Inductive knowledge graph completion (KGC) aims to represent unseen entities and complete triplets in emerging knowledge graphs (KGs), while the existing studies ignore that unseen elements combined with seen ones constitute a holistic new relational graph, where emerging KGs have inescapable impacts backtracking to original ones. Therefore, it is not only necessary to predict triplets in emerging KGs, but also with particular significance to further improve the completeness of original ones, considering the semantic and topological variations in the holistic new graph. To fill in this gap, we formulate a newIT(Inductive-Transductive) KGC task to transductively complete triplets inside original KGs after entities in the emerging scenario are represented and fine-tuned in an inductive manner. In order to handle this task, a novel model entitled StaR (Self-adaptive Retroaction-awareRepresentation) is proposed consisting of the following two modules: 1) a self-adaptive semantic encoding network is designed to adaptively adjust embeddings of seen entities to their surrounding semantic mutations; 2) a relation-aware transformer layer is developed to represent both seen and unseen entities in a unified representation space and generalize evolving reasoning paradigms to the whole graph. Our experimental results demonstrate that, compared with state-of-the-art methods, StaR is not only competitive in inductive KGC for unseen entities, but also ulteriorly improves the completeness of original parts inside the holistic new relational graph in ourITKGC task.

Trajectory anomaly detection, as a fundamental operation for moving object pattern discovery, plays an irreplaceable and critical role in spatio-temporal location-based services. Conducting online detection based on the current positions and their contextual semantics can significantly enhance the value of trajectory data. However, existing approaches suffer from two fundamental limitations: 1) treat trajectories as indivisible sequences or apply rigid segmentation strategies, and 2) use of a single detection model that struggles to adapt to concept drift caused by evolving trajectory distributions. Such limitations make it impossible to detect abnormal trajectories in a timely and semantically comprehensive manner. To fill this gap, we propose Stamp, a novel framework for Semantic-aware sub-Trajectory Anomaly detection with a diffusion Multi-model Pool. In particular, Stamp comprises three key innovations: 1. It employs a semantic-driven dynamic segmentation mechanism that identifies natural breakpoints in trajectories based on changes in road semantics, rather than fixed rules. 2. It enhances trajectory representation by embedding road network semantic vectors, capturing both spatial geometry and functional urban characteristics. 3. It employs a pool of diffusion models that dynamically evolves through reliability assessment, similarity measurement, and strategic merging operations, ensuring adaptability to concept drift while leveraging the superior generative capabilities of diffusion models over traditional autoencoders. Experimental results demonstrate that Stamp improves detection efficiency by 35%, AUPR by 5.6%, and F1-score by 2.7% on two large-scale real-world urban trajectory datasets when compared to state-of-the-art methods, demonstrating its effectiveness for real-time anomaly detection in complex urban environments.

Cardinality estimation has long been crucial for cost-based database optimizers in identifying optimal query execution plans, attracting significant attention over the past decades. While recent advancements have significantly improved the accuracy of multi-table join query estimations, these methods introduce challenges such as higher space overhead, increased latency, and greater complexity, especially when integrated with the binary join framework. In this paper, we introduce a novel cardinality estimation method named TKHist, which addresses these challenges by relaxing the uniformity assumption in histograms. TKHist captures bin-wise non-uniformity information, enabling accurate cardinality estimation for join queries without filter predicates. Furthermore, we explore the attribute independent assumption, which can lead to significant over-estimation rather than under-estimation in multi-table join queries. To address this issue, we propose the dominating join path correlation discovery algorithm to highlight and manage correlations between join keys and filter predicates. Our extensive experiments on popular benchmarks demonstrate that TKHist reduces error variance by 2-3 orders of magnitude compared to SOTA methods, while maintaining comparable or lower memory usage.

Data isolation poses a significant challenge to efficient big data query processing, as data providers are often reluctant to share their raw data due to security concerns. Current federated query systems address this issue by employing Secure Multi-Party Computation (SMC) and Differential Privacy (DP) to facilitate secure and collaborative computation. However, these privacy-preserving methods rely on cryptographic protocols, which introduce substantial computational overhead, slowing query processing by up to 1,000 times compared to plaintext queries. While sampling methods have been explored to enhance federated query systems, they frequently fail to strike a balance between accuracy and speed. To address the limitations above, we propose a secure federated approximate query system based on a deep classifier (SAQDC). This system utilizes deep learning techniques to accelerate query processing while integrating SMC and Differential Privacy to achieve an optimal balance between privacy and efficiency by allowing each data provider to train classifiers using Multi-Layer Perceptron (MLP) and Deep Set architectures, which predict query relative errors across different modules.Based on the prediction errors generated by the classifier, queries are assigned to the most appropriate approximate query model and the differential privacy parameters are adjusted to enhance query accuracy. This approach enhances query speed, preserves accuracy, and effectively mitigates malicious differential privacy attacks. We demonstrate SAQDC's superior performance through extensive experiments on three large-scale datasets.

Entity Alignment (EA) aims to identify equivalent entities across multiple Knowledge Graphs (KGs). However, when applied to larger-scale KGs, most existing EA approaches suffer from the scalability issue due to excessive GPU memory and time consumption. To mitigate this, recent advances have introduced the Large-scale EA (LsEA) task, which divides large-scale KG pairs into smaller sub-graph pairs. Despite their promising results, several notable challenges remain, preventing these advances from achieving optimal performance: 1) How to effectively utilize critical structures when generating sub-tasks? 2) How to supplement high-quality context to enhance LsEA performance? 3) How to address scenarios without alignment seeds? To tackle these challenges, we propose a novel method called ELsEA. It comprises three main components: (1) Source and Target Graph Partition, using a Metis-based weighted partitioner and a counter-part candidate generator to partition source and target graphs respectively, aiming to utilize critical structures effectively; (2) Supplement High-quality Context, which utilizes a value-based informativeness-evaluation module and a neighbor enrichment module to assess each entity's informativeness effectively, then supplement high-quality context based on this informativeness; and (3) Seed-free Setup, introducing a mixed-info pseudo-seed generation strategy to mitigate name bias, generating accurate pseudo-seeds when alignment seeds are unavailable. Extensive experiments demonstrate that ELsEA outperforms state-of-the-art baselines. The code of ELsEA is available online11https://githuh.com/wx-qzhou/ELsEA.git.

