Last decade has seen the emergence of numerous methods for learning on graphs, particularly Graph Neural Networks (GNNs). These methods, however, are often not directly applicable to more complex structures like bipartite graphs (equivalent to hypergraphs), which represent interactions among two entity types (e.g. a user liking a movie). This paper proposes Convolutional Signal Propagation (CSP), a non-parametric simple and scalable method that natively operates on bipartite graphs (hypergraphs) and can be implemented with just a few lines of code. After defining CSP, we demonstrate its relationship with well-established methods like label propagation, Naive Bayes, and Hypergraph Convolutional Networks. We evaluate CSP against several reference methods on real-world datasets from multiple domains, focusing on retrieval and classification tasks. Our results show that CSP offers competitive performance while maintaining low computational complexity, making it an ideal first choice as a baseline for hypergraph node classification and retrieval. Moreover, despite operating on hypergraphs, CSP achieves good results in tasks typically not associated with hypergraphs, such as natural language processing.
Heterophily, or the tendency of connected nodes in networks to have different class labels or dissimilar features, has been identified as challenging for many Graph Neural Network (GNN) models. While the challenges of applying GNNs for node classification when class labels display strong heterophily are well understood, it is unclear how heterophily affects GNN performance in other important graph learning tasks where class labels are not available. In this work, we focus on the link prediction task and systematically analyze the impact of heterophily in node features on GNN performance. Theoretically, we first introduce formal definitions of homophilic and heterophilic link prediction tasks, and present a theoretical framework that highlights the different optimizations needed for the respective tasks. We then analyze how different link prediction encoders and decoders adapt to varying levels of feature homophily and introduce designs for improved performance. Our empirical analysis on a variety of synthetic and real-world datasets confirms our theoretical insights and highlights the importance of adopting learnable decoders and GNN encoders with ego- and neighbor-embedding separation in message passing for link prediction tasks beyond homophily.
Explainability is crucial for the application of black-box Graph Neural Networks (GNNs) in critical fields such as healthcare, finance, cybersecurity, and more. Various feature attribution methods, especially the perturbation-based methods, have been proposed to indicate how much each node/edge contributes to the model predictions. However, these methods fail to generate connected explanatory subgraphs that consider the causal interaction between edges within different coalition scales, which will result in unfaithful explanations. In our study, we propose GISExplainer, a novel game-theoretic interaction based explanation method that uncovers what the underlying GNNs have learned for node classification by discovering human-interpretable causal explanatory subgraphs. First, GISExplainer defines a causal attribution mechanism that considers the game-theoretic interaction of multi-granularity coalitions in candidate explanatory subgraph to quantify the causal effect of an edge on the prediction. Second, GISExplainer assumes that the coalitions with negative effects on the predictions are also significant for model interpretation, and the contribution of the computation graph stems from the combined influence of both positive and negative interactions within the coalitions. Then, GISExplainer regards the explanation task as a sequential decision process, in which a salient edges is successively selected and connected to the previously selected subgraph based on its causal effect to form an explanatory subgraph, ultimately striving for better explanations. Additionally, an efficiency optimization scheme is proposed for the causal attribution mechanism through coalition sampling. Extensive experiments demonstrate that GISExplainer achieves better performance than state-of-the-art approaches w.r.t. two quantitative metrics: Fidelity and Sparsity.
With the prosperity of contrastive learning for visual representation learning (VCL), it is also adapted to the graph domain and yields promising performance. However, through a systematic study of various graph contrastive learning (GCL) methods, we observe that some common phenomena among existing GCL methods that are quite different from the original VCL methods, including 1) positive samples are not a must for GCL; 2) negative samples are not necessary for graph classification, neither for node classification when adopting specific normalization modules; 3) data augmentations have much less influence on GCL, as simple domain-agnostic augmentations (e.g., Gaussian noise) can also attain fairly good performance. By uncovering how the implicit inductive bias of GNNs works in contrastive learning, we theoretically provide insights into the above intriguing properties of GCL. Rather than directly porting existing VCL methods to GCL, we advocate for more attention toward the unique architecture of graph learning and consider its implicit influence when designing GCL methods. Code is available at https: //github.com/PKU-ML/ArchitectureMattersGCL.
