Graph data structures are widely used to store relational information between several entities. With data being generated worldwide on a large scale, we see a significant growth in the generation of knowledge graphs. Thing in the future is Orange's take on a knowledge graph in the domain of the Web Of Things (WoT), where the main objective of the platform is to provide a digital representation of the physical world and enable cross-domain applications to be built upon this massive and highly connected graph of things. In this context, as the knowledge graph grows in size, it is prone to have noisy and messy data. In this paper, we explore state-of-the-art knowledge graph embedding (KGE) methods to learn numerical representations of the graph entities and, subsequently, explore downstream tasks like link prediction, node classification, and triple classification. We also investigate Graph neural networks (GNN) alongside KGEs and compare their performance on the same downstream tasks. Our evaluation highlights the encouraging performance of both KGE and GNN-based methods on node classification, and the superiority of GNN approaches in the link prediction task. Overall, we show that state-of-the-art approaches are relevant in a WoT context, and this preliminary work provides insights to implement and evaluate them in this context.
Graph Neural Networks (GNNs) have shown remarkable merit in performing various learning-based tasks in complex networks. The superior performance of GNNs often correlates with the availability and quality of node-level features in the input networks. However, for many network applications, such node-level information may be missing or unreliable, thereby limiting the applicability and efficacy of GNNs. To address this limitation, we present a novel approach denoted as Ego-centric Spectral subGraph Embedding Augmentation (ESGEA), which aims to enhance and design node features, particularly in scenarios where information is lacking. Our method leverages the topological structure of the local subgraph to create topology-aware node features. The subgraph features are generated using an efficient spectral graph embedding technique, and they serve as node features that capture the local topological organization of the network. The explicit node features, if present, are then enhanced with the subgraph embeddings in order to improve the overall performance. ESGEA is compatible with any GNN-based architecture and is effective even in the absence of node features. We evaluate the proposed method in a social network graph classification task where node attributes are unavailable, as well as in a node classification task where node features are corrupted or even absent. The evaluation results on seven datasets and eight baseline models indicate up to a 10% improvement in AUC and a 7% improvement in accuracy for graph and node classification tasks, respectively.
In many real-world scenarios (e.g., academic networks, social platforms), different types of entities are not only associated with texts but also connected by various relationships, which can be abstracted as Text-Attributed Heterogeneous Graphs (TAHGs). Current pretraining tasks for Language Models (LMs) primarily focus on separately learning the textual information of each entity and overlook the crucial aspect of capturing topological connections among entities in TAHGs. In this paper, we present a new pretraining framework for LMs that explicitly considers the topological and heterogeneous information in TAHGs. Firstly, we define a context graph as neighborhoods of a target node within specific orders and propose a topology-aware pretraining task to predict nodes involved in the context graph by jointly optimizing an LM and an auxiliary heterogeneous graph neural network. Secondly, based on the observation that some nodes are text-rich while others have little text, we devise a text augmentation strategy to enrich textless nodes with their neighbors' texts for handling the imbalance issue. We conduct link prediction and node classification tasks on three datasets from various domains. Experimental results demonstrate the superiority of our approach over existing methods and the rationality of each design. Our code is available at https://github.com/Hope-Rita/THLM.
Graph embedding has become a powerful tool for learning latent representations of nodes in a graph. Despite its superior performance in various graph-based machine learning tasks, serious privacy concerns arise when the graph data contains personal or sensitive information. To address this issue, we investigate and develop graph embedding algorithms that satisfy local differential privacy (LDP). We introduce a novel privacy-preserving graph embedding framework, named PrivGE, to protect node data privacy. Specifically, we propose an LDP mechanism to obfuscate node data and utilize personalized PageRank as the proximity measure to learn node representations. Furthermore, we provide a theoretical analysis of the privacy guarantees and utility offered by the PrivGE framework. Extensive experiments on several real-world graph datasets demonstrate that PrivGE achieves an optimal balance between privacy and utility, and significantly outperforms existing methods in node classification and link prediction tasks.
