Federated learning (FL) has rapidly evolved as a promising paradigm that enables collaborative model training across distributed participants without exchanging their local data. Despite its broad applications in fields such as computer vision, graph learning, and natural language processing, the development of a data projection model that can be effectively used to visualize data in the context of FL is crucial yet remains heavily under-explored. Neighbor embedding (NE) is an essential technique for visualizing complex high-dimensional data, but collaboratively learning a joint NE model is difficult. The key challenge lies in the objective function, as effective visualization algorithms like NE require computing loss functions among pairs of data. In this paper, we introduce \textsc{FedNE}, a novel approach that integrates the \textsc{FedAvg} framework with the contrastive NE technique, without any requirements of shareable data. To address the lack of inter-client repulsion which is crucial for the alignment in the global embedding space, we develop a surrogate loss function that each client learns and shares with each other. Additionally, we propose a data-mixing strategy to augment the local data, aiming to relax the problems of invisible neighbors and false neighbors constructed by the local $k$NN graphs. We conduct comprehensive experiments on both synthetic and real-world datasets. The results demonstrate that our \textsc{FedNE} can effectively preserve the neighborhood data structures and enhance the alignment in the global embedding space compared to several baseline methods.
The ability of Graph Neural Networks (GNNs) to capture long-range and global topology information is limited by the scope of conventional graph Laplacian, leading to unsatisfactory performance on some datasets, particularly on heterophilic graphs. To address this limitation, we propose a new class of parameterized Laplacian matrices, which provably offers more flexibility in controlling the diffusion distance between nodes than the conventional graph Laplacian, allowing long-range information to be adaptively captured through diffusion on graph. Specifically, we first prove that the diffusion distance and spectral distance on graph have an order-preserving relationship. With this result, we demonstrate that the parameterized Laplacian can accelerate the diffusion of long-range information, and the parameters in the Laplacian enable flexibility of the diffusion scopes. Based on the theoretical results, we propose topology-guided rewiring mechanism to capture helpful long-range neighborhood information for heterophilic graphs. With this mechanism and the new Laplacian, we propose two GNNs with flexible diffusion scopes: namely the Parameterized Diffusion based Graph Convolutional Networks (PD-GCN) and Graph Attention Networks (PD-GAT). Synthetic experiments reveal the high correlations between the parameters of the new Laplacian and the performance of parameterized GNNs under various graph homophily levels, which verifies that our new proposed GNNs indeed have the ability to adjust the parameters to adaptively capture the global information for different levels of heterophilic graphs. They also outperform the state-of-the-art (SOTA) models on 6 out of 7 real-world benchmark datasets, which further confirms their superiority.
Graph learning is the fundamental task of estimating unknown graph connectivity from available data. Typical approaches assume that not only is all information available simultaneously but also that all nodes can be observed. However, in many real-world scenarios, data can neither be known completely nor obtained all at once. We present a novel method for online graph estimation that accounts for the presence of hidden nodes. We consider signals that are stationary on the underlying graph, which provides a model for the unknown connections to hidden nodes. We then formulate a convex optimization problem for graph learning from streaming, incomplete graph signals. We solve the proposed problem through an efficient proximal gradient algorithm that can run in real-time as data arrives sequentially. Additionally, we provide theoretical conditions under which our online algorithm is similar to batch-wise solutions. Through experimental results on synthetic and real-world data, we demonstrate the viability of our approach for online graph learning in the presence of missing observations.
This paper addresses the problem of online network topology inference for expanding graphs from a stream of spatiotemporal signals. Online algorithms for dynamic graph learning are crucial in delay-sensitive applications or when changes in topology occur rapidly. While existing works focus on inferring the connectivity within a fixed set of nodes, in practice, the graph can grow as new nodes join the network. This poses additional challenges like modeling temporal dynamics involving signals and graphs of different sizes. This growth also increases the computational complexity of the learning process, which may become prohibitive. To the best of our knowledge, this is the first work to tackle this setting. We propose a general online algorithm based on projected proximal gradient descent that accounts for the increasing graph size at each iteration. Recursively updating the sample covariance matrix is a key aspect of our approach. We introduce a strategy that enables different types of updates for nodes that just joined the network and for previously existing nodes. To provide further insights into the proposed method, we specialize it in Gaussian Markov random field settings, where we analyze the computational complexity and characterize the dynamic cumulative regret. Finally, we demonstrate the effectiveness of the proposed approach using both controlled experiments and real-world datasets from epidemic and financial networks.
Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map simply to ones in a similarity-transformed positive graph Laplacian, thus enabling reuse of well-studied spectral filters designed for positive graphs. We propose a fast method to learn a balanced signed graph Laplacian directly from data. Specifically, for each node $i$, to determine its polarity $\beta_i \in \{-1,1\}$ and edge weights $\{w_{i,j}\}_{j=1}^N$, we extend a sparse inverse covariance formulation based on linear programming (LP) called CLIME, by adding linear constraints to enforce ``consistent" signs of edge weights $\{w_{i,j}\}_{j=1}^N$ with the polarities of connected nodes -- i.e., positive/negative edges connect nodes of same/opposing polarities. For each LP, we adapt projections on convex set (POCS) to determine a suitable CLIME parameter $\rho > 0$ that guarantees LP feasibility. We solve the resulting LP via an off-the-shelf LP solver in $\mathcal{O}(N^{2.055})$. Experiments on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables the use of spectral filters and graph convolutional networks (GCNs) designed for positive graphs on signed graphs.
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.
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 contrastive learning (GCL) has been extensively studied and leveraged as a potent tool in recommender systems. Most existing GCL-based recommenders generate contrastive views by altering the graph structure or introducing perturbations to embedding. While these methods effectively enhance learning from sparse data, they risk performance degradation or even training collapse when the differences between contrastive views become too pronounced. To mitigate this issue, we employ curriculum learning to incrementally increase the disparity between contrastive views, enabling the model to gain from more challenging scenarios. In this paper, we propose a dual-adversarial graph learning approach, AvoGCL, which emulates curriculum learning by progressively applying adversarial training to graph structures and embedding perturbations. Specifically, AvoGCL construct contrastive views by reducing graph redundancy and generating adversarial perturbations in the embedding space, and achieve better results by gradually increasing the difficulty of contrastive views. Extensive experiments on three real-world datasets demonstrate that AvoGCL significantly outperforms the state-of-the-art competitors.
Autism Spectrum Disorder (ASD) is a neurodevelopmental disorder characterized by complex physiological processes. Previous research has predominantly focused on static cerebral interactions, often neglecting the brain's dynamic nature and the challenges posed by network noise. To address these gaps, we introduce the Masked Connection-based Dynamic Graph Learning Network (MCDGLN). Our approach first segments BOLD signals using sliding temporal windows to capture dynamic brain characteristics. We then employ a specialized weighted edge aggregation (WEA) module, which uses the cross convolution with channel-wise element-wise convolutional kernel, to integrate dynamic functional connectivity and to isolating task-relevant connections. This is followed by topological feature extraction via a hierarchical graph convolutional network (HGCN), with key attributes highlighted by a self-attention module. Crucially, we refine static functional connections using a customized task-specific mask, reducing noise and pruning irrelevant links. The attention-based connection encoder (ACE) then enhances critical connections and compresses static features. The combined features are subsequently used for classification. Applied to the Autism Brain Imaging Data Exchange I (ABIDE I) dataset, our framework achieves a 73.3\% classification accuracy between ASD and Typical Control (TC) groups among 1,035 subjects. The pivotal roles of WEA and ACE in refining connectivity and enhancing classification accuracy underscore their importance in capturing ASD-specific features, offering new insights into the disorder.