The ability of message-passing neural networks (MPNNs) to fit complex functions over graphs is limited as most graph convolutions amplify the same signal across all feature channels, a phenomenon known as rank collapse, and over-smoothing as a special case. Most approaches to mitigate over-smoothing extend common message-passing schemes, e.g., the graph convolutional network, by utilizing residual connections, gating mechanisms, normalization, or regularization techniques. Our work contrarily proposes to directly tackle the cause of this issue by modifying the message-passing scheme and exchanging different types of messages using multi-relational graphs. We identify a sufficient condition to ensure linearly independent node representations. As one instantion, we show that operating on multiple directed acyclic graphs always satisfies our condition and propose to obtain these by defining a strict partial ordering of the nodes. We conduct comprehensive experiments that confirm the benefits of operating on multi-relational graphs to achieve more informative node representations.
In the area of large-scale training of graph embeddings, effective training frameworks and partitioning methods are critical for handling large networks. However, they face two major challenges: 1) existing synchronized distributed frameworks require continuous communication to access information from other machines, and 2) the inability of current partitioning methods to ensure that subgraphs remain connected components without isolated nodes, which is essential for effective training of GNNs since training relies on information aggregation from neighboring nodes. To address these issues, we introduce a novel partitioning method, named Leiden-Fusion, designed for large-scale training of graphs with minimal communication. Our method extends the Leiden community detection algorithm with a greedy algorithm that merges the smallest communities with highly connected neighboring communities. Our method guarantees that, for an initially connected graph, each partition is a densely connected subgraph with no isolated nodes. After obtaining the partitions, we train a GNN for each partition independently, and finally integrate all embeddings for node classification tasks, which significantly reduces the need for network communication and enhances the efficiency of distributed graph training. We demonstrate the effectiveness of our method through extensive evaluations on several benchmark datasets, achieving high efficiency while preserving the quality of the graph embeddings for node classification tasks.
Hypergraphs tackle the limitations of traditional graphs by introducing {\em hyperedges}. While graph edges connect only two nodes, hyperedges connect an arbitrary number of nodes along their edges. Also, the underlying message-passing mechanisms in Hypergraph Neural Networks (HGNNs) are in the form of vertex-hyperedge-vertex, which let HGNNs capture and utilize richer and more complex structural information than traditional Graph Neural Networks (GNNs). More recently, the idea of overlapping subgraphs has emerged. These subgraphs can capture more information about subgroups of vertices without limiting one vertex belonging to just one group, allowing vertices to belong to multiple groups or subgraphs. In addition, one of the most important problems in graph clustering is to find densest overlapping subgraphs (DOS). In this paper, we propose a solution to the DOS problem via Agglomerative Greedy Enumeration (DOSAGE) algorithm as a novel approach to enhance the process of generating the densest overlapping subgraphs and, hence, a robust construction of the hypergraphs. Experiments on standard benchmarks show that the DOSAGE algorithm significantly outperforms the HGNNs and six other methods on the node classification task.
In the broader machine learning literature, data-generation methods demonstrate promising results by generating additional informative training examples via augmenting sparse labels. Such methods are less studied in graphs due to the intricate dependencies among nodes in complex topology structures. This paper presents a novel node generation method that infuses a small set of high-quality synthesized nodes into the graph as additional labeled nodes to optimally expand the propagation of labeled information. By simply infusing additional nodes, the framework is orthogonal to the graph learning and downstream classification techniques, and thus is compatible with most popular graph pre-training (self-supervised learning), semi-supervised learning, and meta-learning methods. The contribution lies in designing the generated node set by solving a novel optimization problem. The optimization places the generated nodes in a manner that: (1) minimizes the classification loss to guarantee training accuracy and (2) maximizes label propagation to low-confidence nodes in the downstream task to ensure high-quality propagation. Theoretically, we show that the above dual optimization maximizes the global confidence of node classification. Our Experiments demonstrate statistically significant performance improvements over 14 baselines on 10 publicly available datasets.