Trajectory similarity computation is a fundamental functionality in trajectory data mining, with wide-ranging applications in location-based services. Position embedding, which transforms GPS points into embedding vectors, plays a critical role in learning-based trajectory similarity models. The quality of these embeddings significantly impacts the performance of the models on downstream tasks. Existing methods fail to satisfy all good properties, i.e., global, continuous, unique, and dynamic, thereby limiting the development of trajectory similarity computation in both local and global scenarios. Inspired by linear counting systems, such as the decimal system, we first propose the łambda-base circular system to embed positions on the circle, then introduce the multi-base global embedding method GPE to encode global positions into vectors. Experiments conducted on five real-world datasets with nine baseline methods demonstrate that the GPE achieves state-of-the-art performance across four key evaluations in downstream tasks.

Multi-modal recommender systems (MMRSs) have demonstrated significant potential in mitigating data sparsity and cold start problems by leveraging diverse multi-modal data, such as text and images. To further improve the recommendation accuracy, some MMRSs have integrated knowledge graphs (KGs) to enrich the graph structure with meaningful relationships between entities, giving rise to the task of KG-based MMRSs. Despite the promising results achieved by existing studies on this task, (i) they overlook the substantial noise introduced within the auxiliary information (i.e., both KGs and multi-modal data), and (ii) most of them struggle to effectively align the knowledge from history user-item interactions and auxiliary information. To tackle these limitations, we propose a novel model entitled MAGIC (noise Mitigation and knowledge Aignment for knowledge Graph-based multI-modal reCommendation). Specifically, to tackle the limitation (i), we design a noise-aware heterogeneous aggregation layer in the KG-based modal enhancement module. To address the limitation (ii), MAGIC introduces adversarial learning in the CF-based adversarial learning module, and exploits contrastive learning in the fusion and prediction module. The experiments conducted on two extended real-world datasets from different domains demonstrate the superiority of MAGIC over state-of-the-art baselines.

Abstract Recommender systems utilize data analysis and predictive algorithms to suggest relevant items to users, enhancing their experiences and engagements across various digital platforms, particularly in e-commerce. To obtain satisfactory representations of items and user preferences, many existing studies (multi-modal recommendation approaches) integrate diverse data (e.g., text and images) into the recommendation process to enhance item embeddings. However, the capability of these methods is restricted due to the following problems: (1) insufficient utilization of multi-modal information; (2) lack of deeper and more adequate insights from user-item interactions after multi-modal fusion, as well as the inability to uncover more intricate or hidden knowledge in the users’ modality preference. To address these problems, we propose HUMP, which Highlights Users’ Modality Preference for multi-modal recommender systems, featuring two key components: (1) a users’ modality preference guided data fusion module for integrating users’ modality preference into user and item representations which is more appropriate for recommendation scenarios; (2) a global representation enhancement module, designed to learn the deeper relationships of fused information and enhance the representations through a user-item layered heterogeneous graph. Experiments on real-world datasets demonstrate the superiority of our model over state-of-the-art baselines.

A multi-modal knowledge graph (MKG) includes triplets that consist of entities and relations and multi-modal auxiliary data. In recent years, multi-hop multi-modal knowledge graph reasoning (MMKGR) based on reinforcement learning (RL) has received extensive attention because it addresses the intrinsic incompleteness of MKG in an interpretable manner. However, its performance is limited by empirically designed rewards and sparse relations. In addition, this method has been designed for the transductive setting where test entities have been seen during training, and it works poorly in the inductive setting where test entities do not appear in the training set. To overcome these issues, we proposeTMR(Topology-awareMulti-hopReasoning), which can conduct MKG reasoning under inductive and transductive settings. Specifically, TMR mainly consists of two components. (1) The topology-aware inductive representation captures information from the directed relations of unseen entities, and aggregates query-related topology features in an attentive manner to generate the fine-grained entity-independent features. (2) After completing multi-modal feature fusion, the relation-augmented adaptive RL conducts multi-hop reasoning by eliminating manual rewards and dynamically adding actions. Finally, we construct new MKG datasets with different scales for inductive reasoning evaluation. Experimental results demonstrate that TMP outperforms state-of-the-art MKGR methods under both inductive and transductive settings.

Multi-Modal Knowledge Graphs (MMKGs), comprising relational triples and related multi-modal data (e.g., text and images), usually suffer from the problems of low coverage and incompleteness. To mitigate this, existing studies introduce a fundamental MMKG fusion task, i.e., Multi-Modal Entity Alignment (MMEA) that identifies equivalent entities across multiple MMKGs. Despite MMEA's significant advancements, effectively integrating MMKGs remains challenging, mainly stemming from two core limitations: 1) entity ambiguity, where real-world entities across different MMKGs may possess multiple corresponding counterparts or alternative identities; and 2) severe noise within multi-modal data. To tackle these limitations, a new task MMER (Multi-Modal Entity Resolution), which expands the scope of MMEA to encompass entity ambiguity, is introduced. To tackle this task effectively, we develop a novel model ADMH-ER (Adaptive Denoising Multi-modal Hybrid for Entity Resolution) that incorporates several crucial modules: 1) multi-modal knowledge encoders, which are crafted to obtain entity representations based on multi-modal data sources; 2) an adaptive denoising multi-modal hybrid module that is designed to tackle challenges including noise interference, multi-modal heterogeneity, and semantic irrelevance across modalities; and 3) a hierarchical multi-objective learning strategy, which is proposed to ensure diverse convergence capabilities among different learning objectives. Experimental results demonstrate that ADMH-ER outperforms state-of-the-art methods.

With the widespread use of GPS devices and the advancement of location-based services, a vast amount of trajectory data has been collected and mined for various applications. Trajectory clustering, which categorizes trajectories into distinct groups, is the fundamental functionality of trajectory data mining. The challenge is how to cluster on a mass of trajectory data efficiently and universally with satisfying results. The raw trajectory clustering algorithms are universal, but trapped in the dilemma between efficiency and desirable results. Other approaches, such as density-based, road network-based, and deep learning-based algorithms, encounter issues like high time complexity, loss of trajectory integrity, reliance on road networks, and data quality during training. To tackle these challenges, we first propose the efficient KMCT (k-Means Clustering of Trajectories) algorithm based on a semantic interpolation transformation to cluster raw trajectories and achieve satisfying results. Additionally, we introduce the DA-KMCT (Density Accelerated k-Means Clustering of Trajectories) algorithm to further boost the clustering process based on trajectory densities and an optimized centroid selecting strategy. Moreover, we present a novel clustering evaluation method called IOD, which efficiently estimates clustering results on large-scale datasets with linear time complexity. Experimental results on real-world datasets demonstrate that KMCT and DA-KMCT outperform five related methods in terms of clustering quality and time efficiency, and the proposed IOD evaluation shows a strong correlation with the Silhouette Coefficient, offering a reliable and efficient alternative for evaluating clustering results.

