Existing Graph Neural Networks (GNNs) usually assume a balanced situation where both the class distribution and the node degree distribution are balanced. However, in real-world situations, we often encounter cases where a few classes (i.e., head class) dominate other classes (i.e., tail class) as well as in the node degree perspective, and thus naively applying existing GNNs eventually fall short of generalizing to the tail cases. Although recent studies proposed methods to handle long-tail situations on graphs, they only focus on either the class long-tailedness or the degree long-tailedness. In this paper, we propose a novel framework for training GNNs, called Long-Tail Experts for Graphs (LTE4G), which jointly considers the class long-tailedness, and the degree long-tailedness for node classification. The core idea is to assign an expert GNN model to each subset of nodes that are split in a balanced manner considering both the class and degree long-tailedness. After having trained an expert for each balanced subset, we adopt knowledge distillation to obtain two class-wise students, i.e., Head class student and Tail class student, each of which is responsible for classifying nodes in the head classes and tail classes, respectively. We demonstrate that LTE4G outperforms a wide range of state-of-the-art methods in node classification evaluated on both manual and natural imbalanced graphs. The source code of LTE4G can be found at https://github.com/SukwonYun/LTE4G.
Routine clinical visits of a patient produce not only image data, but also non-image data containing clinical information regarding the patient, i.e., medical data is multi-modal in nature. Such heterogeneous modalities offer different and complementary perspectives on the same patient, resulting in more accurate clinical decisions when they are properly combined. However, despite its significance, how to effectively fuse the multi-modal medical data into a unified framework has received relatively little attention. In this paper, we propose an effective graph-based framework called HetMed (Heterogeneous Graph Learning for Multi-modal Medical Data Analysis) for fusing the multi-modal medical data. Specifically, we construct a multiplex network that incorporates multiple types of non-image features of patients to capture the complex relationship between patients in a systematic way, which leads to more accurate clinical decisions. Extensive experiments on various real-world datasets demonstrate the superiority and practicality of HetMed. The source code for HetMed is available at https://github.com/Sein-Kim/Multimodal-Medical.
Molecular relational learning, whose goal is to learn the interaction behavior between molecular pairs, got a surge of interest in molecular sciences due to its wide range of applications. Recently, graph neural networks have recently shown great success in molecular relational learning by modeling a molecule as a graph structure, and considering atom-level interactions between two molecules. Despite their success, existing molecular relational learning methods tend to overlook the nature of chemistry, i.e., a chemical compound is composed of multiple substructures such as functional groups that cause distinctive chemical reactions. In this work, we propose a novel relational learning framework, called CGIB, that predicts the interaction behavior between a pair of graphs by detecting core subgraphs therein. The main idea is, given a pair of graphs, to find a subgraph from a graph that contains the minimal sufficient information regarding the task at hand conditioned on the paired graph based on the principle of conditional graph information bottleneck. We argue that our proposed method mimics the nature of chemical reactions, i.e., the core substructure of a molecule varies depending on which other molecule it interacts with. Extensive experiments on various tasks with real-world datasets demonstrate the superiority of CGIB over state-of-the-art baselines. Our code is available at https://github.com/Namkyeong/CGIB.
Sequential recommender systems have shown effective suggestions by capturing users' interest drift. There have been two groups of existing sequential models: user- and item-centric models. The user-centric models capture personalized interest drift based on each user's sequential consumption history, but do not explicitly consider whether users' interest in items sustains beyond the training time, i.e., interest sustainability. On the other hand, the item-centric models consider whether users' general interest sustains after the training time, but it is not personalized. In this work, we propose a recommender system taking advantages of the models in both categories. Our proposed model captures personalized interest sustainability, indicating whether each user's interest in items will sustain beyond the training time or not. We first formulate a task that requires to predict which items each user will consume in the recent period of the training time based on users' consumption history. We then propose simple yet effective schemes to augment users' sparse consumption history. Extensive experiments show that the proposed model outperforms 10 baseline models on 11 real-world datasets. The codes are available at https://github.com/dmhyun/PERIS.
Over the past few years, graph representation learning (GRL) has been a powerful strategy for analyzing graph-structured data. Recently, GRL methods have shown promising results by adopting self-supervised learning methods developed for learning representations of images. Despite their success, existing GRL methods tend to overlook an inherent distinction between images and graphs, i.e., images are assumed to be independently and identically distributed, whereas graphs exhibit relational information among data instances, i.e., nodes. To fully benefit from the relational information inherent in the graph-structured data, we propose a novel GRL method, called RGRL, that learns from the relational information generated from the graph itself. RGRL learns node representations such that the relationship among nodes is invariant to augmentations, i.e., augmentation-invariant relationship, which allows the node representations to vary as long as the relationship among the nodes is preserved. By considering the relationship among nodes in both global and local perspectives, RGRL overcomes limitations of previous contrastive and non-contrastive methods, and achieves the best of both worlds. Extensive experiments on fourteen benchmark datasets over various downstream tasks demonstrate the superiority of RGRL over state-of-the-art baselines. The source code for RGRL is available at https://github.com/Namkyeong/RGRL.
Machine learning (ML) has seen promising developments in materials science, yet its efficacy largely depends on detailed crystal structural data, which are often complex and hard to obtain, limiting their applicability in real-world material synthesis processes. An alternative, using compositional descriptors, offers a simpler approach by indicating the elemental ratios of compounds without detailed structural insights. However, accurately representing materials solely with compositional descriptors presents challenges due to polymorphism, where a single composition can correspond to various structural arrangements, creating ambiguities in its representation. To this end, we introduce PCRL, a novel approach that employs probabilistic modeling of composition to capture the diverse polymorphs from available structural information. Extensive evaluations on sixteen datasets demonstrate the effectiveness of PCRL in learning compositional representation, and our analysis highlights its potential applicability of PCRL in material discovery. The source code for PCRL is available at https://github.com/Namkyeong/PCRL.