Heterophilous graphs, where dissimilar nodes tend to connect, pose a challenge for graph neural networks (GNNs). Increasing the GNN depth can expand the scope (i.e., receptive field), potentially finding homophily from the higher-order neighborhoods. However, GNNs suffer from performance degradation as depth increases. Despite having better expressivity, state-of-the-art deeper GNNs achieve only marginal improvements compared to their shallow variants. Through theoretical and empirical analysis, we systematically demonstrate a shift in GNN generalization preferences across nodes with different homophily levels as depth increases. This creates a disparity in generalization patterns between GNN models with varying depth. Based on these findings, we propose to improve deeper GNN generalization while maintaining high expressivity by Mixture of scope experts at test (Moscat). Experimental results show that Moscat works flexibly with various GNNs across a wide range of datasets while significantly improving accuracy. Our code is available at (https://github.com/Hydrapse/moscat).
In this study, we undertake a reproducibility analysis of 'Learning Fair Graph Representations Via Automated Data Augmentations' by Ling et al. (2022). We assess the validity of the original claims focused on node classification tasks and explore the performance of the Graphair framework in link prediction tasks. Our investigation reveals that we can partially reproduce one of the original three claims and fully substantiate the other two. Additionally, we broaden the application of Graphair from node classification to link prediction across various datasets. Our findings indicate that, while Graphair demonstrates a comparable fairness-accuracy trade-off to baseline models for mixed dyadic-level fairness, it has a superior trade-off for subgroup dyadic-level fairness. These findings underscore Graphair's potential for wider adoption in graph-based learning. Our code base can be found on GitHub at https://github.com/juellsprott/graphair-reproducibility.
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order information, i.e., information that goes \emph{beyond} pairwise interactions. Recent work has shown that persistent homology, a tool from topological data analysis, can enrich graph neural networks with topological information that they otherwise could not capture. Calculating such features is efficient for dimension 0 (connected components) and dimension 1 (cycles). However, when it comes to higher-order structures, it does not scale well, with a complexity of $O(n^d)$, where $n$ is the number of nodes and $d$ is the order of the structures. In this work, we introduce a novel method that extracts information about higher-order structures in the graph while still using the efficient low-dimensional persistent homology algorithm. On standard benchmark datasets, we show that our method can lead to up to $31\%$ improvements in test accuracy.
Graph representation learning has emerged as a powerful tool for preserving graph topology when mapping nodes to vector representations, enabling various downstream tasks such as node classification and community detection. However, most current graph neural network models face the challenge of requiring extensive labeled data, which limits their practical applicability in real-world scenarios where labeled data is scarce. To address this challenge, researchers have explored Graph Contrastive Learning (GCL), which leverages enhanced graph data and contrastive learning techniques. While promising, existing GCL methods often struggle with effectively capturing both local and global graph structures, and balancing the trade-off between nodelevel and graph-level representations. In this work, we propose Graph Representation Embedding Enhanced via Multidimensional Contrastive Learning (GRE2-MDCL). Our model introduces a novel triple network architecture with a multi-head attention GNN as the core. GRE2-MDCL first globally and locally augments the input graph using SVD and LAGNN techniques. It then constructs a multidimensional contrastive loss, incorporating cross-network, cross-view, and neighbor contrast, to optimize the model. Extensive experiments on benchmark datasets Cora, Citeseer, and PubMed demonstrate that GRE2-MDCL achieves state-of-the-art performance, with average accuracies of 82.5%, 72.5%, and 81.6% respectively. Visualizations further show tighter intra-cluster aggregation and clearer inter-cluster boundaries, highlighting the effectiveness of our framework in improving upon baseline GCL models.
