One of the key tasks in graph learning is node classification. While Graph neural networks have been used for various applications, their adaptivity to reject option setting is not previously explored. In this paper, we propose NCwR, a novel approach to node classification in Graph Neural Networks (GNNs) with an integrated reject option, which allows the model to abstain from making predictions when uncertainty is high. We propose both cost-based and coverage-based methods for classification with abstention in node classification setting using GNNs. We perform experiments using our method on three standard citation network datasets Cora, Citeseer and Pubmed and compare with relevant baselines. We also model the Legal judgment prediction problem on ILDC dataset as a node classification problem where nodes represent legal cases and edges represent citations. We further interpret the model by analyzing the cases that the model abstains from predicting by visualizing which part of the input features influenced this decision.
GNAS (Graph Neural Architecture Search) has demonstrated great effectiveness in automatically designing the optimal graph neural architectures for multiple downstream tasks, such as node classification and link prediction. However, most existing GNAS methods cannot efficiently handle large-scale graphs containing more than million-scale nodes and edges due to the expensive computational and memory overhead. To scale GNAS on large graphs while achieving better performance, we propose SA-GNAS, a novel framework based on seed architecture expansion for efficient large-scale GNAS. Similar to the cell expansion in biotechnology, we first construct a seed architecture and then expand the seed architecture iteratively. Specifically, we first propose a performance ranking consistency-based seed architecture selection method, which selects the architecture searched on the subgraph that best matches the original large-scale graph. Then, we propose an entropy minimization-based seed architecture expansion method to further improve the performance of the seed architecture. Extensive experimental results on five large-scale graphs demonstrate that the proposed SA-GNAS outperforms human-designed state-of-the-art GNN architectures and existing graph NAS methods. Moreover, SA-GNAS can significantly reduce the search time, showing better search efficiency. For the largest graph with billion edges, SA-GNAS can achieve 2.8 times speedup compared to the SOTA large-scale GNAS method GAUSS. Additionally, since SA-GNAS is inherently parallelized, the search efficiency can be further improved with more GPUs. SA-GNAS is available at https://github.com/PasaLab/SAGNAS.
Machine learning models are highly vulnerable to label flipping, i.e., the adversarial modification (poisoning) of training labels to compromise performance. Thus, deriving robustness certificates is important to guarantee that test predictions remain unaffected and to understand worst-case robustness behavior. However, for Graph Neural Networks (GNNs), the problem of certifying label flipping has so far been unsolved. We change this by introducing an exact certification method, deriving both sample-wise and collective certificates. Our method leverages the Neural Tangent Kernel (NTK) to capture the training dynamics of wide networks enabling us to reformulate the bilevel optimization problem representing label flipping into a Mixed-Integer Linear Program (MILP). We apply our method to certify a broad range of GNN architectures in node classification tasks. Thereby, concerning the worst-case robustness to label flipping: $(i)$ we establish hierarchies of GNNs on different benchmark graphs; $(ii)$ quantify the effect of architectural choices such as activations, depth and skip-connections; and surprisingly, $(iii)$ uncover a novel phenomenon of the robustness plateauing for intermediate perturbation budgets across all investigated datasets and architectures. While we focus on GNNs, our certificates are applicable to sufficiently wide NNs in general through their NTK. Thus, our work presents the first exact certificate to a poisoning attack ever derived for neural networks, which could be of independent interest. The code is available at https://github.com/saper0/qpcert.
Nodes in the real-world graphs exhibit diverse patterns in numerous aspects, such as degree and homophily. However, most existent node predictors fail to capture a wide range of node patterns or to make predictions based on distinct node patterns, resulting in unsatisfactory classification performance. In this paper, we reveal that different node predictors are good at handling nodes with specific patterns and only apply one node predictor uniformly could lead to suboptimal result. To mitigate this gap, we propose a mixture of experts framework, MoE-NP, for node classification. Specifically, MoE-NP combines a mixture of node predictors and strategically selects models based on node patterns. Experimental results from a range of real-world datasets demonstrate significant performance improvements from MoE-NP.
