Graph signal processing (GSP) generalizes signal processing (SP) tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph. Graphs are versatile, able to model irregular interactions, easy to interpret, and endowed with a corpus of mathematical results, rendering them natural candidates to serve as the basis for a theory of processing signals in more irregular domains. In this article, we provide an overview of the evolution of GSP, from its origins to the challenges ahead. The first half is devoted to reviewing the history of GSP and explaining how it gave rise to an encompassing framework that shares multiple similarities with SP. A key message is that GSP has been critical to develop novel and technically sound tools, theory, and algorithms that, by leveraging analogies with and the insights of digital SP, provide new ways to analyze, process, and learn from graph signals. In the second half, we shift focus to review the impact of GSP on other disciplines. First, we look at the use of GSP in data science problems, including graph learning and graph-based deep learning. Second, we discuss the impact of GSP on applications, including neuroscience and image and video processing. We conclude with a brief discussion of the emerging and future directions of GSP.
The prompt estimation of traffic incident impacts can guide commuters in their trip planning and improve the resilience of transportation agencies' decision-making on resilience. However, it is more challenging than node-level and graph-level forecasting tasks, as it requires extracting the anomaly subgraph or sub-time-series from dynamic graphs. In this paper, we propose DG-Trans, a novel traffic incident impact prediction framework, to foresee the impact of traffic incidents through dynamic graph learning. The proposed framework contains a dual-level spatial transformer and an importance-score-based temporal transformer, and the performance of this framework is justified by two newly constructed benchmark datasets. The dual-level spatial transformer removes unnecessary edges between nodes to isolate the affected subgraph from the other nodes. Meanwhile, the importance-score-based temporal transformer identifies abnormal changes in node features, causing the predictions to rely more on measurement changes after the incident occurs. Therefore, DG-Trans is equipped with dual abilities that extract spatiotemporal dependency and identify anomaly nodes affected by incidents while removing noise introduced by benign nodes. Extensive experiments on real-world datasets verify that DG-Trans outperforms the existing state-of-the-art methods, especially in extracting spatiotemporal dependency patterns and predicting traffic accident impacts. It offers promising potential for traffic incident management systems.
Dynamic graphs arise in various real-world applications, and it is often welcomed to model the dynamics directly in continuous time domain for its flexibility. This paper aims to design an easy-to-use pipeline (termed as EasyDGL which is also due to its implementation by DGL toolkit) composed of three key modules with both strong fitting ability and interpretability. Specifically the proposed pipeline which involves encoding, training and interpreting: i) a temporal point process (TPP) modulated attention architecture to endow the continuous-time resolution with the coupled spatiotemporal dynamics of the observed graph with edge-addition events; ii) a principled loss composed of task-agnostic TPP posterior maximization based on observed events on the graph, and a task-aware loss with a masking strategy over dynamic graph, where the covered tasks include dynamic link prediction, dynamic node classification and node traffic forecasting; iii) interpretation of the model outputs (e.g., representations and predictions) with scalable perturbation-based quantitative analysis in the graph Fourier domain, which could more comprehensively reflect the behavior of the learned model. Extensive experimental results on public benchmarks show the superior performance of our EasyDGL for time-conditioned predictive tasks, and in particular demonstrate that EasyDGL can effectively quantify the predictive power of frequency content that a model learn from the evolving graph data.
Personalized recommender systems have been widely studied and deployed to reduce information overload and satisfy users' diverse needs. However, conventional recommendation models solely conduct a one-time training-test fashion and can hardly adapt to evolving demands, considering user preference shifts and ever-increasing users and items in the real world. To tackle such challenges, the streaming recommendation is proposed and has attracted great attention recently. Among these, continual graph learning is widely regarded as a promising approach for the streaming recommendation by academia and industry. However, existing methods either rely on the historical data replay which is often not practical under increasingly strict data regulations, or can seldom solve the \textit{over-stability} issue. To overcome these difficulties, we propose a novel \textbf{D}ynamically \textbf{E}xpandable \textbf{G}raph \textbf{C}onvolution (DEGC) algorithm from a \textit{model isolation} perspective for the streaming recommendation which is orthogonal to previous methods. Based on the motivation of disentangling outdated short-term preferences from useful long-term preferences, we design a sequence of operations including graph convolution pruning, refining, and expanding to only preserve beneficial long-term preference-related parameters and extract fresh short-term preferences. Moreover, we model the temporal user preference, which is utilized as user embedding initialization, for better capturing the individual-level preference shifts. Extensive experiments on the three most representative GCN-based recommendation models and four industrial datasets demonstrate the effectiveness and robustness of our method.
