Graph neural networks (GNNs) have shown promising results across various graph learning tasks, but they often assume homophily, which can result in poor performance on heterophilic graphs. The connected nodes are likely to be from different classes or have dissimilar features on heterophilic graphs. In this paper, we propose a novel GNN that incorporates the principle of heterophily by modeling the flow of information on nodes using the convection-diffusion equation (CDE). This allows the CDE to take into account both the diffusion of information due to homophily and the ``convection'' of information due to heterophily. We conduct extensive experiments, which suggest that our framework can achieve competitive performance on node classification tasks for heterophilic graphs, compared to the state-of-the-art methods. The code is available at \url{https://github.com/zknus/Graph-Diffusion-CDE}.
This paper investigates a missing feature imputation problem for graph learning tasks. Several methods have previously addressed learning tasks on graphs with missing features. However, in cases of high rates of missing features, they were unable to avoid significant performance degradation. To overcome this limitation, we introduce a novel concept of channel-wise confidence in a node feature, which is assigned to each imputed channel feature of a node for reflecting certainty of the imputation. We then design pseudo-confidence using the channel-wise shortest path distance between a missing-feature node and its nearest known-feature node to replace unavailable true confidence in an actual learning process. Based on the pseudo-confidence, we propose a novel feature imputation scheme that performs channel-wise inter-node diffusion and node-wise inter-channel propagation. The scheme can endure even at an exceedingly high missing rate (e.g., 99.5\%) and it achieves state-of-the-art accuracy for both semi-supervised node classification and link prediction on various datasets containing a high rate of missing features. Codes are available at https://github.com/daehoum1/pcfi.
Many real-world graph learning tasks require handling dynamic graphs where new nodes and edges emerge. Dynamic graph learning methods commonly suffer from the catastrophic forgetting problem, where knowledge learned for previous graphs is overwritten by updates for new graphs. To alleviate the problem, continual graph learning methods are proposed. However, existing continual graph learning methods aim to learn new patterns and maintain old ones with the same set of parameters of fixed size, and thus face a fundamental tradeoff between both goals. In this paper, we propose Parameter Isolation GNN (PI-GNN) for continual learning on dynamic graphs that circumvents the tradeoff via parameter isolation and expansion. Our motivation lies in that different parameters contribute to learning different graph patterns. Based on the idea, we expand model parameters to continually learn emerging graph patterns. Meanwhile, to effectively preserve knowledge for unaffected patterns, we find parameters that correspond to them via optimization and freeze them to prevent them from being rewritten. Experiments on eight real-world datasets corroborate the effectiveness of PI-GNN compared to state-of-the-art baselines.
Link prediction, which consists of predicting edges based on graph features, is a fundamental task in many graph applications. As for several related problems, Graph Neural Networks (GNNs), which are based on an attribute-centric message-passing paradigm, have become the predominant framework for link prediction. GNNs have consistently outperformed traditional topology-based heuristics, but what contributes to their performance? Are there simpler approaches that achieve comparable or better results? To answer these questions, we first identify important limitations in how GNN-based link prediction methods handle the intrinsic class imbalance of the problem -- due to the graph sparsity -- in their training and evaluation. Moreover, we propose Gelato, a novel topology-centric framework that applies a topological heuristic to a graph enhanced by attribute information via graph learning. Our model is trained end-to-end with an N-pair loss on an unbiased training set to address class imbalance. Experiments show that Gelato is 145% more accurate, trains 11 times faster, infers 6,000 times faster, and has less than half of the trainable parameters compared to state-of-the-art GNNs for link prediction.
This paper presents a novel transformer architecture for graph representation learning. The core insight of our method is to fully consider the information propagation among nodes and edges in a graph when building the attention module in the transformer blocks. Specifically, we propose a new attention mechanism called Graph Propagation Attention (GPA). It explicitly passes the information among nodes and edges in three ways, i.e. node-to-node, node-to-edge, and edge-to-node, which is essential for learning graph-structured data. On this basis, we design an effective transformer architecture named Graph Propagation Transformer (GPTrans) to further help learn graph data. We verify the performance of GPTrans in a wide range of graph learning experiments on several benchmark datasets. These results show that our method outperforms many state-of-the-art transformer-based graph models with better performance. The code will be released at https://github.com/czczup/GPTrans.