Recent works demonstrate that GNN models are vulnerable to adversarial attacks, which refer to imperceptible perturbation on the graph structure and node features. Among various GNN models, graph contrastive learning (GCL) based methods specifically suffer from adversarial attacks due to their inherent design that highly depends on the self-supervision signals derived from the original graph, which however already contains noise when the graph is attacked. To achieve adversarial robustness against such attacks, existing methods adopt adversarial training (AT) to the GCL framework, which considers the attacked graph as an augmentation under the GCL framework. However, we find that existing adversarially trained GCL methods achieve robustness at the expense of not being able to preserve the node feature similarity. In this paper, we propose a similarity-preserving adversarial graph contrastive learning (SP-AGCL) framework that contrasts the clean graph with two auxiliary views of different properties (i.e., the node similarity-preserving view and the adversarial view). Extensive experiments demonstrate that SP-AGCL achieves a competitive performance on several downstream tasks, and shows its effectiveness in various scenarios, e.g., a network with adversarial attacks, noisy labels, and heterophilous neighbors. Our code is available at https://github.com/yeonjun-in/torch-SP-AGCL.
Unsupervised GAD methods assume the lack of anomaly labels, i.e., whether a node is anomalous or not. One common observation we made from previous unsupervised methods is that they not only assume the absence of such anomaly labels, but also the absence of class labels (the class a node belongs to used in a general node classification task). In this work, we study the utility of class labels for unsupervised GAD; in particular, how they enhance the detection of structural anomalies. To this end, we propose a Class Label-aware Graph Anomaly Detection framework (CLAD) that utilizes a limited amount of labeled nodes to enhance the performance of unsupervised GAD. Extensive experiments on ten datasets demonstrate the superior performance of CLAD in comparison to existing unsupervised GAD methods, even in the absence of ground-truth class label information. The source code for CLAD is available at \url{https://github.com/jhkim611/CLAD}.
User modeling, which learns to represent users into a low-dimensional representation space based on their past behaviors, got a surge of interest from the industry for providing personalized services to users. Previous efforts in user modeling mainly focus on learning a task-specific user representation that is designed for a single task. However, since learning task-specific user representations for every task is infeasible, recent studies introduce the concept of universal user representation, which is a more generalized representation of a user that is relevant to a variety of tasks. Despite their effectiveness, existing approaches for learning universal user representations are impractical in real-world applications due to the data requirement, catastrophic forgetting and the limited learning capability for continually added tasks. In this paper, we propose a novel continual user representation learning method, called TERACON, whose learning capability is not limited as the number of learned tasks increases while capturing the relationship between the tasks. The main idea is to introduce an embedding for each task, i.e., task embedding, which is utilized to generate task-specific soft masks that not only allow the entire model parameters to be updated until the end of training sequence, but also facilitate the relationship between the tasks to be captured. Moreover, we introduce a novel knowledge retention module with pseudo-labeling strategy that successfully alleviates the long-standing problem of continual learning, i.e., catastrophic forgetting. Extensive experiments on public and proprietary real-world datasets demonstrate the superiority and practicality of TERACON. Our code is available at https://github.com/Sein-Kim/TERACON.
The density of states (DOS) is a spectral property of materials, which provides fundamental insights on various characteristics of materials. In this paper, we propose a model to predict the DOS by reflecting the nature of DOS: DOS determines the general distribution of states as a function of energy. Specifically, we integrate the heterogeneous information obtained from the crystal structure and the energies via multi-modal transformer, thereby modeling the complex relationships between the atoms in the crystal structure, and various energy levels. Extensive experiments on two types of DOS, i.e., Phonon DOS and Electron DOS, with various real-world scenarios demonstrate the superiority of DOSTransformer. The source code for DOSTransformer is available at https://github.com/HeewoongNoh/DOSTransformer.
Qi Zhu, Chao Zhang, Chanyoung Park et al. · tsinghua
Graph Neural Networks (GNNs) are de facto node classification models in graph structured data. However, during testing-time, these algorithms assume no data shift, i.e., $\Pr_\text{train}(X,Y) = \Pr_\text{test}(X,Y)$. Domain adaption methods can be adopted for data shift, yet most of them are designed to only encourage similar feature distribution between source and target data. Conditional shift on classes can still affect such adaption. Fortunately, graph yields graph homophily across different data distributions. In response, we propose Shift-Robust Node Classification (SRNC) to address these limitations. We introduce an unsupervised cluster GNN on target graph to group the similar nodes by graph homophily. An adversarial loss with label information on source graph is used upon clustering objective. Then a shift-robust classifier is optimized on training graph and adversarial samples on target graph, which are generated by cluster GNN. We conduct experiments on both open-set shift and representation-shift, which demonstrates the superior accuracy of SRNC on generalizing to test graph with data shift. SRNC is consistently better than previous SoTA domain adaption algorithm on graph that progressively use model predictions on target graph for training.
Existing studies for applying the mixup technique on graphs mainly focus on graph classification tasks, while the research in node classification is still under-explored. In this paper, we propose a novel mixup augmentation for node classification called Structural Mixup (S-Mixup). The core idea is to take into account the structural information while mixing nodes. Specifically, S-Mixup obtains pseudo-labels for unlabeled nodes in a graph along with their prediction confidence via a Graph Neural Network (GNN) classifier. These serve as the criteria for the composition of the mixup pool for both inter and intra-class mixups. Furthermore, we utilize the edge gradient obtained from the GNN training and propose a gradient-based edge selection strategy for selecting edges to be attached to the nodes generated by the mixup. Through extensive experiments on real-world benchmark datasets, we demonstrate the effectiveness of S-Mixup evaluated on the node classification task. We observe that S-Mixup enhances the robustness and generalization performance of GNNs, especially in heterophilous situations. The source code of S-Mixup can be found at \url{https://github.com/SukwonYun/S-Mixup}
The density of states (DOS) is a spectral property of crystalline materials, which provides fundamental insights into various characteristics of the materials. While previous works mainly focus on obtaining high-quality representations of crystalline materials for DOS prediction, we focus on predicting the DOS from the obtained representations by reflecting the nature of DOS: DOS determines the general distribution of states as a function of energy. That is, DOS is not solely determined by the crystalline material but also by the energy levels, which has been neglected in previous works. In this paper, we propose to integrate heterogeneous information obtained from the crystalline materials and the energies via a multi-modal transformer, thereby modeling the complex relationships between the atoms in the crystalline materials and various energy levels for DOS prediction. Moreover, we propose to utilize prompts to guide the model to learn the crystal structural system-specific interactions between crystalline materials and energies. Extensive experiments on two types of DOS, i.e., Phonon DOS and Electron DOS, with various real-world scenarios demonstrate the superiority of DOSTransformer. The source code for DOSTransformer is available at https://github.com/HeewoongNoh/DOSTransformer.