Graph partitioning (GP) is a classic problem that divides the node set of a graph into densely-connected blocks. Following the IEEE HPEC Graph Challenge and recent advances in pre-training techniques (e.g., large-language models), we propose PR-GPT (Pre-trained & Refined Graph ParTitioning) based on a novel pre-training & refinement paradigm. We first conduct the offline pre-training of a deep graph learning (DGL) model on small synthetic graphs with various topology properties. By using the inductive inference of DGL, one can directly generalize the pre-trained model (with frozen model parameters) to large graphs and derive feasible GP results. We also use the derived partition as a good initialization of an efficient GP method (e.g., InfoMap) to further refine the quality of partitioning. In this setting, the online generalization and refinement of PR-GPT can not only benefit from the transfer ability regarding quality but also ensure high inference efficiency without re-training. Based on a mechanism of reducing the scale of a graph to be processed by the refinement method, PR-GPT also has the potential to support streaming GP. Experiments on the Graph Challenge benchmark demonstrate that PR-GPT can ensure faster GP on large-scale graphs without significant quality degradation, compared with running a refinement method from scratch. We will make our code public at https://github.com/KuroginQin/PRGPT.
Graph Contrastive Learning (GCL) is a potent paradigm for self-supervised graph learning that has attracted attention across various application scenarios. However, GCL for learning on Text-Attributed Graphs (TAGs) has yet to be explored. Because conventional augmentation techniques like feature embedding masking cannot directly process textual attributes on TAGs. A naive strategy for applying GCL to TAGs is to encode the textual attributes into feature embeddings via a language model and then feed the embeddings into the following GCL module for processing. Such a strategy faces three key challenges: I) failure to avoid information loss, II) semantic loss during the text encoding phase, and III) implicit augmentation constraints that lead to uncontrollable and incomprehensible results. In this paper, we propose a novel GCL framework named LATEX-GCL to utilize Large Language Models (LLMs) to produce textual augmentations and LLMs' powerful natural language processing (NLP) abilities to address the three limitations aforementioned to pave the way for applying GCL to TAG tasks. Extensive experiments on four high-quality TAG datasets illustrate the superiority of the proposed LATEX-GCL method. The source codes and datasets are released to ease the reproducibility, which can be accessed via this link: https://anonymous.4open.science/r/LATEX-GCL-0712.
Federated graph learning (FGL) is a promising distributed training paradigm for graph neural networks across multiple local systems without direct data sharing. This approach inherently involves large-scale distributed graph processing, which closely aligns with the challenges and research focuses of graph-based data systems. Despite the proliferation of FGL, the diverse motivations from real-world applications, spanning various research backgrounds and settings, pose a significant challenge to fair evaluation. To fill this gap, we propose OpenFGL, a unified benchmark designed for the primary FGL scenarios: Graph-FL and Subgraph-FL. Specifically, OpenFGL includes 42 graph datasets from 18 application domains, 8 federated data simulation strategies that emphasize different graph properties, and 5 graph-based downstream tasks. Additionally, it offers 18 recently proposed SOTA FGL algorithms through a user-friendly API, enabling a thorough comparison and comprehensive evaluation of their effectiveness, robustness, and efficiency. Our empirical results demonstrate the capabilities of FGL while also highlighting its potential limitations, providing valuable insights for future research in this growing field, particularly in fostering greater interdisciplinary collaboration between FGL and data systems.
Recently, generative graph models have shown promising results in learning graph representations through self-supervised methods. However, most existing generative graph representation learning (GRL) approaches rely on random masking across the entire graph, which overlooks the entanglement of learned representations. This oversight results in non-robustness and a lack of explainability. Furthermore, disentangling the learned representations remains a significant challenge and has not been sufficiently explored in GRL research. Based on these insights, this paper introduces DiGGR (Disentangled Generative Graph Representation Learning), a self-supervised learning framework. DiGGR aims to learn latent disentangled factors and utilizes them to guide graph mask modeling, thereby enhancing the disentanglement of learned representations and enabling end-to-end joint learning. Extensive experiments on 11 public datasets for two different graph learning tasks demonstrate that DiGGR consistently outperforms many previous self-supervised methods, verifying the effectiveness of the proposed approach.
Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning. We then propose a new framework Graph invAriant Learning Assistant (GALA). GALA incorporates an assistant model that needs to be sensitive to graph environment changes or distribution shifts. The correctness of the proxy predictions by the assistant model hence can differentiate the variations in spurious subgraphs. We show that extracting the maximally invariant subgraph to the proxy predictions provably identifies the underlying invariant subgraph for successful OOD generalization under the established minimal assumptions. Extensive experiments on datasets including DrugOOD with various graph distribution shifts confirm the effectiveness of GALA.
The household rearrangement task involves spotting misplaced objects in a scene and accommodate them with proper places. It depends both on common-sense knowledge on the objective side and human user preference on the subjective side. In achieving such task, we propose to mine object functionality with user preference alignment directly from the scene itself, without relying on human intervention. To do so, we work with scene graph representation and propose LLM-enhanced scene graph learning which transforms the input scene graph into an affordance-enhanced graph (AEG) with information-enhanced nodes and newly discovered edges (relations). In AEG, the nodes corresponding to the receptacle objects are augmented with context-induced affordance which encodes what kind of carriable objects can be placed on it. New edges are discovered with newly discovered non-local relations. With AEG, we perform task planning for scene rearrangement by detecting misplaced carriables and determining a proper placement for each of them. We test our method by implementing a tiding robot in simulator and perform evaluation on a new benchmark we build. Extensive evaluations demonstrate that our method achieves state-of-the-art performance on misplacement detection and the following rearrangement planning.
In this paper, the causal bandit problem is investigated, in which the objective is to select an optimal sequence of interventions on nodes in a causal graph. It is assumed that the graph is governed by linear structural equations; it is further assumed that both the causal topology and the distribution of interventions are unknown. By exploiting the causal relationships between the nodes whose signals contribute to the reward, interventions are optimized. First, based on the difference between the two types of graph identification errors (false positives and negatives), a causal graph learning method is proposed, which strongly reduces sample complexity relative to the prior art by learning sub-graphs. Under the assumption of Gaussian exogenous inputs and minimum-mean squared error weight estimation, a new uncertainty bound tailored to the causal bandit problem is derived. This uncertainty bound drives an upper confidence bound based intervention selection to optimize the reward. To cope with non-stationary bandits, a sub-graph change detection mechanism is proposed, with high sample efficiency. Numerical results compare the new methodology to existing schemes and show a substantial performance improvement in both stationary and non-stationary settings. Compared to existing approaches, the proposed scheme takes 67% fewer samples to learn the causal structure and achieves an average reward gain of 85%.
Federated Graph Learning (FGL) is an emerging technology that enables clients to collaboratively train powerful Graph Neural Networks (GNNs) in a distributed manner without exposing their private data. Nevertheless, FGL still faces the challenge of the severe non-Independent and Identically Distributed (non-IID) nature of graphs, which possess diverse node and edge structures, especially across varied domains. Thus, exploring the knowledge inherent in these structures becomes significantly crucial. Existing methods, however, either overlook the inherent structural knowledge in graph data or capture it at the cost of significantly increased resource demands (e.g., FLOPs and communication bandwidth), which can be detrimental to distributed paradigms. Inspired by this, we propose FedDense, a novel FGL framework that optimizes the utilization efficiency of inherent structural knowledge. To better acquire knowledge of diverse and underexploited structures, FedDense first explicitly encodes the structural knowledge inherent within graph data itself alongside node features. Besides, FedDense introduces a Dual-Densely Connected (DDC) GNN architecture that exploits the multi-scale (i.e., one-hop to multi-hop) feature and structure insights embedded in the aggregated feature maps at each layer. In addition to the exploitation of inherent structures, we consider resource limitations in FGL, devising exceedingly narrow layers atop the DDC architecture and adopting a selective parameter sharing strategy to reduce resource costs substantially. We conduct extensive experiments using 15 datasets across 4 different domains, demonstrating that FedDense consistently surpasses baselines by a large margin in training performance, while demanding minimal resources.