Graph Neural Networks (GNNs) have emerged as a powerful tool to capture intricate network patterns, achieving success across different domains. However, existing GNNs require careful domain-specific architecture designs and training from scratch on each dataset, leading to an expertise-intensive process with difficulty in generalizing across graphs from different domains. Therefore, it can be hard for practitioners to infer which GNN model can generalize well to graphs from their domains. To address this challenge, we propose a novel cross-domain pretraining framework, "one model for one graph," which overcomes the limitations of previous approaches that failed to use a single GNN to capture diverse graph patterns across domains with significant gaps. Specifically, we pretrain a bank of expert models, with each one corresponding to a specific dataset. When inferring to a new graph, gating functions choose a subset of experts to effectively integrate prior model knowledge while avoiding negative transfer. Extensive experiments consistently demonstrate the superiority of our proposed method on both link prediction and node classification tasks.
Recent advancements in Spectral Graph Convolutional Networks (SpecGCNs) have led to state-of-the-art performance in various graph representation learning tasks. To exploit the potential of SpecGCNs, we analyze corresponding graph filters via polynomial interpolation, the cornerstone of graph signal processing. Different polynomial bases, such as Bernstein, Chebyshev, and monomial basis, have various convergence rates that will affect the error in polynomial interpolation. Although adopting Chebyshev basis for interpolation can minimize maximum error, the performance of ChebNet is still weaker than GPR-GNN and BernNet. \textbf{We point out it is caused by the Gibbs phenomenon, which occurs when the graph frequency response function approximates the target function.} It reduces the approximation ability of a truncated polynomial interpolation. In order to mitigate the Gibbs phenomenon, we propose to add the Gibbs damping factor with each term of Chebyshev polynomials on ChebNet. As a result, our lightweight approach leads to a significant performance boost. Afterwards, we reorganize ChebNet via decoupling feature propagation and transformation. We name this variant as \textbf{ChebGibbsNet}. Our experiments indicate that ChebGibbsNet is superior to other advanced SpecGCNs, such as GPR-GNN and BernNet, in both homogeneous graphs and heterogeneous graphs.
We address two fundamental challenges in Graph Neural Networks (GNNs): (1) the lack of theoretical support for invariance learning, a critical property in image processing, and (2) the absence of a unified model capable of excelling on both homophilic and heterophilic graph datasets. To tackle these issues, we establish and prove scale invariance in graphs, extending this key property to graph learning, and validate it through experiments on real-world datasets. Leveraging directed multi-scaled graphs and an adaptive self-loop strategy, we propose ScaleNet, a unified network architecture that achieves state-of-the-art performance across four homophilic and two heterophilic benchmark datasets. Furthermore, we show that through graph transformation based on scale invariance, uniform weights can replace computationally expensive edge weights in digraph inception networks while maintaining or improving performance. For another popular GNN approach to digraphs, we demonstrate the equivalence between Hermitian Laplacian methods and GraphSAGE with incidence normalization. ScaleNet bridges the gap between homophilic and heterophilic graph learning, offering both theoretical insights into scale invariance and practical advancements in unified graph learning. Our implementation is publicly available at https://github.com/Qin87/ScaleNet/tree/Aug23.
Graph federated learning is of essential importance for training over large graph datasets while protecting data privacy, where each client stores a subset of local graph data, while the server collects the local gradients and broadcasts only the aggregated gradients. Recent studies reveal that a malicious attacker can steal private image data from gradient exchanging of neural networks during federated learning. However, none of the existing works have studied the vulnerability of graph data and graph neural networks under such attack. To answer this question, the present paper studies the problem of whether private data can be recovered from leaked gradients in both node classification and graph classification tasks and { proposes a novel attack named Graph Leakage from Gradients (GLG)}. Two widely-used GNN frameworks are analyzed, namely GCN and GraphSAGE. The effects of different model settings on recovery are extensively discussed. Through theoretical analysis and empirical validation, it is shown that parts of the graph data can be leaked from the gradients.