We propose Unsupervised Episode Generation method called Neighbors as Queries (NaQ) to solve the Few-Shot Node-Classification (FSNC) task by unsupervised Graph Meta-learning. Doing so enables full utilization of the information of all nodes in a graph, which is not possible in current supervised meta-learning methods for FSNC due to the label-scarcity problem. In addition, unlike unsupervised Graph Contrastive Learning (GCL) methods that overlook the downstream task to be solved at the training phase resulting in vulnerability to class imbalance of a graph, we adopt the episodic learning framework that allows the model to be aware of the downstream task format, i.e., FSNC. The proposed NaQ is a simple but effective unsupervised episode generation method that randomly samples nodes from a graph to make a support set, followed by similarity-based sampling of nodes to make the corresponding query set. Since NaQ is model-agnostic, any existing supervised graph meta-learning methods can be trained in an unsupervised manner, while not sacrificing much of their performance or sometimes even improving them. Extensive experimental results demonstrate the effectiveness of our proposed unsupervised episode generation method for graph meta-learning towards the FSNC task. Our code is available at: https://github.com/JhngJng/NaQ-PyTorch.
Hyunjin Hwang, Seungwoo Lee, Chanyoung Park et al.
Hypergraphs (i.e., sets of hyperedges) naturally represent group relations (e.g., researchers co-authoring a paper and ingredients used together in a recipe), each of which corresponds to a hyperedge (i.e., a subset of nodes). Predicting future or missing hyperedges bears significant implications for many applications (e.g., collaboration and recipe recommendation). What makes hyperedge prediction particularly challenging is the vast number of non-hyperedge subsets, which grows exponentially with the number of nodes. Since it is prohibitive to use all of them as negative examples for model training, it is inevitable to sample a very small portion of them, and to this end, heuristic sampling schemes have been employed. However, trained models suffer from poor generalization capability for examples of different natures. In this paper, we propose AHP, an adversarial training-based hyperedge-prediction method. It learns to sample negative examples without relying on any heuristic schemes. Using six real hypergraphs, we show that AHP generalizes better to negative examples of various natures. It yields up to 28.2% higher AUROC than the best existing methods and often even outperforms its variants with sampling schemes tailored to test sets.
Recent scene graph generation (SGG) frameworks have focused on learning complex relationships among multiple objects in an image. Thanks to the nature of the message passing neural network (MPNN) that models high-order interactions between objects and their neighboring objects, they are dominant representation learning modules for SGG. However, existing MPNN-based frameworks assume the scene graph as a homogeneous graph, which restricts the context-awareness of visual relations between objects. That is, they overlook the fact that the relations tend to be highly dependent on the objects with which the relations are associated. In this paper, we propose an unbiased heterogeneous scene graph generation (HetSGG) framework that captures relation-aware context using message passing neural networks. We devise a novel message passing layer, called relation-aware message passing neural network (RMP), that aggregates the contextual information of an image considering the predicate type between objects. Our extensive evaluations demonstrate that HetSGG outperforms state-of-the-art methods, especially outperforming on tail predicate classes.
The long-tailed problem is a long-standing challenge in Sequential Recommender Systems (SRS) in which the problem exists in terms of both users and items. While many existing studies address the long-tailed problem in SRS, they only focus on either the user or item perspective. However, we discover that the long-tailed user and item problems exist at the same time, and considering only either one of them leads to sub-optimal performance of the other one. In this paper, we propose a novel framework for SRS, called Mutual Enhancement of Long-Tailed user and item (MELT), that jointly alleviates the long-tailed problem in the perspectives of both users and items. MELT consists of bilateral branches each of which is responsible for long-tailed users and items, respectively, and the branches are trained to mutually enhance each other, which is trained effectively by a curriculum learning-based training. MELT is model-agnostic in that it can be seamlessly integrated with existing SRS models. Extensive experiments on eight datasets demonstrate the benefit of alleviating the long-tailed problems in terms of both users and items even without sacrificing the performance of head users and items, which has not been achieved by existing methods. To the best of our knowledge, MELT is the first work that jointly alleviates the long-tailed user and item problems in SRS.
A fundamental challenge of bipartite graph representation learning is how to extract informative node embeddings. Self-Supervised Learning (SSL) is a promising paradigm to address this challenge. Most recent bipartite graph SSL methods are based on contrastive learning which learns embeddings by discriminating positive and negative node pairs. Contrastive learning usually requires a large number of negative node pairs, which could lead to computational burden and semantic errors. In this paper, we introduce a novel synergistic representation learning model (STERLING) to learn node embeddings without negative node pairs. STERLING preserves the unique local and global synergies in bipartite graphs. The local synergies are captured by maximizing the similarity of the inter-type and intra-type positive node pairs, and the global synergies are captured by maximizing the mutual information of co-clusters. Theoretical analysis demonstrates that STERLING could improve the connectivity between different node types in the embedding space. Extensive empirical evaluation on various benchmark datasets and tasks demonstrates the effectiveness of STERLING for extracting node embeddings.
Weakly-Supervised Scene Graph Generation (WSSGG) research has recently emerged as an alternative to the fully-supervised approach that heavily relies on costly annotations. In this regard, studies on WSSGG have utilized image captions to obtain unlocalized triplets while primarily focusing on grounding the unlocalized triplets over image regions. However, they have overlooked the two issues involved in the triplet formation process from the captions: 1) Semantic over-simplification issue arises when extracting triplets from captions, where fine-grained predicates in captions are undesirably converted into coarse-grained predicates, resulting in a long-tailed predicate distribution, and 2) Low-density scene graph issue arises when aligning the triplets in the caption with entity/predicate classes of interest, where many triplets are discarded and not used in training, leading to insufficient supervision. To tackle the two issues, we propose a new approach, i.e., Large Language Model for weakly-supervised SGG (LLM4SGG), where we mitigate the two issues by leveraging the LLM's in-depth understanding of language and reasoning ability during the extraction of triplets from captions and alignment of entity/predicate classes with target data. To further engage the LLM in these processes, we adopt the idea of Chain-of-Thought and the in-context few-shot learning strategy. To validate the effectiveness of LLM4SGG, we conduct extensive experiments on Visual Genome and GQA datasets, showing significant improvements in both Recall@K and mean Recall@K compared to the state-of-the-art WSSGG methods. A further appeal is that LLM4SGG is data-efficient, enabling effective model training with a small amount of training images.