Graph Collaborative Filtering (GCF) is designed to leverage high-order connectivity in user-item graphs, thereby significantly enhancing recommendation performance. Recent advancements have seen the integration of contrastive learning into GCF as a strategy to mitigate the challenges of data sparsity. This approach involves creating contrastive views through augmentations, followed by the generation of self-supervised signals. These signals are produced by maximizing the mutual information between the contrastive views. While this method has proven effective, we argue that current CL-based GCF models are still limited to current augmentation techniques. Existing data augmentation or noise perturbation may destroy the structural and semantic features of the original data and node attribute information is not considered. To tackle the above limitations, we propose a Meta-optimized Structure and Semantic Contrastive Learning for Graph Collaborative Filtering, named Meta-SSCL, which utilizes graph structure information and semantic information contrastive learning for recommendation. Specifically, we first model the structural and node semantic information representations with LightGCN and vanilla attention mechanism, respectively. Then consider the structural and semantic information as two contrastive views for recommendation. Next, the meta-optimized two-step training strategy generates adaptive contrastive views. Finally, we fuse structural and semantic representations for recommendation. Extensive experiments on real-world datasets demonstrate that Meta-SSCL consistently outperforms state-of-the-art sequential recommendation methods. The code is available1.

Multi-modal data have recently been utilized to improve the performance of knowledge graph completion (KGC), attracting widespread research interest. However, they have been ignored in few-shot knowledge graph completion (FKGC), which aims to discover potential facts involving unseen relations that only appear in few-shot triples. The most relevant FKGC study simply concatenates various modal features, but the performance is still limited due to the following problems: (1) lack of exploiting significant multi-modal features in neighborhoods, and (2) ineffectively modeling inter-modal interactions in a few-shot setting. To tackle these problems, we propose a novel relational learning model entitled MMSN (Multi-Modal Siamese Network) for few-shot knowledge graph completion, which is composed of the following two primary modules: the Siamese multi-modal neighbor encoder (SMNE) and the meta-learning multi-modal knowledge representation decoder (MKRD). The module SMNE is developed to encode diverse modalities of neighbors by a Siamese attention network, fuse multi-modal information through a gating fusion network, and learn effective relational embeddings using an aggregator. The module MKRD is introduced to handle inter-modal interactions between multiple modalities and train the proposed model in a few-shot scenario. Extensive experiments demonstrate that our proposed model MMSN outperforms the state-of-the-art FKGC models, including uni-modal and multi-modal models, on two real-world few-shot multi-modal datasets.

Extracting entities and relations from text is a significant task of information extraction. Existing extraction models often straightforwardly produce their confident prediction results without any reconsideration or double-checking, resulting in avoidable mistakes and sub-optimal performance. In this paper, we propose a novel coarse-to-fine extraction framework, which first extracts high-potential relations as well as entities via knowledge distillation, and then rechecks the predictions via handcrafted natural language inference (NLI) task in a fine-grained manner. Specifically, based on the knowledge distillation mechanism, we train multiple teacher models iteratively through an adaptive loss function for making one teacher concentrate more on the data that others are incompetent for. Then, these complementary teacher models are utilized to provide valuable soft-label information for training a considerate student model, enabling it to generate reliable preliminary predictions. Further, these generated potential relations and entities are formulated as hypotheses, together with the original sentences as premises, serving as the input for an NLI model. Considering the linguistic diversity of relational expression, we automatically generate various semantic templates for hypotheses through an$\mathcal{N}$-gram mining strategy. Moreover, due to the existence of multi-fact sentences, a relation-guided Gaussian attention is designed to reduce the gap between the single-relation hypothesis and the multi-relation premise. To implement efficient training, we also develop several ways to generate high-quality negative samples, which help the NLI model learn to identify errors. Experimental results show that the proposed method is effective and outperforms other strong baselines on public benchmarks.

Graph collaborative filtering (GCF) has achieved exciting recommendation performance with its ability to aggregate high-order graph structure information. Recently, contrastive learning (CL) has been incorporated into GCF to alleviate data sparsity and noise issues. However, most of the existing methods employ random or manual augmentation to produce contrastive views that may destroy the original topology and amplify the noisy effects. We argue that such augmentation is insufficient to produce the optimal contrastive view, leading to suboptimal recommendation results. In this article, we proposed a L earnable M odel A ugmentation C ontrastive L earning (LMACL) framework for recommendation, which effectively combines graph-level and node-level collaborative relations to enhance the expressiveness of collaborative filtering (CF) paradigm. Specifically, we first use the graph convolution network (GCN) as a backbone encoder to incorporate multi-hop neighbors into graph-level original node representations by leveraging the high-order connectivity in user-item interaction graphs. At the same time, we treat the multi-head graph attention network (GAT) as an augmentation view generator to adaptively generate high-quality node-level augmented views. Finally, joint learning endows the end-to-end training fashion. In this case, the mutual supervision and collaborative cooperation of GCN and GAT achieves learnable model augmentation. Extensive experiments on several benchmark datasets demonstrate that LMACL provides a significant improvement over the strongest baseline in terms of Recall and NDCG by 2.5%–3.8% and 1.6%–4.0%, respectively. Our model implementation code is available at https://github.com/LiuHsinx/LMACL .

Contrastive learning with Transformer-based sequence encoder has gained predominance for sequential recommendation due to its ability to mitigate the data noise and the data sparsity issue. However, existing contrastive learning approaches for sequential recommendation still suffer from two limitations. First, they mainly center on left-to-right unidirectional Transformers as base encoders, which are suboptimal for sequential recommendation because user behaviors may not be a rigid left-to-right sequence. Second, they devise contrastive learning objectives only from the sequence level, neglecting the rich self-supervision signals from the feature level. To address these limitations, we propose a novel framework called Feature-aware Contrastive Learning with bidirectional Transformers for sequential Recommendation (FCLRec) to effectively leverage feature information for sequential recommendation. Specifically, we first augment bidirectional Transformers with a novel feature-aware self-attention module that is able to simultaneously model the complex relationships between sequences and features. Next, we propose a novel feature-aware contrastive learning objective that generates a collection of positive samples via three types of augmentations from three different levels. Finally, we adopt feature prediction as an auxiliary task to strengthen the connections between items and features. Our experimental results on four public benchmark datasets show that FCLRec outperforms the state-of-the-art methods for sequential recommendation.