Node features of graph neural networks (GNNs) tend to become more similar with the increase of the network depth. This effect is known as over-smoothing, which we axiomatically define as the exponential convergence of suitable similarity measures on the node features. Our definition unifies previous approaches and gives rise to new quantitative measures of over-smoothing. Moreover, we empirically demonstrate this behavior for several over-smoothing measures on different graphs (small-, medium-, and large-scale). We also review several approaches for mitigating over-smoothing and empirically test their effectiveness on real-world graph datasets. Through illustrative examples, we demonstrate that mitigating over-smoothing is a necessary but not sufficient condition for building deep GNNs that are expressive on a wide range of graph learning tasks. Finally, we extend our definition of over-smoothing to the rapidly emerging field of continuous-time GNNs.
We investigate the enhancement of graph neural networks' (GNNs) representation power through their ability in substructure counting. Recent advances have seen the adoption of subgraph GNNs, which partition an input graph into numerous subgraphs, subsequently applying GNNs to each to augment the graph's overall representation. Despite their ability to identify various substructures, subgraph GNNs are hindered by significant computational and memory costs. In this paper, we tackle a critical question: Is it possible for GNNs to count substructures both \textbf{efficiently} and \textbf{provably}? Our approach begins with a theoretical demonstration that the distance to rooted nodes in subgraphs is key to boosting the counting power of subgraph GNNs. To avoid the need for repetitively applying GNN across all subgraphs, we introduce precomputed structural embeddings that encapsulate this crucial distance information. Experiments validate that our proposed model retains the counting power of subgraph GNNs while achieving significantly faster performance.
This paper presents our Facial Action Units (AUs) detection submission to the fifth Affective Behavior Analysis in-the-wild Competition (ABAW). Our approach consists of three main modules: (i) a pre-trained facial representation encoder which produce a strong facial representation from each input face image in the input sequence; (ii) an AU-specific feature generator that specifically learns a set of AU features from each facial representation; and (iii) a spatio-temporal graph learning module that constructs a spatio-temporal graph representation. This graph representation describes AUs contained in all frames and predicts the occurrence of each AU based on both the modeled spatial information within the corresponding face and the learned temporal dynamics among frames. The experimental results show that our approach outperformed the baseline and the spatio-temporal graph representation learning allows our model to generate the best results among all ablated systems. Our model ranks at the 4th place in the AU recognition track at the 5th ABAW Competition. Our code is publicly available at https://github.com/wzh125/ABAW-5.
In this paper, we explore the topic of graph learning from the perspective of the Irregularity-Aware Graph Fourier Transform, with the goal of learning the graph signal space inner product to better model data. We propose a novel method to learn a graph with smaller edge weight upper bounds compared to combinatorial Laplacian approaches. Experimentally, our approach yields much sparser graphs compared to a combinatorial Laplacian approach, with a more interpretable model.
Graphs have become pervasive tools to represent information and datasets with irregular support. However, in many cases, the underlying graph is either unavailable or naively obtained, calling for more advanced methods to its estimation. Indeed, graph topology inference methods that estimate the network structure from a set of signal observations have a long and well established history. By assuming that the observations are both Gaussian and stationary in the sought graph, this paper proposes a new scheme to learn the network from nodal observations. Consideration of graph stationarity overcomes some of the limitations of the classical Graphical Lasso algorithm, which is constrained to a more specific class of graphical models. On the other hand, Gaussianity allows us to regularize the estimation, requiring less samples than in existing graph stationarity-based approaches. While the resultant estimation (optimization) problem is more complex and non-convex, we design an alternating convex approach able to find a stationary solution. Numerical tests with synthetic and real data are presented, and the performance of our approach is compared with existing alternatives.