Sets have been used for modeling various types of objects (e.g., a document as the set of keywords in it and a customer as the set of the items that she has purchased). Measuring similarity (e.g., Jaccard Index) between sets has been a key building block of a wide range of applications, including, plagiarism detection, recommendation, and graph compression. However, as sets have grown in numbers and sizes, the computational cost and storage required for set similarity computation have become substantial, and this has led to the development of hashing and sketching based solutions. In this work, we propose Set2Box, a learning-based approach for compressed representations of sets from which various similarity measures can be estimated accurately in constant time. The key idea is to represent sets as boxes to precisely capture overlaps of sets. Additionally, based on the proposed box quantization scheme, we design Set2Box+, which yields more concise but more accurate box representations of sets. Through extensive experiments on 8 real-world datasets, we show that, compared to baseline approaches, Set2Box+ is (a) Accurate: achieving up to 40.8X smaller estimation error while requiring 60% fewer bits to encode sets, (b) Concise: yielding up to 96.8X more concise representations with similar estimation error, and (c) Versatile: enabling the estimation of four set-similarity measures from a single representation of each set.
The success of Graph Neural Networks (GNNs) has led to a need for understanding their decision-making process and providing explanations for their predictions, which has given rise to explainable AI (XAI) that offers transparent explanations for black-box models. Recently, the use of prototypes has successfully improved the explainability of models by learning prototypes to imply training graphs that affect the prediction. However, these approaches tend to provide prototypes with excessive information from the entire graph, leading to the exclusion of key substructures or the inclusion of irrelevant substructures, which can limit both the interpretability and the performance of the model in downstream tasks. In this work, we propose a novel framework of explainable GNNs, called interpretable Prototype-based Graph Information Bottleneck (PGIB) that incorporates prototype learning within the information bottleneck framework to provide prototypes with the key subgraph from the input graph that is important for the model prediction. This is the first work that incorporates prototype learning into the process of identifying the key subgraphs that have a critical impact on the prediction performance. Extensive experiments, including qualitative analysis, demonstrate that PGIB outperforms state-of-the-art methods in terms of both prediction performance and explainability.
Graph neural networks (GNN) are vulnerable to adversarial attacks, which aim to degrade the performance of GNNs through imperceptible changes on the graph. However, we find that in fact the prevalent meta-gradient-based attacks, which utilizes the gradient of the loss w.r.t the adjacency matrix, are biased towards training nodes. That is, their meta-gradient is determined by a training procedure of the surrogate model, which is solely trained on the training nodes. This bias manifests as an uneven perturbation, connecting two nodes when at least one of them is a labeled node, i.e., training node, while it is unlikely to connect two unlabeled nodes. However, these biased attack approaches are sub-optimal as they do not consider flipping edges between two unlabeled nodes at all. This means that they miss the potential attacked edges between unlabeled nodes that significantly alter the representation of a node. In this paper, we investigate the meta-gradients to uncover the root cause of the uneven perturbations of existing attacks. Based on our analysis, we propose a Meta-gradient-based attack method using contrastive surrogate objective (Metacon), which alleviates the bias in meta-gradient using a new surrogate loss. We conduct extensive experiments to show that Metacon outperforms existing meta gradient-based attack methods through benchmark datasets, while showing that alleviating the bias towards training nodes is effective in attacking the graph structure.
Namkyeong Lee, Edward De Brouwer, Ehsan Hajiramezanali et al.
Recent advances in large language models (LLMs) have shown great potential to accelerate drug discovery. However, the specialized nature of biochemical data often necessitates costly domain-specific fine-tuning, posing major challenges. First, it hinders the application of more flexible general-purpose LLMs for cutting-edge drug discovery tasks. More importantly, it limits the rapid integration of the vast amounts of scientific data continuously generated through experiments and research. Compounding these challenges is the fact that real-world scientific questions are typically complex and open-ended, requiring reasoning beyond pattern matching or static knowledge retrieval.To address these challenges, we propose CLADD, a retrieval-augmented generation (RAG)-empowered agentic system tailored to drug discovery tasks. Through the collaboration of multiple LLM agents, CLADD dynamically retrieves information from biomedical knowledge bases, contextualizes query molecules, and integrates relevant evidence to generate responses - all without the need for domain-specific fine-tuning. Crucially, we tackle key obstacles in applying RAG workflows to biochemical data, including data heterogeneity, ambiguity, and multi-source integration. We demonstrate the flexibility and effectiveness of this framework across a variety of drug discovery tasks, showing that it outperforms general-purpose and domain-specific LLMs as well as traditional deep learning approaches. Our code is publicly available at https://github.com/Genentech/CLADD.
We investigate the replay buffer in rehearsal-based approaches for graph continual learning (GCL) methods. Existing rehearsal-based GCL methods select the most representative nodes for each class and store them in a replay buffer for later use in training subsequent tasks. However, we discovered that considering only the class representativeness of each replayed node makes the replayed nodes to be concentrated around the center of each class, incurring a potential risk of overfitting to nodes residing in those regions, which aggravates catastrophic forgetting. Moreover, as the rehearsal-based approach heavily relies on a few replayed nodes to retain knowledge obtained from previous tasks, involving the replayed nodes that have irrelevant neighbors in the model training may have a significant detrimental impact on model performance. In this paper, we propose a GCL model named DSLR, specifically, we devise a coverage-based diversity (CD) approach to consider both the class representativeness and the diversity within each class of the replayed nodes. Moreover, we adopt graph structure learning (GSL) to ensure that the replayed nodes are connected to truly informative neighbors. Extensive experimental results demonstrate the effectiveness and efficiency of DSLR. Our source code is available at https://github.com/seungyoon-Choi/DSLR_official.
Recent studies have revealed that GNNs are vulnerable to adversarial attacks. To defend against such attacks, robust graph structure refinement (GSR) methods aim at minimizing the effect of adversarial edges based on node features, graph structure, or external information. However, we have discovered that existing GSR methods are limited by narrowassumptions, such as assuming clean node features, moderate structural attacks, and the availability of external clean graphs, resulting in the restricted applicability in real-world scenarios. In this paper, we propose a self-guided GSR framework (SG-GSR), which utilizes a clean sub-graph found within the given attacked graph itself. Furthermore, we propose a novel graph augmentation and a group-training strategy to handle the two technical challenges in the clean sub-graph extraction: 1) loss of structural information, and 2) imbalanced node degree distribution. Extensive experiments demonstrate the effectiveness of SG-GSR under various scenarios including non-targeted attacks, targeted attacks, feature attacks, e-commerce fraud, and noisy node labels. Our code is available at https://github.com/yeonjun-in/torch-SG-GSR.