Sequential Recommendation (SR) methods play a crucial role in recommender systems, which aims to capture users' dynamic interest from their historical interactions. Recently, Contrastive Learning (CL), which has emerged as a successful method for sequential recommendation, utilizes various data augmentations to generate contrastive views to mine supervised signals from data to alleviate data sparsity issues. However, most existing sequential data augmentation methods may destroy semantic sequential interaction characteristics. Meanwhile, they often adopt random operations when generating contrastive views leading to suboptimal performance. To this end, in this paper, we propose a Learnable Model Augmentation Contrastive learning for sequential Recommendation (LMA4Rec). Specifically, LMA4Rec first takes the model-based augmentation method to generate constructive views. Then, LMA4Rec uses Learnable Bernoulli Dropout (LBD) to implement learnable model augmentation operations. Next, contrastive learning is used between the contrastive views to extract supervised signals. Furthermore, a novel multi-positive contrastive learning loss alleviates the supervised sparsity issue. Finally, experiments on public datasets show that our LMA4Rec method effectively improved sequential recommendation performance compared with the state-of-the-art baseline methods.

Document-level Relation Extraction (RE) is a promising task aiming at identifying relations of multiple entity pairs in a document. Compared with the sentence-level counterpart, it has raised two significant challenges: a) In most cases, a relational fact can be adequately expressed via a small subset of sentences from the document, namely evidence. But the traditional method cannot model such strong semantic correlations between evidence sentences that collaborate to describe a specific relation; b) The data of this task is extremely long-tail in terms of too many NA instances and imbalanced relational types. Such data can mislead the tail prediction bias to the head categories in the RE model. In this paper, we present a novelEvidence reasoning andCurriculum learning method forDocRE(DRE-EC) to address these challenges. Particularly, we first formulate evidence extraction as a sequential decision problem through a crafted reinforcement learning mechanism with an efficient path searching strategy to reduce the action space. Providing the evidence for each entity pair as a customized-filtered document in advance helps infer the relations better. To address the long-tail issue, we further develop a hybrid curriculum learning method at the NA-level (NC) and relation-level (RC) with our customized difficulty measure score. In NC, the NA samples are scheduled in an easy-to-hard scheme and gradually added, resulting in the data distribution from ideal and balanced to real and unbalanced. In RC, the scheme is switched into hard-to-easy to enhance the hard and tail samples. In addition, we propose a new Equalization adaptive Focal Loss(EFLoss) that can adjust to the changing data distribution and focus more on the tail categories. We conduct various experiments on two document-level RE benchmarks and achieve a remarkable improvement over previous competitive baselines. Furthermore, we provide detailed analyses of the advantages and effectiveness of our method.

Reinforcement learning (RL)-based multi-hop reasoning has become an interpretable way for knowledge graph reasoning owing to its persuasive explanations for the predicted results, but the reasoning performance of these methods drops significantly over few-shot relations (only contain few triplets). To address this problem, recent studies introduce meta-learning into RL-based reasoning methods. However, the performance of these studies is still limited due to the following points: (1) the overall reasoning accuracy is impaired due to the low reasoning accuracies over some hard relations; (2) the reasoning process becomes laborious and ineffective owing to the existence of noisy data; (3) the generalizability is negatively affected due to the lack of knowledge-sharing. To tackle these challenges, we propose a novel modelHMLSconsisting of two modulesHHML(HierarchicalHardness-awareMeta-reinforcementLearning) andHHS(HierarchicalHardness-awareSampling). Specifically,HHMLcontains the following two components: (1) a hardness-aware RL conducts multi-hop reasoning by training hardness-aware batches and reducing noise; (2) a knowledge-sharing meta-learning adapts to few-shot relations by exploiting common features in the hierarchical relation structure. The other moduleHHSgenerates hardness-aware batches from relation and relation-cluster levels. The experimental results demonstrate that this work notably outperforms the state-of-the-art approaches in few-shot scenarios.

Inductive link prediction (ILP) is to predict links for unseen entities in emerging knowledge graphs (KGs), considering the evolving nature of KGs. A more challenging scenario is that emerging KGs consist of only unseen entities without any edge connected to original KGs, called as disconnected emerging KGs (DEKGs). Existing studies for DEKGs only focus on predicting enclosing links, i.e., predicting links inside the emerging KG. The bridging links, which carry the evolutionary information from the original KG to DEKG, have not been investigated by previous work so far. To fill in the gap, we propose a novel model entitled DEKG-ILP (Disconnected Emerging Knowledge Graph Oriented Inductive Link Prediction) that consists of the following two components. (1) The module CLRM (Contrastive Learning-based Relation-specific Feature Modeling) is developed to extract global relation-based semantic features that are shared between original KGs and DEKGs with a novel sampling strategy. (2) The module GSM (GNN-based Subgraph Modeling) is proposed to extract the local subgraph topological information around each link in KGs. The extensive experiments conducted on several benchmark datasets demonstrate that DEKG-ILP has obvious performance improvements compared with state-of-the-art methods for both enclosing and bridging link prediction.

Multi-modal knowledge graphs (MKGs) include not only the relation triplets, but also related multi-modal auxiliary data (i.e., texts and images), which enhance the diversity of knowledge. However, the natural incompleteness has significantly hindered the applications of MKGs. To tackle the problem, existing studies employ the embedding-based reasoning models to infer the missing knowledge after fusing the multi-modal features. However, the reasoning performance of these methods is limited due to the following problems: (1) ineffective fusion of multi-modal auxiliary features; (2) lack of complex reasoning ability as well as inability to conduct the multi-hop reasoning which is able to infer more missing knowledge. To overcome these problems, we propose a novel model entitled MMKGR (Multi-hop Multi-modal Knowledge Graph Reasoning). Specifically, the model contains the following two components: (1) a unified gate-attention network which is designed to generate effective multi-modal complementary features through sufficient attention interaction and noise reduction; (2) a complementary feature-aware reinforcement learning method which is proposed to predict missing elements by performing the multi-hop reasoning process, based on the features obtained in component (1). The experimental results demonstrate that MMKGR outperforms the state-of-the-art approaches in the MKG reasoning task.