Graph representation learning (GRL) models have succeeded in many scenarios. Real-world graphs have imbalanced distribution, such as node labels and degrees, which leaves a critical challenge to GRL. Imbalanced inputs can lead to imbalanced outputs. However, most existing works ignore it and assume that the distribution of input graphs is balanced, which cannot align with real situations, resulting in worse model performance on tail data. The domination of head data makes tail data underrepresented when training graph neural networks (GNNs). Thus, we propose Graffin, a pluggable tail data augmentation module, to address the above issues. Inspired by recurrent neural networks (RNNs), Graffin flows head features into tail data through graph serialization techniques to alleviate the imbalance of tail representation. The local and global structures are fused to form the node representation under the combined effect of neighborhood and sequence information, which enriches the semantics of tail data. We validate the performance of Graffin on four real-world datasets in node classification tasks. Results show that Graffin can improve the adaptation to tail data without significantly degrading the overall model performance.
Spectral Graph Convolutional Networks (GCNs) have gained popularity in graph machine learning applications due, in part, to their flexibility in specification of network propagation rules. These propagation rules are often constructed as polynomial filters whose coefficients are learned using label information during training. In contrast to learned polynomial filters, explicit filter functions are useful in capturing relationships between network topology and distribution of labels across the network. A number of algorithms incorporating either approach have been proposed; however the relationship between filter functions and polynomial approximations is not fully resolved. This is largely due to the ill-conditioned nature of the linear systems that must be solved to derive polynomial approximations of filter functions. To address this challenge, we propose a novel Arnoldi orthonormalization-based algorithm, along with a unifying approach, called G-Arnoldi-GCN that can efficiently and effectively approximate a given filter function with a polynomial. We evaluate G-Arnoldi-GCN in the context of multi-class node classification across ten datasets with diverse topological characteristics. Our experiments show that G-Arnoldi-GCN consistently outperforms state-of-the-art methods when suitable filter functions are employed. Overall, G-Arnoldi-GCN opens important new directions in graph machine learning by enabling the explicit design and application of diverse filter functions. Code link: https://github.com/mustafaCoskunAgu/GArnoldi-GCN
A signed graph (SG) is a graph where edges carry sign information attached to it. The sign of a network can be positive, negative, or neutral. A signed network is ubiquitous in a real-world network like social networks, citation networks, and various technical networks. There are many network embedding models have been proposed and developed for signed networks for both homogeneous and heterogeneous types. SG embedding learns low-dimensional vector representations for nodes of a network, which helps to do many network analysis tasks such as link prediction, node classification, and community detection. In this survey, we perform a comprehensive study of SG embedding methods and applications. We introduce here the basic theories and methods of SGs and survey the current state of the art of signed graph embedding methods. In addition, we explore the applications of different types of SG embedding methods in real-world scenarios. As an application, we have explored the citation network to analyze authorship networks. We also provide source code and datasets to give future direction. Lastly, we explore the challenges of SG embedding and forecast various future research directions in this field.
In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify uncertainty in node classification tasks. Given a graph, it uses Normalizing Flows (NFs) to estimate class densities for each node independently and converts those densities into Dirichlet pseudo-counts, which are then dispersed through the graph using the personalized Page-Rank algorithm. The architecture of GPNs is motivated by a set of three axioms on the properties of its uncertainty estimates. We show that those axioms are not always satisfied in practice and therefore propose the family of Committe-based Uncertainty Quantification Graph Neural Networks (CUQ-GNNs), which combine standard Graph Neural Networks with the NF-based uncertainty estimation of Posterior Networks (PostNets). This approach adapts more flexibly to domain-specific demands on the properties of uncertainty estimates. We compare CUQ-GNN against GPN and other uncertainty quantification approaches on common node classification benchmarks and show that it is effective at producing useful uncertainty estimates.