Social graph-based fake news detection aims to identify news articles containing false information by utilizing social contexts, e.g., user information, tweets and comments. However, conventional methods are evaluated under less realistic scenarios, where the model has access to future knowledge on article-related and context-related data during training. In this work, we newly formalize a more realistic evaluation scheme that mimics real-world scenarios, where the data is temporality-aware and the detection model can only be trained on data collected up to a certain point in time. We show that the discriminative capabilities of conventional methods decrease sharply under this new setting, and further propose DAWN, a method more applicable to such scenarios. Our empirical findings indicate that later engagements (e.g., consuming or reposting news) contribute more to noisy edges that link real news-fake news pairs in the social graph. Motivated by this, we utilize feature representations of engagement earliness to guide an edge weight estimator to suppress the weights of such noisy edges, thereby enhancing the detection performance of DAWN. Through extensive experiments, we demonstrate that DAWN outperforms existing fake news detection methods under real-world environments. The source code is available at https://github.com/LeeJunmo/DAWN.
While inorganic retrosynthesis planning is essential in the field of chemical science, the application of machine learning in this area has been notably less explored compared to organic retrosynthesis planning. In this paper, we propose Retrieval-Retro for inorganic retrosynthesis planning, which implicitly extracts the precursor information of reference materials that are retrieved from the knowledge base regarding domain expertise in the field. Specifically, instead of directly employing the precursor information of reference materials, we propose implicitly extracting it with various attention layers, which enables the model to learn novel synthesis recipes more effectively. Moreover, during retrieval, we consider the thermodynamic relationship between target material and precursors, which is essential domain expertise in identifying the most probable precursor set among various options. Extensive experiments demonstrate the superiority of Retrieval-Retro in retrosynthesis planning, especially in discovering novel synthesis recipes, which is crucial for materials discovery. The source code for Retrieval-Retro is available at https://github.com/HeewoongNoh/Retrieval-Retro.
In real-world graphs, we often encounter missing feature situations where a few or the majority of node features, e.g., sensitive information, are missed. In such scenarios, directly utilizing Graph Neural Networks (GNNs) would yield sub-optimal results in downstream tasks such as node classification. Despite the emergence of a few GNN-based methods attempting to mitigate its missing situation, when only a few features are available, they rather perform worse than traditional structure-based models. To this end, we propose a novel framework that further illuminates the potential of classical Label Propagation (Oldie), taking advantage of Feature Propagation, especially when only a partial feature is available. Now called by GOODIE, it takes a hybrid approach to obtain embeddings from the Label Propagation branch and Feature Propagation branch. To do so, we first design a GNN-based decoder that enables the Label Propagation branch to output hidden embeddings that align with those of the FP branch. Then, GOODIE automatically captures the significance of structure and feature information thanks to the newly designed Structure-Feature Attention. Followed by a novel Pseudo-Label contrastive learning that differentiates the contribution of each positive pair within pseudo-labels originating from the LP branch, GOODIE outputs the final prediction for the unlabeled nodes. Through extensive experiments, we demonstrate that our proposed model, GOODIE, outperforms the existing state-of-the-art methods not only when only a few features are available but also in abundantly available situations. Source code of GOODIE is available at: https://github.com/SukwonYun/GOODIE.
Traditional user modeling (UM) approaches have primarily focused on designing models for a single specific task, but they face limitations in generalization and adaptability across various tasks. Recognizing these challenges, recent studies have shifted towards continual learning (CL)-based universal user representation learning aiming to develop a single model capable of handling multiple tasks. Despite advancements, existing methods are in fact evaluated under an unrealistic scenario that does not consider the passage of time as tasks progress, which overlooks newly emerged items that may change the item distribution of previous tasks. In this paper, we introduce a practical evaluation scenario on which CL-based universal user representation learning approaches should be evaluated, which takes into account the passage of time as tasks progress. Then, we propose a novel framework Dynamic Time-aware continual user representation learner, named DITTO, designed to alleviate catastrophic forgetting despite continuous shifts in item distribution, while also allowing the knowledge acquired from previous tasks to adapt to the current shifted item distribution. Through our extensive experiments, we demonstrate the superiority of DITTO over state-of-the-art methods under a practical evaluation scenario. Our source code is available at https://github.com/seungyoon-Choi/DITTO_official.
Multi-modal recommender systems (MRSs) have achieved notable success in improving personalization by leveraging diverse modalities such as images, text, and audio. However, two key challenges remain insufficiently addressed: (1) Insufficient consideration of missing modality scenarios and (2) the overlooking of unique characteristics of modality features. These challenges result in significant performance degradation in realistic situations where modalities are missing. To address these issues, we propose Disentangling and Generating Modality Recommender (DGMRec), a novel framework tailored for missing modality scenarios. DGMRec disentangles modality features into general and specific modality features from an information-based perspective, enabling richer representations for recommendation. Building on this, it generates missing modality features by integrating aligned features from other modalities and leveraging user modality preferences. Extensive experiments show that DGMRec consistently outperforms state-of-the-art MRSs in challenging scenarios, including missing modalities and new item settings as well as diverse missing ratios and varying levels of missing modalities. Moreover, DGMRec's generation-based approach enables cross-modal retrieval, a task inapplicable for existing MRSs, highlighting its adaptability and potential for real-world applications. Our code is available at https://github.com/ptkjw1997/DGMRec.
In real-world applications, node features in graphs often contain noise from various sources, leading to significant performance degradation in GNNs. Although several methods have been developed to enhance robustness, they rely on the unrealistic assumption that noise in node features is independent of the graph structure and node labels, thereby limiting their applicability. To this end, we introduce a more realistic noise scenario, dependency-aware noise on graphs (DANG), where noise in node features create a chain of noise dependencies that propagates to the graph structure and node labels. We propose a novel robust GNN, DA-GNN, which captures the causal relationships among variables in the data generating process (DGP) of DANG using variational inference. In addition, we present new benchmark datasets that simulate DANG in real-world applications, enabling more practical research on robust GNNs. Extensive experiments demonstrate that DA-GNN consistently outperforms existing baselines across various noise scenarios, including both DANG and conventional noise models commonly considered in this field. Our code is available at https://github.com/yeonjun-in/torch-DA-GNN.