Sequential recommendation aims to capture users' dynamic interest and predicts the next item of users' preference. Most sequential recommendation methods use a deep neural network as sequence encoder to generate user and item representations. Existing works mainly center upon designing a stronger sequence encoder. However, few attempts have been made with training an ensemble of networks as sequence encoders, which is more powerful than a single network because an ensemble of parallel networks can yield diverse prediction results and hence better accuracy. In this paper, we present Ensemble Modeling with contrastive Knowledge Distillation for sequential recommendation (EMKD). Our framework adopts multiple parallel networks as an ensemble of sequence encoders and recommends items based on the output distributions of all these networks. To facilitate knowledge transfer between parallel networks, we propose a novel contrastive knowledge distillation approach, which performs knowledge transfer from the representation level via Intra-network Contrastive Learning (ICL) and Cross-network Contrastive Learning (CCL), as well as Knowledge Distillation (KD) from the logits level via minimizing the Kullback-Leibler divergence between the output distributions of the teacher network and the student network. To leverage contextual information, we train the primary masked item prediction task alongside the auxiliary attribute prediction task as a multi-task learning scheme. Extensive experiments on public benchmark datasets show that EMKD achieves a significant improvement compared with the state-of-the-art methods. Besides, we demonstrate that our ensemble method is a generalized approach that can also improve the performance of other sequential recommenders. Our code is available at this link: https://github.com/hw-du/EMKD.

Temporal knowledge graphs (TKGs) model the temporal evolution of events and have recently attracted increasing attention. Since TKGs are intrinsically incomplete, it is necessary to reason out missing elements. Although existing TKG reasoning methods have the ability to predict missing future events, they fail to generate explicit reasoning paths and lack explainability. As reinforcement learning (RL) for multi-hop reasoning on traditional knowledge graphs starts showing superior explainability and performance in recent advances, it has opened up opportunities for exploring RL techniques on TKG reasoning. However, the performance of RL-based TKG reasoning methods is limited due to: (1) lack of ability to capture temporal evolution and semantic dependence jointly; (2) excessive reliance on manually designed rewards. To overcome these challenges, we propose an adaptive reinforcement learning model based on attention mechanism (DREAM) to predict missing elements in the future. Specifically, the model contains two components: (1) a multi-faceted attention representation learning method that captures semantic dependence and temporal evolution jointly; (2) an adaptive RL framework that conducts multi-hop reasoning by adaptively learning the reward functions. Experimental results demonstrate DREAM outperforms state-of-the-art models on public datasets.

Cross-Lingual Summarization (CLS) aims at generating summaries in one language for the given documents in another language. CLS has attracted wide research attention due to its practical significance in the multi-lingual world. Though great contributions have been made, existing CLS works typically focus on short documents, such as news and guides. Different from these short texts, long documents such as academic articles usually discuss complicated subjects and consist of thousands of words, making them non-trivial to process and summarize. To promote CLS research on long documents, we construct Perseus, the first long-document CLS dataset which collects about 94K Chinese scientific documents paired with English summaries. The average length of documents in Perseus is more than 2000 tokens. As a preliminary study on long-document CLS, we build and evaluate various CLS baselines, including pipeline and end-to-end methods. Experimental results on Perseus show the superiority of the end-to-end baseline, which performs the best among all methods. Furthermore, to provide a deeper understanding, we manually analyze the model outputs and discuss specific challenges faced by current approaches. We hope that our work could benchmark long-document CLS and benefit future studies.

Contrastive learning with Transformer-based sequence encoder has gained predominance for sequential recommendation. It maximizes the agreements between paired sequence augmentations that share similar semantics. However, existing contrastive learning approaches in sequential recommendation mainly center upon left-to-right unidirectional Transformers as base encoders, which are suboptimal for sequential recommendation because user behaviors may not be a rigid left-to-right sequence. To tackle that, we propose a novel framework named Contrastive learning with Bidirectional Transformers for sequential recommendation (CBiT). Specifically, we first apply the slide window technique for long user sequences in bidirectional Transformers, which allows for a more fine-grained division of user sequences. Then we combine the cloze task mask and the dropout mask to generate high-quality positive samples and perform multi-pair contrastive learning, which demonstrates better performance and adaptability compared with the normal one-pair contrastive learning. Moreover, we introduce a novel dynamic loss reweighting strategy to balance between the cloze task loss and the contrastive loss. Experiment results on three public benchmark datasets show that our model outperforms state-of-the-art models for sequential recommendation. Our code is available at this link: https://github.com/hw-du/CBiT/tree/master.

With the prevalence of location-based services (LBS), trajectories are being generated rapidly. As is widely used in LBS, top-k trajectory similarity query serves as a key operation, deeply empowering applications such as travel route recommendation and carpooling. Given the rise of deep learning, trajectory representation has been well-proven to speed up this operator. However, existing representation-based computing modes remain two major problems understudied: the low quality of trajectory representation and insufficient support for various trajectory similarity metrics, which make them difficult to apply in practice. Therefore, we propose an Accurate metric-based representation learning approach for fast top-k trajectory similarity query, named Aries. Specifically, Aries has two sophisticated modules: (1) An novel trajectory embedding strategy enhanced by the bidirectional LSTM encoder and spatial attention mechanism, which can extract more precise and comprehensive knowledge. (2) A deep metric learning network aggregating multiple measures for better top-k query. Extensive experiments conducted on real trajectory dataset show that Aries achieves both impressive accuracy and lower training time compared with state-of-the-art solutions. In particular, it achieves 5x-10x speedup and 10%-20% accuracy improvement over Euclidean, Hausdorff, DTW, and EDR measures. Besides, our method can maintain stable performance when handling various scenarios, without repeated training in order to adapt to diverse similarity metrics.

In this paper, we study the problem of on-demand food delivery in a new setting where two groups of workers -- riders and taxi drivers (drivers for short) -- cooperate with each other for better service. The riders are responsible for the first and the last mile, and the drivers are in charge of the cross-community transportation. We show this problem is generally NP-hard by a reduction from the well-known 3-dimensional matching (3DM). To tackle with this problem, we first reduce it to the maximum independent set problem and use a simple greedy strategy to design an approximate algorithm which has a polynomial time. Considering the exponents in the polynomial are not very small, we then transform the 3DM into two rounds of 2-dimensional matching and propose a fast algorithm to solve it. Though 3DM problem is NP-hard, we find the cooperation between riders and drivers form a special tripartite graph, based on which we construct a flow network and employ the min-cost max-flow algorithm to efficiently compute the exact solution. We conduct extensive experiments to show the efficiency and the effectiveness of our proposed algorithms.