Deep graph clustering has recently received significant attention due to its ability to enhance the representation learning capabilities of models in unsupervised scenarios. Nevertheless, deep clustering for temporal graphs, which could capture crucial dynamic interaction information, has not been fully explored. It means that in many clustering-oriented real-world scenarios, temporal graphs can only be processed as static graphs. This not only causes the loss of dynamic information but also triggers huge computational consumption. To solve the problem, we propose a general framework for deep Temporal Graph Clustering called TGC, which introduces deep clustering techniques to suit the interaction sequence-based batch-processing pattern of temporal graphs. In addition, we discuss differences between temporal graph clustering and static graph clustering from several levels. To verify the superiority of the proposed framework TGC, we conduct extensive experiments. The experimental results show that temporal graph clustering enables more flexibility in finding a balance between time and space requirements, and our framework can effectively improve the performance of existing temporal graph learning methods. The code is released: https://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.
Heterogeneous graph neural networks (HGNNs) can learn from typed and relational graph data more effectively than conventional GNNs. With larger parameter spaces, HGNNs may require more training data, which is often scarce in real-world applications due to privacy regulations (e.g., GDPR). Federated graph learning (FGL) enables multiple clients to train a GNN collaboratively without sharing their local data. However, existing FGL methods mainly focus on homogeneous GNNs or knowledge graph embeddings; few have considered heterogeneous graphs and HGNNs. In federated heterogeneous graph learning, clients may have private graph schemas. Conventional FL/FGL methods attempting to define a global HGNN model would violate schema privacy. To address these challenges, we propose FedHGN, a novel and general FGL framework for HGNNs. FedHGN adopts schema-weight decoupling to enable schema-agnostic knowledge sharing and employs coefficients alignment to stabilize the training process and improve HGNN performance. With better privacy preservation, FedHGN consistently outperforms local training and conventional FL methods on three widely adopted heterogeneous graph datasets with varying client numbers. The code is available at https://github.com/cynricfu/FedHGN .
Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.
Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.), and draw upon data from neighboring strata to enhance the parameter learning of each sub-problem. They have been widely applied in machine learning and signal processing problems, including but not limited to time series forecasting, representation learning, graph clustering, max-margin classification, and general few-shot learning. Nevertheless, existing works on LRSM have either assumed a known graph or are restricted to specific applications. In this paper, we start by showing the importance and sensitivity of graph weights in LRSM, and provably show that the sensitivity can be arbitrarily large when the parameter scales and sample sizes are heavily imbalanced across nodes. We then propose a generic approach to jointly learn the graph while fitting the model parameters by solving a single optimization problem. We interpret the proposed formulation from both a graph connectivity viewpoint and an end-to-end Bayesian perspective, and propose an efficient algorithm to solve the problem. Convergence guarantees of the proposed optimization algorithm is also provided despite the lack of global strongly smoothness of the Laplacian regularization term typically required in the existing literature, which may be of independent interest. Finally, we illustrate the efficiency of our approach compared to existing methods by various real-world numerical examples.
The potential impact of a paper is often quantified by how many citations it will receive. However, most commonly used models may underestimate the influence of newly published papers over time, and fail to encapsulate this dynamics of citation network into the graph. In this study, we construct hierarchical and heterogeneous graphs for target papers with an annual perspective. The constructed graphs can record the annual dynamics of target papers' scientific context information. Then, a novel graph neural network, Hierarchical and Heterogeneous Contrastive Graph Learning Model (H2CGL), is proposed to incorporate heterogeneity and dynamics of the citation network. H2CGL separately aggregates the heterogeneous information for each year and prioritizes the highly-cited papers and relationships among references, citations, and the target paper. It then employs a weighted GIN to capture dynamics between heterogeneous subgraphs over years. Moreover, it leverages contrastive learning to make the graph representations more sensitive to potential citations. Particularly, co-cited or co-citing papers of the target paper with large citation gap are taken as hard negative samples, while randomly dropping low-cited papers could generate positive samples. Extensive experimental results on two scholarly datasets demonstrate that the proposed H2CGL significantly outperforms a series of baseline approaches for both previously and freshly published papers. Additional analyses highlight the significance of the proposed modules. Our codes and settings have been released on Github (https://github.com/ECNU-Text-Computing/H2CGL)
Skeleton-based action recognition has achieved remarkable results in human action recognition with the development of graph convolutional networks (GCNs). However, the recent works tend to construct complex learning mechanisms with redundant training and exist a bottleneck for long time-series. To solve these problems, we propose the Temporal-Spatio Graph ConvNeXt (TSGCNeXt) to explore efficient learning mechanism of long temporal skeleton sequences. Firstly, a new graph learning mechanism with simple structure, Dynamic-Static Separate Multi-graph Convolution (DS-SMG) is proposed to aggregate features of multiple independent topological graphs and avoid the node information being ignored during dynamic convolution. Next, we construct a graph convolution training acceleration mechanism to optimize the back-propagation computing of dynamic graph learning with 55.08\% speed-up. Finally, the TSGCNeXt restructure the overall structure of GCN with three Spatio-temporal learning modules,efficiently modeling long temporal features. In comparison with existing previous methods on large-scale datasets NTU RGB+D 60 and 120, TSGCNeXt outperforms on single-stream networks. In addition, with the ema model introduced into the multi-stream fusion, TSGCNeXt achieves SOTA levels. On the cross-subject and cross-set of the NTU 120, accuracies reach 90.22% and 91.74%.