Although Graph Neural Networks (GNNs) have been successful in node classification tasks, their performance heavily relies on the availability of a sufficient number of labeled nodes per class. In real-world situations, not all classes have many labeled nodes and there may be instances where the model needs to classify new classes, making manual labeling difficult. To solve this problem, it is important for GNNs to be able to classify nodes with a limited number of labeled nodes, known as few-shot node classification. Previous episodic meta-learning based methods have demonstrated success in few-shot node classification, but our findings suggest that optimal performance can only be achieved with a substantial amount of diverse training meta-tasks. To address this challenge of meta-learning based few-shot learning (FSL), we propose a new approach, the Task-Equivariant Graph few-shot learning (TEG) framework. Our TEG framework enables the model to learn transferable task-adaptation strategies using a limited number of training meta-tasks, allowing it to acquire meta-knowledge for a wide range of meta-tasks. By incorporating equivariant neural networks, TEG can utilize their strong generalization abilities to learn highly adaptable task-specific strategies. As a result, TEG achieves state-of-the-art performance with limited training meta-tasks. Our experiments on various benchmark datasets demonstrate TEG's superiority in terms of accuracy and generalization ability, even when using minimal meta-training data, highlighting the effectiveness of our proposed approach in addressing the challenges of meta-learning based few-shot node classification. Our code is available at the following link: https://github.com/sung-won-kim/TEG
Recently, molecular relational learning, whose goal is to predict the interaction behavior between molecular pairs, got a surge of interest in molecular sciences due to its wide range of applications. In this work, we propose CMRL that is robust to the distributional shift in molecular relational learning by detecting the core substructure that is causally related to chemical reactions. To do so, we first assume a causal relationship based on the domain knowledge of molecular sciences and construct a structural causal model (SCM) that reveals the relationship between variables. Based on the SCM, we introduce a novel conditional intervention framework whose intervention is conditioned on the paired molecule. With the conditional intervention framework, our model successfully learns from the causal substructure and alleviates the confounding effect of shortcut substructures that are spuriously correlated to chemical reactions. Extensive experiments on various tasks with real-world and synthetic datasets demonstrate the superiority of CMRL over state-of-the-art baseline models. Our code is available at https://github.com/Namkyeong/CMRL.
Inspired by the recent success of self-supervised methods applied on images, self-supervised learning on graph structured data has seen rapid growth especially centered on augmentation-based contrastive methods. However, we argue that without carefully designed augmentation techniques, augmentations on graphs may behave arbitrarily in that the underlying semantics of graphs can drastically change. As a consequence, the performance of existing augmentation-based methods is highly dependent on the choice of augmentation scheme, i.e., hyperparameters associated with augmentations. In this paper, we propose a novel augmentation-free self-supervised learning framework for graphs, named AFGRL. Specifically, we generate an alternative view of a graph by discovering nodes that share the local structural information and the global semantics with the graph. Extensive experiments towards various node-level tasks, i.e., node classification, clustering, and similarity search on various real-world datasets demonstrate the superiority of AFGRL. The source code for AFGRL is available at https://github.com/Namkyeong/AFGRL.
Scene Graph Generation (SGG) research has suffered from two fundamental challenges: the long-tailed predicate distribution and semantic ambiguity between predicates. These challenges lead to a bias towards head predicates in SGG models, favoring dominant general predicates while overlooking fine-grained predicates. In this paper, we address the challenges of SGG by framing it as multi-label classification problem with partial annotation, where relevant labels of fine-grained predicates are missing. Under the new frame, we propose Retrieval-Augmented Scene Graph Generation (RA-SGG), which identifies potential instances to be multi-labeled and enriches the single-label with multi-labels that are semantically similar to the original label by retrieving relevant samples from our established memory bank. Based on augmented relations (i.e., discovered multi-labels), we apply multi-prototype learning to train our SGG model. Several comprehensive experiments have demonstrated that RA-SGG outperforms state-of-the-art baselines by up to 3.6% on VG and 5.9% on GQA, particularly in terms of F@K, showing that RA-SGG effectively alleviates the issue of biased prediction caused by the long-tailed distribution and semantic ambiguity of predicates.
Adversarial attacks are allegedly unnoticeable. Prior studies have designed attack noticeability measures on graphs, primarily using statistical tests to compare the topology of original and (possibly) attacked graphs. However, we observe two critical limitations in the existing measures. First, because the measures rely on simple rules, attackers can readily enhance their attacks to bypass them, reducing their attack "noticeability" and, yet, maintaining their attack performance. Second, because the measures naively leverage global statistics, such as degree distributions, they may entirely overlook attacks until severe perturbations occur, letting the attacks be almost "totally unnoticeable." To address the limitations, we introduce HideNSeek, a learnable measure for graph attack noticeability. First, to mitigate the bypass problem, HideNSeek learns to distinguish the original and (potential) attack edges using a learnable edge scorer (LEO), which scores each edge on its likelihood of being an attack. Second, to mitigate the overlooking problem, HideNSeek conducts imbalance-aware aggregation of all the edge scores to obtain the final noticeability score. Using six real-world graphs, we empirically demonstrate that HideNSeek effectively alleviates the observed limitations, and LEO (i.e., our learnable edge scorer) outperforms eleven competitors in distinguishing attack edges under five different attack methods. For an additional application, we show that LEO boost the performance of robust GNNs by removing attack-like edges.
Mesh-based simulation using Graph Neural Networks (GNNs) has been recognized as a promising approach for modeling fluid dynamics. However, the mesh refinement techniques which allocate finer resolution to regions with steep gradients can induce the over-squashing problem in mesh-based GNNs, which prevents the capture of long-range physical interactions. Conventional graph rewiring methods attempt to alleviate this issue by adding new edges, but they typically complete all rewiring operations before applying them to the GNN. These approaches are physically unrealistic, as they assume instantaneous interactions between distant nodes and disregard the distance information between particles. To address these limitations, we propose a novel framework, called Adaptive Graph Rewiring in Mesh-Based Graph Neural Networks (AdaMeshNet), that introduces an adaptive rewiring process into the message-passing procedure to model the gradual propagation of physical interactions. Our method computes a rewiring delay score for bottleneck nodes in the mesh graph, based on the shortest-path distance and the velocity difference. Using this score, it dynamically selects the message-passing layer at which new edges are rewired, which can lead to adaptive rewiring in a mesh graph. Extensive experiments on mesh-based fluid simulations demonstrate that AdaMeshNet outperforms conventional rewiring methods, effectively modeling the sequential nature of physical interactions and enabling more accurate predictions.