Document-level Relation Extraction (RE) is a promising task aiming at identifying relations of multiple entity pairs in a document. However, in most cases, a relational fact can be expressed enough via a small subset of sentences from the document, namely evidence sentence. Moreover, there often exist strong semantic correlations between evidence sentences that collaborate together to describe a specific relation. To address these challenges, we propose a novel evidence-aware model for document-level RE. Particularly, we formulate evidence sentence selection as a sequential decision problem through a crafted reinforcement learning mechanism. Considering the explosive search space of our agent, an efficient path searching strategy is executed on the converted document graph to heuristically obtain hopeful sentences and feed them to reinforcement learning. Finally, each entity pair owns a customized-filtered document for further inferring the relation between them. We conduct various experiments on two document-level RE benchmarks and achieve a remarkable improvement over previous competitive baselines, verifying the effectiveness of our method.

Trajectory prediction is a fundamental problem for a wide spectrum of location-based applications. Existing methods can achieve inspiring results in predicting personal frequent routes conditioned on massive historical data. However, trajectory estimation may involve cold-start routes or users due to the data sparsity problem, which severely limits the performance of spatial trajectory prediction. Although meta-learning models can alleviate the cold-start problem, they simply utilize the same initialization for all tasks and thus cannot fit each user well due to users' varying travel preferences. To this end, we propose an adaptive meta-optimized model called MetaPTP for personalized spatial trajectory prediction. Specifically, it adopts a soft-clustering based method to guide the network initialization in a finer granularity, so that shared knowledge can be better transferred across users with similar travel preferences. Besides, towards model fine-tuning, an effective trajectory sampling method is introduced to generate meaningful support set, which simultaneously considers user preference and spatial trace similarities to provide task-related information for model adaptation. In addition, we design a weight generator to adaptively assign reasonable weights to trajectories in support set to avoid sub-optimal results which will occur when fine-tuning the initial network with the same weight for trajectories with different user preferences and spatial distributions. Finally, extensive experiments on two real-world datasets demonstrate the superiority of our model.

Sports game summarization aims at generating sports news from live commentaries. However, existing datasets are all constructed through automated collection and cleaning processes, resulting in a lot of noise. Besides, current works neglect the knowledge gap between live commentaries and sports news, which limits the performance of sports game summarization. In this paper, we introduce K-SportsSum, a new dataset with two characteristics: (1) K-SportsSum collects a large amount of data from massive games. It has 7,854 commentary-news pairs. To improve the quality, K-SportsSum employs a manual cleaning process; (2) Different from existing datasets, to narrow the knowledge gap, K-SportsSum further provides a large-scale knowledge corpus that contains the information of 523 sports teams and 14,724 sports players. Additionally, we also introduce a knowledge-enhanced summarizer that utilizes both live commentaries and the knowledge to generate sports news. Extensive experiments on K-SportsSum and SportsSum datasets show that our model achieves new state-of-the-art performances. Qualitative analysis and human study further verify that our model generates more informative sports news.

Abstract The unprecedented growth of publications in many research domains brings the great convenience for tracing and analyzing the evolution and development of research topics. Despite the significant contributions made by existing studies, they usually extract topics from the titles of papers, instead of obtaining topics from the authoritative sessions provided by venues (e.g., AAAI, NeurIPS, and SIGMOD). To make up for the shortcoming of existing work, we develop a novel framework namely RTTP(Research Topic Trend Prediction). Specifically, the framework contains the following two components: (1) a topic alignment strategy called TAS is designed to obtain the detailed contents of research topics in each year, (2) an enhanced prediction network called EPN is designed to capture the research trend of known years for prediction. In addition, we construct two real-world datasets of specific research domains in computer science, i.e., database and data mining, computer architecture and parallel programming. The experimental results demonstrate that the problem is well solved and our solution outperforms the state-of-the-art methods.

Massive trajectory data stem from the prevalence of equipment-supporting GPS and wireless communication technology. Especially, activity trajectory from Location-based Social Network (LBSN) endows traditional trajectory data with additional user semantic activities, e.g., visiting work/home/entertainment places. Measuring the similarity between activity trajectories is to compare their proximity in multiple dimensions such as time, location, and semantics. In this way, we can mine implicit user preference and apply it to route planning, POI recommendation or any other online tasks. The key challenge of comparing activity trajectories (i.e., computing their similarity) lies in two aspects. One is the uneven sampling rate in both time and space. The other is the discrepancy of individual activities. Previous effort alleviates the issue of uneven sampling rate via trajectory complements, which is limited to spatial-temporal information. In this paper, we propose to learn a representation for one activity trajectory by jointly considering the spatio-temporal characteristics and the activity semantics. The similarity of two trajectories is computed by weighting individual trajectory points and contextual features with multi-level attention mechanisms. In specific, we propose a point-level and feature-level attention mechanism to adaptively select critical elements and contextual factors for learning trajectory representation. Our proposed approach, called At2vec, demonstrates better performance than existing baselines in extensive experimental evaluation on real trajectory databases.

Knowledge graph (KG) embedding aims to encode both entities and relations into a continuous vector space. Most existing methods require that all entities should be observed during training while ignoring the evolving nature of KG. Major recent efforts on this issue embed new entities by aggregating neighborhood information from existing entities and relations with Graph Neural Network (GNN). However, these methods rely on the neighbors seen during training and suffer from the embedding of new entities with insufficient triplets or triplets with the unseen-to-unseen form. To relieve this problem, we propose a two-stage learning model referred as Hyper-Relation Feature Learning Network (HRFN) for effective out-of-knowledge-base embedding. For the first stage, HRFN learns pre-representations for emerging entities using hyper-relation features meta-learned from the training set. A novel feature aggregating network that involves an entity-centered Graph Convolutional Network (GCN) and a relation-centered GCN is proposed to aggregate information from both new entities themselves and their neighbors. For stage two, a transductive learning network is employed to learn finer-grained embeddings based on above-mentioned pre-representations of new entities. Experimental results on the link prediction task demonstrate the superiority of our model. Further analysis is also done to validate the effectiveness and efficiency of pre-representing emerging entities with the hyper-relation feature.