Shape assembly composes complex shapes geometries by arranging simple part geometries and has wide applications in autonomous robotic assembly and CAD modeling. Existing works focus on geometry reasoning and neglect the actual physical assembly process of matching and fitting joints, which are the contact surfaces connecting different parts. In this paper, we consider contacting joints for the task of multi-part assembly. A successful joint-optimized assembly needs to satisfy the bilateral objectives of shape structure and joint alignment. We propose a hierarchical graph learning approach composed of two levels of graph representation learning. The part graph takes part geometries as input to build the desired shape structure. The joint-level graph uses part joints information and focuses on matching and aligning joints. The two kinds of information are combined to achieve the bilateral objectives. Extensive experiments demonstrate that our method outperforms previous methods, achieving better shape structure and higher joint alignment accuracy.
Graph transformers have emerged as a promising architecture for a variety of graph learning and representation tasks. Despite their successes, though, it remains challenging to scale graph transformers to large graphs while maintaining accuracy competitive with message-passing networks. In this paper, we introduce Exphormer, a framework for building powerful and scalable graph transformers. Exphormer consists of a sparse attention mechanism based on two mechanisms: virtual global nodes and expander graphs, whose mathematical characteristics, such as spectral expansion, pseduorandomness, and sparsity, yield graph transformers with complexity only linear in the size of the graph, while allowing us to prove desirable theoretical properties of the resulting transformer models. We show that incorporating Exphormer into the recently-proposed GraphGPS framework produces models with competitive empirical results on a wide variety of graph datasets, including state-of-the-art results on three datasets. We also show that Exphormer can scale to datasets on larger graphs than shown in previous graph transformer architectures. Code can be found at \url{https://github.com/hamed1375/Exphormer}.
Due to its complexity, graph learning-based multi-modal integration and classification is one of the most challenging obstacles for disease prediction. To effectively offset the negative impact between modalities in the process of multi-modal integration and extract heterogeneous information from graphs, we propose a novel method called MMKGL (Multi-modal Multi-Kernel Graph Learning). For the problem of negative impact between modalities, we propose a multi-modal graph embedding module to construct a multi-modal graph. Different from conventional methods that manually construct static graphs for all modalities, each modality generates a separate graph by adaptive learning, where a function graph and a supervision graph are introduced for optimization during the multi-graph fusion embedding process. We then propose a multi-kernel graph learning module to extract heterogeneous information from the multi-modal graph. The information in the multi-modal graph at different levels is aggregated by convolutional kernels with different receptive field sizes, followed by generating a cross-kernel discovery tensor for disease prediction. Our method is evaluated on the benchmark Autism Brain Imaging Data Exchange (ABIDE) dataset and outperforms the state-of-the-art methods. In addition, discriminative brain regions associated with autism are identified by our model, providing guidance for the study of autism pathology.
Most codec designs rely on the mean squared error (MSE) as a fidelity metric in rate-distortion optimization, which allows to choose the optimal parameters in the transform domain but may fail to reflect perceptual quality. Alternative distortion metrics, such as the structural similarity index (SSIM), can be computed only pixel-wise, so they cannot be used directly for transform-domain bit allocation. Recently, the irregularity-aware graph Fourier transform (IAGFT) emerged as a means to include pixel-wise perceptual information in the transform design. This paper extends this idea by also learning a graph (and corresponding transform) for sets of blocks that share similar perceptual characteristics and are observed to differ statistically, leading to different learned graphs. We demonstrate the effectiveness of our method with both SSIM- and saliency-based criteria. We also propose a framework to derive separable transforms, including separable IAGFTs. An empirical evaluation based on the 5th CLIC dataset shows that our approach achieves improvements in terms of MS-SSIM with respect to existing methods.