Mesh-based 3D static analysis methods have recently emerged as efficient alternatives to traditional computational numerical solvers, significantly reducing computational costs and runtime for various physics-based analyses. However, these methods primarily focus on surface topology and geometry, often overlooking the inherent thickness of real-world 3D objects, which exhibits high correlations and similar behavior between opposing surfaces. This limitation arises from the disconnected nature of these surfaces and the absence of internal edge connections within the mesh. In this work, we propose a novel framework, the Thickness-aware E(3)-Equivariant 3D Mesh Neural Network (T-EMNN), that effectively integrates the thickness of 3D objects while maintaining the computational efficiency of surface meshes. Additionally, we introduce data-driven coordinates that encode spatial information while preserving E(3)-equivariance or invariance properties, ensuring consistent and robust analysis. Evaluations on a real-world industrial dataset demonstrate the superior performance of T-EMNN in accurately predicting node-level 3D deformations, effectively capturing thickness effects while maintaining computational efficiency.
Temporal Graph Neural Networks (TGNN) have the ability to capture both the graph topology and dynamic dependencies of interactions within a graph over time. There has been a growing need to explain the predictions of TGNN models due to the difficulty in identifying how past events influence their predictions. Since the explanation model for a static graph cannot be readily applied to temporal graphs due to its inability to capture temporal dependencies, recent studies proposed explanation models for temporal graphs. However, existing explanation models for temporal graphs rely on post-hoc explanations, requiring separate models for prediction and explanation, which is limited in two aspects: efficiency and accuracy of explanation. In this work, we propose a novel built-in explanation framework for temporal graphs, called Self-Explainable Temporal Graph Networks based on Graph Information Bottleneck (TGIB). TGIB provides explanations for event occurrences by introducing stochasticity in each temporal event based on the Information Bottleneck theory. Experimental results demonstrate the superiority of TGIB in terms of both the link prediction performance and explainability compared to state-of-the-art methods. This is the first work that simultaneously performs prediction and explanation for temporal graphs in an end-to-end manner.
Scene graph generation (SGG) models have suffered from inherent problems regarding the benchmark datasets such as the long-tailed predicate distribution and missing annotation problems. In this work, we aim to alleviate the long-tailed problem of SGG by utilizing unannotated triplets. To this end, we introduce a Self-Training framework for SGG (ST-SGG) that assigns pseudo-labels for unannotated triplets based on which the SGG models are trained. While there has been significant progress in self-training for image recognition, designing a self-training framework for the SGG task is more challenging due to its inherent nature such as the semantic ambiguity and the long-tailed distribution of predicate classes. Hence, we propose a novel pseudo-labeling technique for SGG, called Class-specific Adaptive Thresholding with Momentum (CATM), which is a model-agnostic framework that can be applied to any existing SGG models. Furthermore, we devise a graph structure learner (GSL) that is beneficial when adopting our proposed self-training framework to the state-of-the-art message-passing neural network (MPNN)-based SGG models. Our extensive experiments verify the effectiveness of ST-SGG on various SGG models, particularly in enhancing the performance on fine-grained predicate classes.
With the great success of deep learning in various domains, graph neural networks (GNNs) also become a dominant approach to graph classification. By the help of a global readout operation that simply aggregates all node (or node-cluster) representations, existing GNN classifiers obtain a graph-level representation of an input graph and predict its class label using the representation. However, such global aggregation does not consider the structural information of each node, which results in information loss on the global structure. Particularly, it limits the discrimination power by enforcing the same weight parameters of the classifier for all the node representations; in practice, each of them contributes to target classes differently depending on its structural semantic. In this work, we propose structural semantic readout (SSRead) to summarize the node representations at the position-level, which allows to model the position-specific weight parameters for classification as well as to effectively capture the graph semantic relevant to the global structure. Given an input graph, SSRead aims to identify structurally-meaningful positions by using the semantic alignment between its nodes and structural prototypes, which encode the prototypical features of each position. The structural prototypes are optimized to minimize the alignment cost for all training graphs, while the other GNN parameters are trained to predict the class labels. Our experimental results demonstrate that SSRead significantly improves the classification performance and interpretability of GNN classifiers while being compatible with a variety of aggregation functions, GNN architectures, and learning frameworks.
The goal of one-class collaborative filtering (OCCF) is to identify the user-item pairs that are positively-related but have not been interacted yet, where only a small portion of positive user-item interactions (e.g., users' implicit feedback) are observed. For discriminative modeling between positive and negative interactions, most previous work relied on negative sampling to some extent, which refers to considering unobserved user-item pairs as negative, as actual negative ones are unknown. However, the negative sampling scheme has critical limitations because it may choose "positive but unobserved" pairs as negative. This paper proposes a novel OCCF framework, named as BUIR, which does not require negative sampling. To make the representations of positively-related users and items similar to each other while avoiding a collapsed solution, BUIR adopts two distinct encoder networks that learn from each other; the first encoder is trained to predict the output of the second encoder as its target, while the second encoder provides the consistent targets by slowly approximating the first encoder. In addition, BUIR effectively alleviates the data sparsity issue of OCCF, by applying stochastic data augmentation to encoder inputs. Based on the neighborhood information of users and items, BUIR randomly generates the augmented views of each positive interaction each time it encodes, then further trains the model by this self-supervision. Our extensive experiments demonstrate that BUIR consistently and significantly outperforms all baseline methods by a large margin especially for much sparse datasets in which any assumptions about negative interactions are less valid.
Networks have been widely used to represent the relations between objects such as academic networks and social networks, and learning embedding for networks has thus garnered plenty of research attention. Self-supervised network representation learning aims at extracting node embedding without external supervision. Recently, maximizing the mutual information between the local node embedding and the global summary (e.g. Deep Graph Infomax, or DGI for short) has shown promising results on many downstream tasks such as node classification. However, there are two major limitations of DGI. Firstly, DGI merely considers the extrinsic supervision signal (i.e., the mutual information between node embedding and global summary) while ignores the intrinsic signal (i.e., the mutual dependence between node embedding and node attributes). Secondly, nodes in a real-world network are usually connected by multiple edges with different relations, while DGI does not fully explore the various relations among nodes. To address the above-mentioned problems, we propose a novel framework, called High-order Deep Multiplex Infomax (HDMI), for learning node embedding on multiplex networks in a self-supervised way. To be more specific, we first design a joint supervision signal containing both extrinsic and intrinsic mutual information by high-order mutual information, and we propose a High-order Deep Infomax (HDI) to optimize the proposed supervision signal. Then we propose an attention based fusion module to combine node embedding from different layers of the multiplex network. Finally, we evaluate the proposed HDMI on various downstream tasks such as unsupervised clustering and supervised classification. The experimental results show that HDMI achieves state-of-the-art performance on these tasks.