As graphs grow larger, full-batch GNN training becomes hard for single GPU memory. Therefore, to enhance the scalability of GNN training, some studies have proposed sampling-based mini-batch training and distributed graph learning. However, these methods still have drawbacks, such as performance degradation and heavy communication. This paper introduces SliceGCN, a feature-sliced distributed large-scale graph learning method. SliceGCN slices the node features, with each computing device, i.e., GPU, handling partial features. After each GPU processes its share, partial representations are obtained and concatenated to form complete representations, enabling a single GPU's memory to handle the entire graph structure. This aims to avoid the accuracy loss typically associated with mini-batch training (due to incomplete graph structures) and to reduce inter-GPU communication during message passing (the forward propagation process of GNNs). To study and mitigate potential accuracy reductions due to slicing features, this paper proposes feature fusion and slice encoding. Experiments were conducted on six node classification datasets, yielding some interesting analytical results. These results indicate that while SliceGCN does not enhance efficiency on smaller datasets, it does improve efficiency on larger datasets. Additionally, we found that SliceGCN and its variants have better convergence, feature fusion and slice encoding can make training more stable, reduce accuracy fluctuations, and this study also discovered that the design of SliceGCN has a potentially parameter-efficient nature.
The growing ubiquity of relational data structured as graphs has underscored the need for graph learning models with exceptional generalization capabilities. However, current approaches often struggle to effectively extract generalizable insights, frequently requiring extensive fine-tuning and limiting their versatility. Graph foundation models offer a transformative solution, with the potential to learn robust, generalizable representations from graph data. This enables more effective and adaptable applications across a wide spectrum of tasks and domains. In this work, we investigate a unified graph model, AnyGraph, designed to handle key challenges: i) Structure Heterogenity. Addressing distribution shift in graph structural information; ii) Feature Heterogenity. Handling diverse feature representation spaces across graph datasets; iii) Fast Adaptation. Efficiently adapting the model to new graph domains; iv) Scaling Law Emergence. Enabling the model to exhibit scaling law behavior, where its performance scales favorably with the amount of data and parameter sizes. To tackle these critical challenges, we build the AnyGraph upon a Graph Mixture-of-Experts (MoE) architecture. This approach empowers the model to effectively manage both the in-domain and cross-domain distribution shift concerning structure-level and feature-level heterogeneity. Furthermore, a lightweight graph expert routing mechanism is proposed to facilitate AnyGraph's fast adaptability to new data and domains. Our extensive experiments on diverse 38 graph datasets have demonstrated the strong zero-shot learning performance of AnyGraph across diverse graph domains with significant distribution shift. Furthermore, we have validated the model's fast adaptation ability and scaling law emergence, showcasing its versatility.
Federated Graph Learning (FGL) aims to learn graph learning models over graph data distributed in multiple data owners, which has been applied in various applications such as social recommendation and financial fraud detection. Inherited from generic Federated Learning (FL), FGL similarly has the data heterogeneity issue where the label distribution may vary significantly for distributed graph data across clients. For instance, a client can have the majority of nodes from a class, while another client may have only a few nodes from the same class. This issue results in divergent local objectives and impairs FGL convergence for node-level tasks, especially for node classification. Moreover, FGL also encounters a unique challenge for the node classification task: the nodes from a minority class in a client are more likely to have biased neighboring information, which prevents FGL from learning expressive node embeddings with Graph Neural Networks (GNNs). To grapple with the challenge, we propose FedSpray, a novel FGL framework that learns local class-wise structure proxies in the latent space and aligns them to obtain global structure proxies in the server. Our goal is to obtain the aligned structure proxies that can serve as reliable, unbiased neighboring information for node classification. To achieve this, FedSpray trains a global feature-structure encoder and generates unbiased soft targets with structure proxies to regularize local training of GNN models in a personalized way. We conduct extensive experiments over four datasets, and experiment results validate the superiority of FedSpray compared with other baselines. Our code is available at https://github.com/xbfu/FedSpray.