Knowledge graph (KG) reasoning is a significant method for KG completion. To enhance the explainability of KG reasoning, some studies adopt reinforcement learning (RL) to complete the multi-hop reasoning. However, RL-based reasoning methods are severely limited by few-shot relations (only contain few triplets). To tackle the problem, recent studies introduce meta-learning into RL-based methods to improve reasoning performance. However, the generalization abilities of their models are limited due to the problem of low reasoning accuracies over hard relations (e.g., language and title). To overcome this problem, we propose a novel model called THML (Two-level Hardness-aware Meta-reinforcement Learning). Specifically, the model contains the following two components: (1) A hardness-aware meta-reinforcement learning method is proposed to predict the missing element by training hardness-aware batches. (2) A two-level hardness-aware sampling is proposed to effectively generate new hardness-aware batches from relation level and relation-cluster level. The generalization ability of our model is significantly improved by repeating the process of these two components in an alternate way. The experimental results demonstrate that THML notably outperforms the state-of-the-art approaches in few-shot scenarios.

Sequential recommendation has become an attractive topic in recommender systems. Existing sequential recommendation methods, including the methods based on the state-of-the-art self-attention mechanism, usually employ deterministic neural networks to represent user preferences as fixed-points in the latent feature spaces. However, the fixed-point vector lacks the ability to capture the uncertainty and dynamics of user preferences that are prevalent in recommender systems. In this paper, we propose a new Variational Self-Attention Network (VSAN), which introduces a variational autoencoder (VAE) into the self-attention network to capture latent user preferences. Specifically, we represent the obtained self-attention vector as density via variational inference, whose variance well characterizes the uncertainty of user preferences. Furthermore, we employ self-attention networks to learn the inference process and generative process of VAE, which well captures long-range and local dependencies. Finally, we evaluate our proposed method VSAN with two public real-world datasets. Our experimental results show the effectiveness of our model compared to the state-of-the-art approaches.

Travel time estimation has been recognized as an important research topic that can find broad applications. Existing approaches aim to explore mobility patterns via trajectory embedding for travel time estimation. Though state-of-the-art methods utilize estimated traffic condition (by explicit features such as average traffic speed) for auxiliary supervision of travel time estimation, they fail to model their mutual influence and result in inaccuracy accordingly. To this end, in this article, we propose an improved traffic-aware model, called TAML, which adopts a multi-task learning network to integrate a travel time estimator and a traffic estimator in a shared space and improves the accuracy of estimation by enhanced representation of traffic condition, such that more meaningful implicit features are fully captured. In TAML, multi-task learning is further applied for travel time estimation in multi-granularities (including road segment, sub-path, and entire path). The multiple loss functions are combined by considering the homoscedastic uncertainty of each task. Extensive experiments on two real trajectory datasets demonstrate the effectiveness of our proposed methods.

Data incompleteness is a common data quality problem in databases. Recent work proposes to retrieve missing string values from the World Wide Web for higher imputation recall, but on the other hand, takes the risk of introducing web noises into the imputation results. So far there lacks an effective way to control the quality of web-based data imputation, given the complexity of the quality model and lacking of enough ground truth data. In this article, an EM-based quality model is first built for web-based data imputation which investigates three key factors jointly, i.e., precision of web sources, correlation among web sources, and precision and recall of the employed extractors. However, the accuracy of the EM-based quality model could be harmed when the EM (Expectation Maximization) assumption that “the majority agree on the truth” does not hold in some cases. To solve this problem, we introduce crowd intervention to help improve the quality model. While a straightforward but expensive way is to let the crowd to identify all these undesirable cases and provide the right imputation values for these blanks, a most crowd-economic way is to select a small set of blanks for crowd-based imputation, whose results could help to adjust the EM-based quality model towards a better one. To achieve this, an adaptive blank selection strategy is proposed to select a sequence of blanks for crowd-based imputation. Also, we work on finding a proper time to stop further crowd intervention for the balance of crowd efficiency and quality improvement. Our experiments performed on three real world and one simulated data collections prove that the proposed quality model can effectively help improve the quality of the web-based imputation results by more than 15 percent, while our crowd cost saving strategy saves more than 75 percent crowd cost.

Destination prediction is known as an important problem for many location based services (LBSs). Existing solutions generally apply probabilistic models or neural network models to predict destinations over a subtrajectory, and adopt the standard attention mechanism to improve the prediction accuracy. However, the standard attention mechanism uses fixed feature representations, and has a limited ability to represent distinct features of locations. Besides, existing methods rarely take the impact of spatial and temporal characteristics of the trajectory into account. Their accuracies in fine-granularity prediction are always not satisfactory due to the data sparsity problem. Thus, in this paper, a carefully designed deep learning model called LATL model is presented. It not only adopts an adaptive attention network to model the distinct features of locations, but also implements time gates and distance gates into the Long Short-Term Memory (LSTM) network to capture the spatial-temporal relation between consecutive locations. Furthermore, to better understand the mobility patterns in different spatial granularities, and explore the fusion of multi-granularity learning capability, a hierarchical model that utilizes tailored combination of different neural networks under multiple spatial granularities is further proposed. Extensive empirical studies verify that the newly proposed models perform effectively and settle the problem nicely.

Abstract Online group buying is a burgeoning business model of Internet shopping, in which people with the same merchandise interests form a group and co-purchase goods with favorable prices. The buyer who launches the co-purchase is called the initiator, and other buyers are called the co-purchasers. Although recommending co-purchasers for a target buyer (co-purchase initiator) on the group buying is an interesting problem, existing studies have paid few attention to this topic. Different from the collaborator recommendation that only considers users with high similarity to the target user, co-purchaser recommendation takes both users with high and weak similarity into account, and the recommendation results can achieve high recall and diversity. However, the task turns out to be a challenging problem since it is hard to make a precise recommendation for buyers with weak similarity. To address the problem, we propose the following two methods. In the first one, we directly impose a penalty to the weak similar co-purchasers in the embedding space. To further improve the recommendation performance, in the second one, we smoothly increase the co-occurrence probability of the weak similar co-purchasers by truncated bias walk. Our experimental results on real datasets show that the proposed methods, particularly the latter, can effectively complete the co-purchaser recommendation and has high recommendation performance. In addition, considering that co-purchase may last longer, the total recommendation result can be generated in multiple stages and adjust the current recommendation list based on the feedback from the recommendation of previous stages. It is a trick for all co-purchaser recommendation methods to make the total result better.