The goal of network embedding is to transform nodes in a network to a low-dimensional embedding vectors. Recently, heterogeneous network has shown to be effective in representing diverse information in data. However, heterogeneous network embedding suffers from the imbalance issue, i.e. the size of relation types (or the number of edges in the network regarding the type) is imbalanced. In this paper, we devise a new heterogeneous network embedding method, called BHIN2vec, which considers the balance among all relation types in a network. We view the heterogeneous network embedding as simultaneously solving multiple tasks in which each task corresponds to each relation type in a network. After splitting the skip-gram loss into multiple losses corresponding to different tasks, we propose a novel random-walk strategy to focus on the tasks with high loss values by considering the relative training ratio. Unlike previous random walk strategies, our proposed random-walk strategy generates training samples according to the relative training ratio among different tasks, which results in a balanced training for the node embedding. Our extensive experiments on node classification and recommendation demonstrate the superiority of BHIN2vec compared to the state-of-the-art methods. Also, based on the relative training ratio, we analyze how much each relation type is represented in the embedding space.
Nodes in a multiplex network are connected by multiple types of relations. However, most existing network embedding methods assume that only a single type of relation exists between nodes. Even for those that consider the multiplexity of a network, they overlook node attributes, resort to node labels for training, and fail to model the global properties of a graph. We present a simple yet effective unsupervised network embedding method for attributed multiplex network called DMGI, inspired by Deep Graph Infomax (DGI) that maximizes the mutual information between local patches of a graph, and the global representation of the entire graph. We devise a systematic way to jointly integrate the node embeddings from multiple graphs by introducing 1) the consensus regularization framework that minimizes the disagreements among the relation-type specific node embeddings, and 2) the universal discriminator that discriminates true samples regardless of the relation types. We also show that the attention mechanism infers the importance of each relation type, and thus can be useful for filtering unnecessary relation types as a preprocessing step. Extensive experiments on various downstream tasks demonstrate that DMGI outperforms the state-of-the-art methods, even though DMGI is fully unsupervised.
Recently, matrix factorization-based recommendation methods have been criticized for the problem raised by the triangle inequality violation. Although several metric learning-based approaches have been proposed to overcome this issue, existing approaches typically project each user to a single point in the metric space, and thus do not suffice for properly modeling the intensity and the heterogeneity of user-item relationships in implicit feedback. In this paper, we propose TransCF to discover such latent user-item relationships embodied in implicit user-item interactions. Inspired by the translation mechanism popularized by knowledge graph embedding, we construct user-item specific translation vectors by employing the neighborhood information of users and items, and translate each user toward items according to the user's relationships with the items. Our proposed method outperforms several state-of-the-art methods for top-N recommendation on seven real-world data by up to 17% in terms of hit ratio. We also conduct extensive qualitative evaluations on the translation vectors learned by our proposed method to ascertain the benefit of adopting the translation mechanism for implicit feedback-based recommendations.
Many real-world tasks solved by heterogeneous network embedding methods can be cast as modeling the likelihood of pairwise relationship between two nodes. For example, the goal of author identification task is to model the likelihood of a paper being written by an author (paper-author pairwise relationship). Existing task-guided embedding methods are node-centric in that they simply measure the similarity between the node embeddings to compute the likelihood of a pairwise relationship between two nodes. However, we claim that for task-guided embeddings, it is crucial to focus on directly modeling the pairwise relationship. In this paper, we propose a novel task-guided pair embedding framework in heterogeneous network, called TaPEm, that directly models the relationship between a pair of nodes that are related to a specific task (e.g., paper-author relationship in author identification). To this end, we 1) propose to learn a pair embedding under the guidance of its associated context path, i.e., a sequence of nodes between the pair, and 2) devise the pair validity classifier to distinguish whether the pair is valid with respect to the specific task at hand. By introducing pair embeddings that capture the semantics behind the pairwise relationships, we are able to learn the fine-grained pairwise relationship between two nodes, which is paramount for task-guided embedding methods. Extensive experiments on author identification task demonstrate that TaPEm outperforms the state-of-the-art methods, especially for authors with few publication records.
The long-tail phenomenon tells us that there are many items in the tail. However, not all tail items are the same. Each item acquires different kinds of users. Some items are loved by the general public, while some items are consumed by eccentric fans. In this paper, we propose a novel metric, item eccentricity, to incorporate this difference between consumers of the items. Eccentric items are defined as items that are consumed by eccentric users. We used this metric to analyze two real-world datasets of music and movies and observed the characteristics of items in terms of eccentricity. The results showed that our defined eccentricity of an item does not change much over time, and classified eccentric and noneccentric items present significantly distinct characteristics. The proposed metric effectively separates the eccentric and noneccentric items mixed in the tail, which could not be done with the previous measures, which only consider the popularity of items.
Chanyoung Park, Donghyun Kim, Min-Chul Yang et al.
Eliciting user preferences from purchase records for performing purchase prediction is challenging because negative feedback is not explicitly observed, and because treating all non-purchased items equally as negative feedback is unrealistic. Therefore, in this study, we present a framework that leverages the past click records of users to compensate for the missing user-item interactions of purchase records, i.e., non-purchased items. We begin by formulating various model assumptions, each one assuming a different order of user preferences among purchased, clicked-but-not-purchased, and non-clicked items, to study the usefulness of leveraging click records. We implement the model assumptions using the Bayesian personalized ranking model, which maximizes the area under the curve for bipartite ranking. However, we argue that using click records for bipartite ranking needs a meticulously designed model because of the relative unreliableness of click records compared with that of purchase records. Therefore, we ultimately propose a novel learning-to-rank method, called P3Stop, for performing purchase prediction. The proposed model is customized to be robust to relatively unreliable click records by particularly focusing on the accuracy of top-ranked items. Experimental results on two real-world e-commerce datasets demonstrate that P3STop considerably outperforms the state-of-the-art implicit-feedback-based recommendation methods, especially for top-ranked items.