We study the problem of learning the clusters of a given graph in the self-directed learning setup. This learning setting is a variant of online learning, where rather than an adversary determining the sequence in which nodes are presented, the learner autonomously and adaptively selects them. While self-directed learning of Euclidean halfspaces, linear functions, and general abstract multi-class hypothesis classes was recently considered, no results previously existed specifically for self-directed node classification on graphs. In this paper, we address this problem developing efficient algorithms for it. More specifically, we focus on the case of (geodesically) convex clusters, i.e., for every two nodes sharing the same label, all nodes on every shortest path between them also share the same label. In particular, we devise a polynomial-time algorithm that makes only $3(h(G)+1)^4 \ln n$ mistakes on graphs with two convex clusters, where $n$ is the total number of nodes and $h(G)$ is the Hadwiger number, i.e., the size of the largest clique minor of the graph $G$. We also show that our algorithm is robust to the case that clusters are slightly non-convex, still achieving a mistake bound logarithmic in $n$. Finally, for the more standard case of homophilic clusters, where strongly connected nodes tend to belong the same class, we devise a simple and efficient algorithm.
Text-attributed graph (TAG) is an important type of graph structured data with text descriptions for each node. Few- and zero-shot node classification on TAGs have many applications in fields such as academia and social networks. However, the two tasks are challenging due to the lack of supervision signals, and existing methods only use the contrastive loss to align graph-based node embedding and language-based text embedding. In this paper, we propose Hound to improve accuracy by introducing more supervision signals, and the core idea is to go beyond the node-text pairs that come with data. Specifically, we design three augmentation techniques, i.e., node perturbation, text matching, and semantics negation to provide more reference nodes for each text and vice versa. Node perturbation adds/drops edges to produce diversified node embeddings that can be matched with a text. Text matching retrieves texts with similar embeddings to match with a node. Semantics negation uses a negative prompt to construct a negative text with the opposite semantics, which is contrasted with the original node and text. We evaluate Hound on 5 datasets and compare with 13 state-of-the-art baselines. The results show that Hound consistently outperforms all baselines, and its accuracy improvements over the best-performing baseline are usually over 5%.
Graph distillation has emerged as a solution for reducing large graph datasets to smaller, more manageable, and informative ones. Existing methods primarily target node classification, involve computationally intensive processes, and fail to capture the true distribution of the full graph dataset. To address these issues, we introduce Graph Distillation with Structural Attention Matching (GSTAM), a novel method for condensing graph classification datasets. GSTAM leverages the attention maps of GNNs to distill structural information from the original dataset into synthetic graphs. The structural attention-matching mechanism exploits the areas of the input graph that GNNs prioritize for classification, effectively distilling such information into the synthetic graphs and improving overall distillation performance. Comprehensive experiments demonstrate GSTAM's superiority over existing methods, achieving 0.45% to 6.5% better performance in extreme condensation ratios, highlighting its potential use in advancing distillation for graph classification tasks (Code available at https://github.com/arashrasti96/GSTAM).
Graph Neural Networks (GNNs) have demonstrated commendable performance for graph-structured data. Yet, GNNs are often vulnerable to adversarial structural attacks as embedding generation relies on graph topology. Existing efforts are dedicated to purifying the maliciously modified structure or applying adaptive aggregation, thereby enhancing the robustness against adversarial structural attacks. It is inevitable for a defender to consume heavy computational costs due to lacking prior knowledge about modified structures. To this end, we propose an efficient defense method, called Simple and Fast Robust Graph Neural Network (SFR-GNN), supported by mutual information theory. The SFR-GNN first pre-trains a GNN model using node attributes and then fine-tunes it over the modified graph in the manner of contrastive learning, which is free of purifying modified structures and adaptive aggregation, thus achieving great efficiency gains. Consequently, SFR-GNN exhibits a 24%--162% speedup compared to advanced robust models, demonstrating superior robustness for node classification tasks.