications. Individuals more often than not join in multiple social networks and it is in fact intractable or even impossible to acquiring supervision for guiding the alignment. However, to the best of our knowledge, none of existing methods can align multiple social networks without supervision. In this paper, we propose to study the problem of unsupervised multiple social network alignment. To address this problem, we propose a novel unsupervised model of Matrix factorization with diagonal Cone under orthogonal Constraint, referred to as MC2. Its core idea is to embed and align multiple social networks in the common subspace via an unsupervised approach. Specifically, in MC2model, we first design a matrix optimization to infer the common subspace from different social networks. To address the nonconvex optimization, we then design an efficient alternating algorithm by leveraging its inherent functional property. Through extensive experiments on real-world datasets, we demonstrate that the proposed MC2model significantly outperforms the state-of-the-art methods.

Social network alignment, aligning different social networks on their common users, is receiving dramatic attention from both academic and industry. All existing studies consider the social network to be static and neglect its inherent dynamics. In fact, the dynamics of social networks contain the discriminative pattern of an individual, which can be leveraged to facilitate social network alignment. Hence, we for the first time propose to study the problem of aligning dynamic social networks. Towards this end, we propose a novel Dynamic social Network Alignment (DNA) framework, a unified optimization approach over deep neural architectures, to unfold the fruitful dynamics to perform alignment. However, it faces tremendous challenges in both modeling and optimization: (1) To model the intra-network dynamics, we explore the local dynamics of the latent pattern in friending evolvement and the global consistency of the representation similarity with neighbors. We design a novel deep neural architecture to obtain the dual embedding capturing local dynamics and global consistency for each user. (2) To model the inter-network alignment, we exploit the underlying identity of an individual from the dual embedding in each dynamic social network. We design a unified optimization approach interplaying proposed deep neural architectures to construct a common subspace of identity embeddings. (3) To address this optimization problem, we design an effective alternating algorithm with solid theoretical guarantees. We conduct extensive experiments on real-world datasets and show that the proposed DNA framework substantially outperforms the state-of-the-art methods.

In social networks, one of the most significant challenges is how to estimate the tweet popularity. Prior studies about this problem focus on leveraging different aspects of just a single tweet, while ignoring the impact of historical tweets. In this paper, we propose to leverage such historical information and rethink the problem of tweet popularity estimation. From historical information, there are two important factors that can be extracted: (1) user reputation feature, which can represent coarse-grained level of tweet popularity; (2) tweet related features, which can represent fine-grained level of tweet popularity. To incorporate two factors from historical information, we design a novel deep neural architecture, a Bi-layered LSTM for tweet popularity Estimation, called DeepBlue. Specifically, we first propose a user-reputation aware mechanism to combine coarse-grained and fine-grained level estimation into a unified LSTM model. We then propose a time aware mechanism to address the time interval irregularity issue in standard LSTM. Finally, we apply the Poisson regression model to obtain the overall loss for tweet popularity estimation. Extensive experiments demonstrate the superiority of our proposed approach to other state-of-the-arts in terms of MAE and SRC.

Supervised topic classifiers for Twitter and other media sources are important in a variety of long-term topic tracking tasks. Unfortunately, over long periods of time, features that are predictive during the training period may prove ephemeral and fail to generalize to prediction at future times. For example, if we trained a classifier to identify tweets concerning the topic of “Celebrity Death”, individual celebrity names and terms associated with these celebrities such as “Nelson Mandela” or “South Africa” would prove to be temporally unstable since they would not generalize over long periods of time; in contrast, terms like “RIP” (rest in peace) would prove to be temporally stable predictors of this topic over long periods of time. In this paper, we aim to design supervised learning methods for Twitter topic classifiers that are capable of automatically downweighting temporally unstable features to improve future generalization. To do this, we first begin with an oracular approach that chooses temporally stable features based on knowledge of both train and test data labels. We then search for feature metrics evaluated on only the training data that are capable of recovering the temporally stable features identified by our oracular definition. We next embed the top-performing metric as a temporal stability regularizer in logistic regression with the important property that the overall training objective retains convexity, hence enabling a globally optimal solution. Finally, we train our topic classifiers on 6 Twitter topics over roughly one year of data and evaluate on the following year of data, showing that logistic regression with our temporal stability regularizer generally outperforms logistic regression without such regularization across the full precision-recall continuum. Overall, these results establish a novel regularizer for training long-term temporally stable topic classifiers for Twitter and beyond.