In this paper, we aim to develop a large language model (LLM) with the reasoning ability on complex graph data. Currently, LLMs have achieved very impressive performance on various natural language learning tasks, extensions of which have also been applied to study the vision tasks with multi-modal data. However, when it comes to the graph learning tasks, existing LLMs present very serious flaws due to their several inherited weaknesses in performing {multi-step logic reasoning}, {precise mathematical calculation} and {perception about the spatial and temporal factors}. To address such challenges, in this paper, we will investigate the principles, methodologies and algorithms to empower existing LLMs with graph reasoning ability, which will have tremendous impacts on the current research of both LLMs and graph learning. Inspired by the latest ChatGPT and Toolformer models, we propose the Graph-ToolFormer (Graph Reasoning oriented Toolformer) framework to teach LLMs themselves with prompts augmented by ChatGPT to use external graph reasoning API tools. Specifically, we will investigate to teach Graph-ToolFormer to handle various graph data reasoning tasks in this paper, including both (1) very basic graph data loading and graph property reasoning tasks, ranging from simple graph order and size to the graph diameter and periphery, and (2) more advanced reasoning tasks on real-world graph data, such as bibliographic networks, protein molecules, sequential recommender systems, social networks and knowledge graphs.
Effectively capturing intricate interactions among road users is of critical importance to achieving safe navigation for autonomous vehicles. While graph learning (GL) has emerged as a promising approach to tackle this challenge, existing GL models rely on predefined domain-specific graph extraction rules that often fail in real-world drastically changing scenarios. Additionally, these graph extraction rules severely impede the capability of existing GL methods to generalize knowledge across domains. To address this issue, we propose RoadScene2Graph (RS2G), an innovative autonomous scenario understanding framework with a novel data-driven graph extraction and modeling approach that dynamically captures the diverse relations among road users. Our evaluations demonstrate that on average RS2G outperforms the state-of-the-art (SOTA) rule-based graph extraction method by 4.47% and the SOTA deep learning model by 22.19% in subjective risk assessment. More importantly, RS2G delivers notably better performance in transferring knowledge gained from simulation environments to unseen real-world scenarios.
Multivariate time series classification (MTSC) is an important data mining task, which can be effectively solved by popular deep learning technology. Unfortunately, the existing deep learning-based methods neglect the hidden dependencies in different dimensions and also rarely consider the unique dynamic features of time series, which lack sufficient feature extraction capability to obtain satisfactory classification accuracy. To address this problem, we propose a novel temporal dynamic graph neural network (TodyNet) that can extract hidden spatio-temporal dependencies without undefined graph structure. It enables information flow among isolated but implicit interdependent variables and captures the associations between different time slots by dynamic graph mechanism, which further improves the classification performance of the model. Meanwhile, the hierarchical representations of graphs cannot be learned due to the limitation of GNNs. Thus, we also design a temporal graph pooling layer to obtain a global graph-level representation for graph learning with learnable temporal parameters. The dynamic graph, graph information propagation, and temporal convolution are jointly learned in an end-to-end framework. The experiments on 26 UEA benchmark datasets illustrate that the proposed TodyNet outperforms existing deep learning-based methods in the MTSC tasks.
Automated computational analysis of the vast chemical space is critical for numerous fields of research such as drug discovery and material science. Representation learning techniques have recently been employed with the primary objective of generating compact and informative numerical expressions of complex data. One approach to efficiently learn molecular representations is processing string-based notations of chemicals via natural language processing (NLP) algorithms. Majority of the methods proposed so far utilize SMILES notations for this purpose; however, SMILES is associated with numerous problems related to validity and robustness, which may prevent the model from effectively uncovering the knowledge hidden in the data. In this study, we propose SELFormer, a transformer architecture-based chemical language model that utilizes a 100% valid, compact and expressive notation, SELFIES, as input, in order to learn flexible and high-quality molecular representations. SELFormer is pre-trained on two million drug-like compounds and fine-tuned for diverse molecular property prediction tasks. Our performance evaluation has revealed that, SELFormer outperforms all competing methods, including graph learning-based approaches and SMILES-based chemical language models, on predicting aqueous solubility of molecules and adverse drug reactions. We also visualized molecular representations learned by SELFormer via dimensionality reduction, which indicated that even the pre-trained model can discriminate molecules with differing structural properties. We shared SELFormer as a programmatic tool, together with its datasets and pre-trained models. Overall, our research demonstrates the benefit of using the SELFIES notations in the context of chemical language modeling and opens up new possibilities for the design and discovery of novel drug candidates with desired features.