Text-attributed graphs have recently garnered significant attention due to their wide range of applications in web domains. Existing methodologies employ word embedding models for acquiring text representations as node features, which are subsequently fed into Graph Neural Networks (GNNs) for training. Recently, the advent of Large Language Models (LLMs) has introduced their powerful capabilities in information retrieval and text generation, which can greatly enhance the text attributes of graph data. Furthermore, the acquisition and labeling of extensive datasets are both costly and time-consuming endeavors. Consequently, few-shot learning has emerged as a crucial problem in the context of graph learning tasks. In order to tackle this challenge, we propose a lightweight paradigm called LLM4NG, which adopts a plug-and-play approach to empower text-attributed graphs through node generation using LLMs. Specifically, we utilize LLMs to extract semantic information from the labels and generate samples that belong to these categories as exemplars. Subsequently, we employ an edge predictor to capture the structural information inherent in the raw dataset and integrate the newly generated samples into the original graph. This approach harnesses LLMs for enhancing class-level information and seamlessly introduces labeled nodes and edges without modifying the raw dataset, thereby facilitating the node classification task in few-shot scenarios. Extensive experiments demonstrate the outstanding performance of our proposed paradigm, particularly in low-shot scenarios. For instance, in the 1-shot setting of the ogbn-arxiv dataset, LLM4NG achieves a 76% improvement over the baseline model.
Most existing methods that address out-of-distribution (OOD) generalization for node classification on graphs primarily focus on a specific type of data biases, such as label selection bias or structural bias. However, anticipating the type of bias in advance is extremely challenging, and designing models solely for one specific type may not necessarily improve overall generalization performance. Moreover, limited research has focused on the impact of mixed biases, which are more prevalent and demanding in real-world scenarios. To address these limitations, we propose a novel Causality and Independence Enhancement (CIE) framework, applicable to various graph neural networks (GNNs). Our approach estimates causal and spurious features at the node representation level and mitigates the influence of spurious correlations through the backdoor adjustment. Meanwhile, independence constraint is introduced to improve the discriminability and stability of causal and spurious features in complex biased environments. Essentially, CIE eliminates different types of data biases from a unified perspective, without the need to design separate methods for each bias as before. To evaluate the performance under specific types of data biases, mixed biases, and low-resource scenarios, we conducted comprehensive experiments on five publicly available datasets. Experimental results demonstrate that our approach CIE not only significantly enhances the performance of GNNs but outperforms state-of-the-art debiased node classification methods.
The celebrated message-passing updates for graph neural networks allow representing large-scale graphs with local and computationally tractable updates. However, the updates suffer from backtracking, i.e., a message flowing through the same edge twice and revisiting the previously visited node. Since the number of message flows increases exponentially with the number of updates, the redundancy in local updates prevents the graph neural network from accurately recognizing a particular message flow relevant for downstream tasks. In this work, we propose to resolve such a redundancy issue via the non-backtracking graph neural network (NBA-GNN) that updates a message without incorporating the message from the previously visited node. We theoretically investigate how NBA-GNN alleviates the over-squashing of GNNs, and establish a connection between NBA-GNN and the impressive performance of non-backtracking updates for stochastic block model recovery. Furthermore, we empirically verify the effectiveness of our NBA-GNN on the long-range graph benchmark and transductive node classification problems.
We revisit recent spectral GNN approaches to semi-supervised node classification (SSNC). We posit that state-of-the-art (SOTA) GNN architectures may be over-engineered for common SSNC benchmark datasets (citation networks, page-page networks, etc.). By replacing feature aggregation with a non-parametric learner we are able to streamline the GNN design process and avoid many of the engineering complexities associated with SOTA hyperparameter selection (GNN depth, non-linearity choice, feature dropout probability, etc.). Our empirical experiments suggest conventional methods such as non-parametric regression are well suited for semi-supervised learning on sparse, directed networks and a variety of other graph types commonly found in SSNC benchmarks. Additionally, we bring attention to recent changes in evaluation conventions for SSNC benchmarking and how this may have partially contributed to rising performances over time.
In recent years, there have been remarkable advancements in node classification achieved by Graph Neural Networks (GNNs). However, they necessitate abundant high-quality labels to ensure promising performance. In contrast, Large Language Models (LLMs) exhibit impressive zero-shot proficiency on text-attributed graphs. Yet, they face challenges in efficiently processing structural data and suffer from high inference costs. In light of these observations, this work introduces a label-free node classification on graphs with LLMs pipeline, LLM-GNN. It amalgamates the strengths of both GNNs and LLMs while mitigating their limitations. Specifically, LLMs are leveraged to annotate a small portion of nodes and then GNNs are trained on LLMs' annotations to make predictions for the remaining large portion of nodes. The implementation of LLM-GNN faces a unique challenge: how can we actively select nodes for LLMs to annotate and consequently enhance the GNN training? How can we leverage LLMs to obtain annotations of high quality, representativeness, and diversity, thereby enhancing GNN performance with less cost? To tackle this challenge, we develop an annotation quality heuristic and leverage the confidence scores derived from LLMs to advanced node selection. Comprehensive experimental results validate the effectiveness of LLM-GNN. In particular, LLM-GNN can achieve an accuracy of 74.9% on a vast-scale dataset \products with a cost less than 1 dollar.