In recent years, graph representation learning has undergone a paradigm shift, driven by the emergence and proliferation of graph neural networks (GNNs) and their heterogeneous counterparts. Heterogeneous GNNs have shown remarkable success in extracting low-dimensional embeddings from complex graphs that encompass diverse entity types and relationships. While meta-path-based techniques have long been recognized for their ability to capture semantic affinities among nodes, their dependence on manual specification poses a significant limitation. In contrast, matrix-focused methods accelerate processing by utilizing structural cues but often overlook contextual richness. In this paper, we challenge the current paradigm by introducing ontology as a fundamental semantic primitive within complex graphs. Our goal is to integrate the strengths of both matrix-centric and meta-path-based approaches into a unified framework. We propose perturbation Ontology-based Graph Attention Networks (POGAT), a novel methodology that combines ontology subgraphs with an advanced self-supervised learning paradigm to achieve a deep contextual understanding. The core innovation of POGAT lies in our enhanced homogeneous perturbing scheme designed to generate rigorous negative samples, encouraging the model to explore minimal contextual features more thoroughly. Through extensive empirical evaluations, we demonstrate that POGAT significantly outperforms state-of-the-art baselines, achieving a groundbreaking improvement of up to 10.78\% in F1-score for the critical task of link prediction and 12.01\% in Micro-F1 for the critical task of node classification.
Multivariate time series (MTS) classification is widely applied in fields such as industry, healthcare, and finance, aiming to extract key features from complex time series data for accurate decision-making and prediction. However, existing methods for MTS often struggle due to the challenges of effectively modeling high-dimensional data and the lack of labeled data, resulting in poor classification performance. To address this issue, we propose a heterogeneous relationships of subjects and shapelets method for semi-supervised MTS classification. This method offers a novel perspective by integrating various types of additional information while capturing the relationships between them. Specifically, we first utilize a contrast temporal self-attention module to obtain sparse MTS representations, and then model the similarities between these representations using soft dynamic time warping to construct a similarity graph. Secondly, we learn the shapelets for different subject types, incorporating both the subject features and their shapelets as additional information to further refine the similarity graph, ultimately generating a heterogeneous graph. Finally, we use a dual level graph attention network to get prediction. Through this method, we successfully transform dataset into a heterogeneous graph, integrating multiple additional information and achieving precise semi-supervised node classification. Experiments on the Human Activity Recognition, sleep stage classification and University of East Anglia datasets demonstrate that our method outperforms current state-of-the-art methods in MTS classification tasks, validating its superiority.
Multi-label node classification is an important yet under-explored domain in graph mining as many real-world nodes belong to multiple categories rather than just a single one. Although a few efforts have been made by utilizing Graph Convolution Networks (GCNs) to learn node representations and model correlations between multiple labels in the embedding space, they still suffer from the ambiguous feature and ambiguous topology induced by multiple labels, which reduces the credibility of the messages delivered in graphs and overlooks the label correlations on graph data. Therefore, it is crucial to reduce the ambiguity and empower the GCNs for accurate classification. However, this is quite challenging due to the requirement of retaining the distinctiveness of each label while fully harnessing the correlation between labels simultaneously. To address these issues, in this paper, we propose a Correlation-aware Graph Convolutional Network (CorGCN) for multi-label node classification. By introducing a novel Correlation-Aware Graph Decomposition module, CorGCN can learn a graph that contains rich label-correlated information for each label. It then employs a Correlation-Enhanced Graph Convolution to model the relationships between labels during message passing to further bolster the classification process. Extensive experiments on five datasets demonstrate the effectiveness of our proposed CorGCN.
Graph Transformers (GTs) have demonstrated remarkable performance in incorporating various graph structure information, e.g., long-range structural dependency, into graph representation learning. However, self-attention -- the core module of GTs -- preserves only low-frequency signals on graph features, retaining only homophilic patterns that capture similar features among the connected nodes. Consequently, it has insufficient capacity in modeling complex node label patterns, such as the opposite of homophilic patterns -- heterophilic patterns. Some improved GTs deal with the problem by learning polynomial filters or performing self-attention over the first-order graph spectrum. However, these GTs either ignore rich information contained in the whole spectrum or neglect higher-order spectrum information, resulting in limited flexibility and frequency response in their spectral filters. To tackle these challenges, we propose a novel GT network, namely Graph Fourier Kolmogorov-Arnold Transformers (GrokFormer), to go beyond the self-attention in GTs. GrokFormer leverages learnable activation functions in order-$K$ graph spectrum through Fourier series modeling to i) learn eigenvalue-targeted filter functions producing learnable base that can capture a broad range of frequency signals flexibly, and ii) extract first- and higher-order graph spectral information adaptively. In doing so, GrokFormer can effectively capture intricate patterns hidden across different orders and levels of frequency signals, learning expressive, order-and-frequency-adaptive graph representations. Comprehensive experiments conducted on 10 node classification datasets across various domains, scales, and levels of graph heterophily, as well as 5 graph classification datasets, demonstrate that GrokFormer outperforms state-of-the-art GTs and other advanced graph neural networks.