Unsupervised Representation Learning on graphs is gaining traction due to the increasing abundance of unlabelled network data and the compactness, richness, and usefulness of the representations generated. In this context, the need to consider fairness and bias constraints while generating the representations has been well-motivated and studied to some extent in prior works. One major limitation of most of the prior works in this setting is that they do not aim to address the bias generated due to connectivity patterns in the graphs, such as varied node centrality, which leads to a disproportionate performance across nodes. In our work, we aim to address this issue of mitigating bias due to inherent graph structure in an unsupervised setting. To this end, we propose CAFIN, a centrality-aware fairness-inducing framework that leverages the structural information of graphs to tune the representations generated by existing frameworks. We deploy it on GraphSAGE (a popular framework in this domain) and showcase its efficacy on two downstream tasks - Node Classification and Link Prediction. Empirically, CAFIN consistently reduces the performance disparity across popular datasets (varying from 18 to 80% reduction in performance disparity) from various domains while incurring only a minimal cost of fairness.
As a way to implement the "right to be forgotten" in machine learning, \textit{machine unlearning} aims to completely remove the contributions and information of the samples to be deleted from a trained model without affecting the contributions of other samples. Recently, many frameworks for machine unlearning have been proposed, and most of them focus on image and text data. To extend machine unlearning to graph data, \textit{GraphEraser} has been proposed. However, a critical issue is that \textit{GraphEraser} is specifically designed for the transductive graph setting, where the graph is static and attributes and edges of test nodes are visible during training. It is unsuitable for the inductive setting, where the graph could be dynamic and the test graph information is invisible in advance. Such inductive capability is essential for production machine learning systems with evolving graphs like social media and transaction networks. To fill this gap, we propose the \underline{{\bf G}}\underline{{\bf U}}ided \underline{{\bf I}}n\underline{{\bf D}}uctiv\underline{{\bf E}} Graph Unlearning framework (GUIDE). GUIDE consists of three components: guided graph partitioning with fairness and balance, efficient subgraph repair, and similarity-based aggregation. Empirically, we evaluate our method on several inductive benchmarks and evolving transaction graphs. Generally speaking, GUIDE can be efficiently implemented on the inductive graph learning tasks for its low graph partition cost, no matter on computation or structure information. The code will be available here: https://github.com/Happy2Git/GUIDE.
Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from graph classification to anomaly detection. There recently has emerged a number of approaches adopting a graph pooling operation within GNNs, with a goal to preserve graph attributive and structural features during the graph representation learning. However, most existing graph pooling operations suffer from the limitations of relying on node-wise neighbor weighting and embedding, which leads to insufficient encoding of rich topological structures and node attributes exhibited by real-world networks. By invoking the machinery of persistent homology and the concept of landmarks, we propose a novel topological pooling layer and witness complex-based topological embedding mechanism that allow us to systematically integrate hidden topological information at both local and global levels. Specifically, we design new learnable local and global topological representations Wit-TopoPool which allow us to simultaneously extract rich discriminative topological information from graphs. Experiments on 11 diverse benchmark datasets against 18 baseline models in conjunction with graph classification tasks indicate that Wit-TopoPool significantly outperforms all competitors across all datasets.
A common issue in graph learning under the semi-supervised setting is referred to as gradient scarcity. That is, learning graphs by minimizing a loss on a subset of nodes causes edges between unlabelled nodes that are far from labelled ones to receive zero gradients. The phenomenon was first described when optimizing the graph and the weights of a Graph Neural Network (GCN) with a joint optimization algorithm. In this work, we give a precise mathematical characterization of this phenomenon, and prove that it also emerges in bilevel optimization, where additional dependency exists between the parameters of the problem. While for GCNs gradient scarcity occurs due to their finite receptive field, we show that it also occurs with the Laplacian regularization model, in the sense that gradients amplitude decreases exponentially with distance to labelled nodes. To alleviate this issue, we study several solutions: we propose to resort to latent graph learning using a Graph-to-Graph model (G2G), graph regularization to impose a prior structure on the graph, or optimizing on a larger graph than the original one with a reduced diameter. Our experiments on synthetic and real datasets validate our analysis and prove the efficiency of the proposed solutions.