Graph neural networks (GNNs) learn to represent nodes by aggregating information from their neighbors. As GNNs increase in depth, their receptive field grows exponentially, leading to high memory costs. Several existing methods address this by sampling a small subset of nodes, scaling GNNs to much larger graphs. These methods are primarily evaluated on homophilous graphs, where neighboring nodes often share the same label. However, most of these methods rely on static heuristics that may not generalize across different graphs or tasks. We argue that the sampling method should be adaptive, adjusting to the complex structural properties of each graph. To this end, we introduce GRAPES, an adaptive sampling method that learns to identify the set of nodes crucial for training a GNN. GRAPES trains a second GNN to predict node sampling probabilities by optimizing the downstream task objective. We evaluate GRAPES on various node classification benchmarks, involving homophilous as well as heterophilous graphs. We demonstrate GRAPES' effectiveness in accuracy and scalability, particularly in multi-label heterophilous graphs. Unlike other sampling methods, GRAPES maintains high accuracy even with smaller sample sizes and, therefore, can scale to massive graphs. Our code is publicly available at https://github.com/dfdazac/grapes.
Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.
Hyperbolic graph convolutional networks (HGCNs) have demonstrated significant potential in extracting information from hierarchical graphs. However, existing HGCNs are limited to shallow architectures due to the computational expense of hyperbolic operations and the issue of over-smoothing as depth increases. Although treatments have been applied to alleviate over-smoothing in GCNs, developing a hyperbolic solution presents distinct challenges since operations must be carefully designed to fit the hyperbolic nature. Addressing these challenges, we propose DeepHGCN, the first deep multi-layer HGCN architecture with dramatically improved computational efficiency and substantially reduced over-smoothing. DeepHGCN features two key innovations: (1) a novel hyperbolic feature transformation layer that enables fast and accurate linear mappings, and (2) techniques such as hyperbolic residual connections and regularization for both weights and features, facilitated by an efficient hyperbolic midpoint method. Extensive experiments demonstrate that DeepHGCN achieves significant improvements in link prediction and node classification tasks compared to both Euclidean and shallow hyperbolic GCN variants.
Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions, optimised with custom-tailored search algorithms, but often without leveraging recent advances in deep learning. Recently, first works have started incorporating such objectives into loss functions for deep graph clustering and pooling. We consider the map equation, a popular information-theoretic objective function for unsupervised community detection, and express it in differentiable tensor form for optimisation through gradient descent. Our formulation turns the map equation compatible with any neural network architecture, enables end-to-end learning, incorporates node features, and chooses the optimal number of clusters automatically, all without requiring explicit regularisation. Applied to unsupervised graph clustering tasks, we achieve competitive performance against state-of-the-art deep graph clustering baselines in synthetic and real-world datasets.
Models with similar performances exhibit significant disagreement in the predictions of individual samples, referred to as prediction churn. Our work explores this phenomenon in graph neural networks by investigating differences between models differing only in their initializations in their utilized features for predictions. We propose a novel metric called Influence Difference (ID) to quantify the variation in reasons used by nodes across models by comparing their influence distribution. Additionally, we consider the differences between nodes with a stable and an unstable prediction, positing that both equally utilize different reasons and thus provide a meaningful gradient signal to closely match two models even when the predictions for nodes are similar. Based on our analysis, we propose to minimize this ID in Knowledge Distillation, a domain where a new model should closely match an established one. As an efficient approximation, we introduce DropDistillation (DD) that matches the output for a graph perturbed by edge deletions. Our empirical evaluation of six benchmark datasets for node classification validates the differences in utilized features. DD outperforms previous methods regarding prediction stability and overall performance in all considered Knowledge Distillation experiments.