Graph neural networks (GNNs) have emerged as powerful models for learning representations of graph data showing state of the art results in various tasks. Nevertheless, the superiority of these methods is usually supported by either evaluating their performance on small subset of benchmark datasets or by reasoning about their expressive power in terms of certain graph isomorphism tests. In this paper we critically analyse both these aspects through a transductive setting for the task of node classification. First, we delve deeper into the case of multi-label node classification which offers a more realistic scenario and has been ignored in most of the related works. Through analysing the training dynamics for GNN methods we highlight the failure of GNNs to learn over multi-label graph datasets even for the case of abundant training data. Second, we show that specifically for transductive node classification, even the most expressive GNN may fail to learn in absence of node attributes and without using explicit label information as input. To overcome this deficit, we propose a straightforward approach, referred to as GNN-MultiFix, that integrates the feature, label, and positional information of a node. GNN-MultiFix demonstrates significant improvement across all the multi-label datasets. We release our code at https://anonymous.4open.science/r/Graph-MultiFix-4121.
In this work, we discover that causal inference provides a promising approach to capture heterophilic message-passing in Graph Neural Network (GNN). By leveraging cause-effect analysis, we can discern heterophilic edges based on asymmetric node dependency. The learned causal structure offers more accurate relationships among nodes. To reduce the computational complexity, we introduce intervention-based causal inference in graph learning. We first simplify causal analysis on graphs by formulating it as a structural learning model and define the optimization problem within the Bayesian scheme. We then present an analysis of decomposing the optimization target into a consistency penalty and a structure modification based on cause-effect relations. We then estimate this target by conditional entropy and present insights into how conditional entropy quantifies the heterophily. Accordingly, we propose CausalMP, a causal message-passing discovery network for heterophilic graph learning, that iteratively learns the explicit causal structure of input graphs. We conduct extensive experiments in both heterophilic and homophilic graph settings. The result demonstrates that the our model achieves superior link prediction performance. Training on causal structure can also enhance node representation in classification task across different base models.
Pseudo labeling (PL) is a wide-applied strategy to enlarge the labeled dataset by self-annotating the potential samples during the training process. Several works have shown that it can improve the graph learning model performance in general. However, we notice that the incorrect labels can be fatal to the graph training process. Inappropriate PL may result in the performance degrading, especially on graph data where the noise can propagate. Surprisingly, the corresponding error is seldom theoretically analyzed in the literature. In this paper, we aim to give deep insights of PL on graph learning models. We first present the error analysis of PL strategy by showing that the error is bounded by the confidence of PL threshold and consistency of multi-view prediction. Then, we theoretically illustrate the effect of PL on convergence property. Based on the analysis, we propose a cautious pseudo labeling methodology in which we pseudo label the samples with highest confidence and multi-view consistency. Finally, extensive experiments demonstrate that the proposed strategy improves graph learning process and outperforms other PL strategies on link prediction and node classification tasks.
We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning techniques to 1) work with attributed graphs, 2) enabling a mini-batch based approach, and 3) achieving scalability. Based on a multi-class tuplet loss function, we present two algorithms -- DMT for semi-supervised learning and DMAT-i for the unsupervised case. Analyzing our methods, we provide a generalization bound for the downstream node classification task and for the first time relate tuplet loss to contrastive learning. Through extensive experiments, we show high scalability of representation construction, and in applying the method for three downstream tasks (node clustering, node classification, and link prediction) better consistency over any single existing method.
Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still struggle to generalise well beyond datasets that exhibit strong homophily, where nodes of the same class tend to connect. This limitation has led to the development of complex neural architectures that pose challenges in terms of efficiency and scalability. In response to these limitations, we focus on simpler and more scalable approaches and introduce Graph-aware Logistic Regression (GLR), a non-neural model designed for node classification tasks. Unlike traditional graph algorithms that use only a fraction of the information accessible to GNNs, our proposed model simultaneously leverages both node features and the relationships between entities. However instead of relying on message passing, our approach encodes each node's relationships as an additional feature vector, which is then combined with the node's self attributes. Extensive experimental results, conducted within a rigorous evaluation framework, show that our proposed GLR approach outperforms both foundational and sophisticated state-of-the-art GNN models in node classification tasks. Going beyond the traditional limited benchmarks, our experiments indicate that GLR increases generalisation ability while reaching performance gains in computation time up to two orders of magnitude compared to it best neural competitor.
Graphs inherently capture dependencies between nodes or variables through their topological structure, with paths between any two nodes indicating a sequential dependency on the nodes traversed. Message Passing Neural Networks (MPNNs) leverage these latent relationships embedded in graph structures, and have become widely adopted across diverse applications. However, many existing methods predominantly rely on local information within the $1$-hop neighborhood. This approach has notable limitations; for example, $1$-hop aggregation schemes inherently lose long-distance information, and are limited in expressive power as defined by the $k$-Weisfeiler-Leman ($k$-WL) isomorphism test. To address these issues, we propose the Higher Order Graphical Attention (HoGA) module, which assigns weights to variable-length paths sampled based on feature-vector diversity, effectively reconstructing the $k$-hop neighborhood. HoGA represents higher-order relationships as a robust form of self-attention, applicable to any single-hop attention mechanism. In empirical studies, applying HoGA to existing attention-based models consistently leads to significant accuracy improvements on benchmark node classification datasets. Furthermore, we observe that the performance degradation typically associated with additional message-passing steps may be mitigated.
Multivariate time series (MTS) data is generated through multiple sensors across various domains such as engineering application, health monitoring, and the internet of things, characterized by its temporal changes and high dimensional characteristics. Over the past few years, many studies have explored the long-range dependencies and similarities in MTS. However, long-range dependencies are difficult to model due to their temporal changes and high dimensionality makes it difficult to obtain similarities effectively and efficiently. Thus, to address these issues, we propose contrast similarity-aware dual-pathway Mamba for MTS node classification (CS-DPMamba). Firstly, to obtain the dynamic similarity of each sample, we initially use temporal contrast learning module to acquire MTS representations. And then we construct a similarity matrix between MTS representations using Fast Dynamic Time Warping (FastDTW). Secondly, we apply the DPMamba to consider the bidirectional nature of MTS, allowing us to better capture long-range and short-range dependencies within the data. Finally, we utilize the Kolmogorov-Arnold Network enhanced Graph Isomorphism Network to complete the information interaction in the matrix and MTS node classification task. By comprehensively considering the long-range dependencies and dynamic similarity features, we achieved precise MTS node classification. We conducted experiments on multiple University of East Anglia (UEA) MTS datasets, which encompass diverse application scenarios. Our results demonstrate the superiority of our method through both supervised and semi-supervised experiments on the MTS classification task.
Federated Graph Learning (FGL) has emerged as a promising paradigm for breaking data silos among distributed private graphs. In practical scenarios involving heterogeneous distributed graph data, personalized Federated Graph Learning (pFGL) aims to enhance model utility by training personalized models tailored to client needs. However, existing pFGL methods often require numerous communication rounds under heterogeneous graphs, leading to significant communication overhead and security concerns. While One-shot Federated Learning (OFL) enables collaboration in a single round, existing OFL methods are designed for image-centric tasks and ineffective for graph data, leaving a critical gap in the field. Additionally, personalized models derived from existing methods suffer from bias, failing to effectively generalize to the minority. To address these challenges, we propose the first $\textbf{O}$ne-shot $\textbf{p}$ersonalized $\textbf{F}$ederated $\textbf{G}$raph $\textbf{L}$earning method ($\textbf{O-pFGL}$) for node classification, compatible with Secure Aggregation protocols for privacy preservation. Specifically, for effective graph learning in one communication round, our method estimates and aggregates class-wise feature distribution statistics to construct a global pseudo-graph on the server, facilitating the training of a global graph model. To mitigate bias, we introduce a two-stage personalized training approach that adaptively balances local personal information and global insights from the pseudo-graph, improving both personalization and generalization. Extensive experiments on 12 multi-scale graph datasets demonstrate that our method significantly outperforms state-of-the-art baselines across various settings.