Sources of complementary information are connected when we link the user accounts belonging to the same user across different domains or devices. The expanded information promotes the development of a wide range of applications, such as cross-domain prediction, cross-domain recommendation, and advertisement. Due to the great significance of user account linkage, there are increasing research works on this study. With the widespread popularization of GPS-enabled mobile devices, linking user accounts with location data has become an important and promising research topic. Being different from most existing studies in this domain that only focus on the effectiveness, we propose novel approaches to improve both effectiveness and efficiency of user account linkage. In this paper, a kernel density estimation (KDE) based method has been proposed to improve the accuracy by alleviating the data sparsity problem in measuring users' similarities. To improve the efficiency, we develop a grid-based structure to organize location data to prune the search space. The extensive experiments conducted on two real-world datasets demonstrate the superiority of the proposed approach in terms of both effectiveness and efficiency compared with the state-of-art methods.

Cross-device and cross-domain user linkage have been attracting a lot of attention recently. An important branch of the study is to achieve user linkage with spatio-temporal data generated by the ubiquitous GPS-enabled devices. The main task in this problem is twofold, i.e., how to extract the representative features of a user; how to measure the similarities between users with the extracted features. To tackle the problem, we propose a novel model STUL (Spatio-Temporal User Linkage) that consists of the following two components. 1) Extract users - spatial features with a density based clustering method, and extract the users - temporal features with the Gaussian Mixture Model. To link user pairs more precisely, we assign different weights to the extracted features, by lightening the common features and highlighting the discriminative features. 2) Propose novel approaches to measure the similarities between users based on the extracted features, and return the pair-wise users with similarity scores higher than a predefined threshold. We have conducted extensive experiments on three real-world datasets, and the results demonstrate the superiority of our proposed STUL over the state-of-the-art methods.

Information Extraction by Text Segmentation (IETS) aims at segmenting text inputs to extract implicit data values contained in them.The state-of-art IETS approaches mainly rely on machine learning techniques, either supervised or unsupervised.However, while the supervised approaches require a large labelled training data, the performance of the unsupervised ones could be unstable on different data sets.To overcome their weaknesses, this paper introduces CNN-IETS, a novel unsupervised probabilistic approach that takes the advantages of pre-existing data and a Convolution Neural Network (CNN)-based probabilistic classification model. While using the CNN model can ease the burden of selecting high-quality features in associating text segments with attributes of a given domain, the pre-existing data as a domain knowledge base can provide training data with a comprehensive list of features for building the CNN model.Given an input text, we do initial segmentation (according to the occurrences of these words in the knowledge base) to generate text segments for CNN classification with probabilities. Then, based on the probabilistic CNN classification results, we work on finding the most probable labelling way to the whole input text.As a complementary, a bidirectional sequencing model learned on-demand from test data is finally deployed to do further adjustment to some problematic labelled segments.Our experimental study conducted on several real data collections shows that CNN-IETS improves the extraction quality of state-of-art approaches by more than 10%.

Schema Matching (SM) and Record Matching (RM) are two necessary steps in integrating multiple relational tables of different schemas, where SM unifies the schemas and RM detects records referring to the same real-world entity. The two processes have been thoroughly studied separately, but few attention has been paid to the interaction of SM and RM. In this work we find that, even alternating them in a simple manner, SM and RM can benefit from each other to reach a better integration performance (i.e., in terms of precision and recall). Therefore, combining SM and RM is a promising solution for improving data integration.

Schema Matching (SM) and Record Matching (RM) are two necessary steps in integrating multiple relational tables of different schemas, where SM unifies the schemas and RM detects records referring to the same real-world entity. The two processes have been thoroughly studied separately, but few attention has been paid to the interaction of SM and RM. In this work, we find that, even alternating them in a simple manner, SM and RM can benefit from each other to reach a better integration performance (i.e., in terms of precision and recall). Therefore, combining SM and RM is a promising solution for improving data integration. To this end, we define novel matching rules for SM and RM, respectively, that is, every SM decision is made based on intermediate RM results, and vice versa, such that SM and RM can be performed alternately. The quality of integration is guaranteed by a Matching Likelihood Estimation model and the control of semantic drift, which prevent the effect of mismatch magnification. To reduce the computational cost, we design an index structure based on q-grams and a greedy search algorithm that can reduce around 90 percent overhead of the interaction. Extensive experiments on three data collections show that the combination and interaction between SM and RM significantly outperforms previous works that conduct SM and RM separately.

Outsourcing database to clouds is a scalable and cost-effective way for large scale data storage, management, and query processing. Trajectory data contain rich spatio-temporal relationships and reveal many forms of individual sensitive information (e.g., home address, health condition), which necessitate them to be encrypted before being outsourced for privacy concerns. However, efficient query processing over encrypted trajectory data is a very challenging task. Though some achievements have been reported very recently for simple queries (e.g., SQL queries, kNN queries) on encrypted data, there is rather limited progress on secure evaluation of trajectory queries because they are more complex and need special treatment. In this paper, we focus on secure trajectory similarity computation that is the cornerstone of secure trajectory query processing. More specifically, we propose an efficient solution to securely compute the similarity between two encrypted trajectories, which reveals nothing about the trajectories, but the final result. We theoretically prove that our solution is secure against the semi-honest adversaries model as all the intermediate information in our protocols can be simulated in polynomial time. Finally we empirically study the efficiency of the proposed method, which demonstrates the feasibility of our solution.

Graph Pattern Matching (GPM) plays a significant role in social network analysis, which has been widely used in, for example, experts finding, social community mining and social position detection. Given a pattern graph GQand a data graph GD, a GPM algorithm finds those subgraphs, GM, that match GQin GD. However, the existing GPM methods do not consider the multiple constraints on edges in GQ, which are commonly exist in various applications such as, crowdsourcing travel, social network based e-commerce and study group selection, etc. In this paper, we first conceptually extend Bounded Simulation to Multi-Constrained Simulation (MCS), and propose a novel NP-Complete Multi-Constrained Graph Pattern Matching (MC-GPM) problem. Then, to address the efficiency issue in large-scale MC-GPM, we propose a new concept called Strong Social Component (SSC), consisting of participants with strong social connections. We also propose an approach to identify SSCs, and propose a novel index method and a graph compression method for SSC. Moreover, we devise a heuristic algorithm to identify MC-GPM results effectively and efficiently without decompressing graphs. An extensive empirical study on five real-world large-scale social graphs has demonstrated the effectiveness, efficiency and scalability of our approach.