Large language models (LLMs) are gaining increasing attention for their capability to process graphs with rich text attributes, especially in a zero-shot fashion. Recent studies demonstrate that LLMs obtain decent text classification performance on common text-rich graph benchmarks, and the performance can be improved by appending encoded structural information as natural languages into prompts. We aim to understand why the incorporation of structural information inherent in graph data can improve the prediction performance of LLMs. First, we rule out the concern of data leakage by curating a novel leakage-free dataset and conducting a comparative analysis alongside a previously widely-used dataset. Second, as past work usually encodes the ego-graph by describing the graph structure in natural language, we ask the question: do LLMs understand the graph structure in accordance with the intent of the prompt designers? Third, we investigate why LLMs can improve their performance after incorporating structural information. Our exploration of these questions reveals that (i) there is no substantial evidence that the performance of LLMs is significantly attributed to data leakage; (ii) instead of understanding prompts as graph structures as intended by the prompt designers, LLMs tend to process prompts more as contextual paragraphs and (iii) the most efficient elements of the local neighborhood included in the prompt are phrases that are pertinent to the node label, rather than the graph structure.
Graph-based semi-supervised learning (GSSL) has long been a hot research topic. Traditional methods are generally shallow learners, based on the cluster assumption. Recently, graph convolutional networks (GCNs) have become the predominant techniques for their promising performance. In this paper, we theoretically discuss the relationship between these two types of methods in a unified optimization framework. One of the most intriguing findings is that, unlike traditional ones, typical GCNs may not jointly consider the graph structure and label information at each layer. Motivated by this, we further propose three simple but powerful graph convolution methods. The first is a supervised method OGC which guides the graph convolution process with labels. The others are two unsupervised methods: GGC and its multi-scale version GGCM, both aiming to preserve the graph structure information during the convolution process. Finally, we conduct extensive experiments to show the effectiveness of our methods.
Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs. Codes and datasets are available at https://github.com/Yiminghh/HiGCN.
Classifying research output into context-specific label taxonomies is a challenging and relevant downstream task, given the volume of existing and newly published articles. We propose a method to enhance the performance of article classification by enriching simple Graph Neural Network (GNN) pipelines with multi-graph representations that simultaneously encode multiple signals of article relatedness, e.g. references, co-authorship, shared publication source, shared subject headings, as distinct edge types. Fully supervised transductive node classification experiments are conducted on the Open Graph Benchmark OGBN-arXiv dataset and the PubMed diabetes dataset, augmented with additional metadata from Microsoft Academic Graph and PubMed Central, respectively. The results demonstrate that multi-graphs consistently improve the performance of a variety of GNN models compared to the default graphs. When deployed with SOTA textual node embedding methods, the transformed multi-graphs enable simple and shallow 2-layer GNN pipelines to achieve results on par with more complex architectures.
Graph Neural Networks (GNNs) have become popular in Graph Representation Learning (GRL). One fundamental application is few-shot node classification. Most existing methods follow the meta learning paradigm, showing the ability of fast generalization to few-shot tasks. However, recent works indicate that graph contrastive learning combined with fine-tuning can significantly outperform meta learning methods. Despite the empirical success, there is limited understanding of the reasons behind it. In our study, we first identify two crucial advantages of contrastive learning compared to meta learning, including (1) the comprehensive utilization of graph nodes and (2) the power of graph augmentations. To integrate the strength of both contrastive learning and meta learning on the few-shot node classification tasks, we introduce a new paradigm: Contrastive Few-Shot Node Classification (COLA). Specifically, COLA employs graph augmentations to identify semantically similar nodes, which enables the construction of meta-tasks without the need for label information. Therefore, COLA can utilize all nodes to construct meta-tasks, further reducing the risk of overfitting. Through extensive experiments, we validate the essentiality of each component in our design and demonstrate that COLA achieves new state-of-the-art on all tasks.
Label scarcity in a graph is frequently encountered in real-world applications due to the high cost of data labeling. To this end, semi-supervised domain adaptation (SSDA) on graphs aims to leverage the knowledge of a labeled source graph to aid in node classification on a target graph with limited labels. SSDA tasks need to overcome the domain gap between the source and target graphs. However, to date, this challenging research problem has yet to be formally considered by the existing approaches designed for cross-graph node classification. This paper proposes a novel method called SemiGCL to tackle the graph \textbf{Semi}-supervised domain adaptation with \textbf{G}raph \textbf{C}ontrastive \textbf{L}earning and minimax entropy training. SemiGCL generates informative node representations by contrasting the representations learned from a graph's local and global views. Additionally, SemiGCL is adversarially optimized with the entropy loss of unlabeled target nodes to reduce domain divergence. Experimental results on benchmark datasets demonstrate that SemiGCL outperforms the state-of-the-art baselines on the SSDA tasks. The source codes of SemiGCL are publicly available at https://github.com/ JiarenX/SemiGCL.