Heterogeneous graphs provide a compact, efficient, and scalable way to model data involving multiple disparate modalities. This makes modeling audiovisual data using heterogeneous graphs an attractive option. However, graph structure does not appear naturally in audiovisual data. Graphs for audiovisual data are constructed manually which is both difficult and sub-optimal. In this work, we address this problem by (i) proposing a parametric graph construction strategy for the intra-modal edges, and (ii) learning the crossmodal edges. To this end, we develop a new model, heterogeneous graph crossmodal network (HGCN) that learns the crossmodal edges. Our proposed model can adapt to various spatial and temporal scales owing to its parametric construction, while the learnable crossmodal edges effectively connect the relevant nodes across modalities. Experiments on a large benchmark dataset (AudioSet) show that our model is state-of-the-art (0.53 mean average precision), outperforming transformer-based models and other graph-based models.
In the semi-supervised setting where labeled data are largely limited, it remains to be a big challenge for message passing based graph neural networks (GNNs) to learn feature representations for the nodes with the same class label that is distributed discontinuously over the graph. To resolve the discontinuous information transmission problem, we propose a control principle to supervise representation learning by leveraging the prototypes (i.e., class centers) of labeled data. Treating graph learning as a discrete dynamic process and the prototypes of labeled data as "desired" class representations, we borrow the pinning control idea from automatic control theory to design learning feedback controllers for the feature learning process, attempting to minimize the differences between message passing derived features and the class prototypes in every round so as to generate class-relevant features. Specifically, we equip every node with an optimal controller in each round through learning the matching relationships between nodes and the class prototypes, enabling nodes to rectify the aggregated information from incompatible neighbors in a graph with strong heterophily. Our experiments demonstrate that the proposed PCGCN model achieves better performances than deep GNNs and other competitive heterophily-oriented methods, especially when the graph has very few labels and strong heterophily.
Graph neural networks (GNN) have been widely deployed in real-world networked applications and systems due to their capability to handle graph-structured data. However, the growing awareness of data privacy severely challenges the traditional centralized model training paradigm, where a server holds all the graph information. Federated learning is an emerging collaborative computing paradigm that allows model training without data centralization. Existing federated GNN studies mainly focus on systems where clients hold distinctive graphs or sub-graphs. The practical node-level federated situation, where each client is only aware of its direct neighbors, has yet to be studied. In this paper, we propose the first federated GNN framework called Lumos that supports supervised and unsupervised learning with feature and degree protection on node-level federated graphs. We first design a tree constructor to improve the representation capability given the limited structural information. We further present a Monte Carlo Markov Chain-based algorithm to mitigate the workload imbalance caused by degree heterogeneity with theoretically-guaranteed performance. Based on the constructed tree for each client, a decentralized tree-based GNN trainer is proposed to support versatile training. Extensive experiments demonstrate that Lumos outperforms the baseline with significantly higher accuracy and greatly reduced communication cost and training time.
Cellular traffic prediction is an indispensable part for intelligent telecommunication networks. Nevertheless, due to the frequent user mobility and complex network scheduling mechanisms, cellular traffic often inherits complicated spatial-temporal patterns, making the prediction incredibly challenging. Although recent advanced algorithms such as graph-based prediction approaches have been proposed, they frequently model spatial dependencies based on static or dynamic graphs and neglect the coexisting multiple spatial correlations induced by traffic generation. Meanwhile, some works lack the consideration of the diverse cellular traffic patterns, result in suboptimal prediction results. In this paper, we propose a novel deep learning network architecture, Adaptive Hybrid Spatial-Temporal Graph Neural Network (AHSTGNN), to tackle the cellular traffic prediction problem. First, we apply adaptive hybrid graph learning to learn the compound spatial correlations among cell towers. Second, we implement a Temporal Convolution Module with multi-periodic temporal data input to capture the nonlinear temporal dependencies. In addition, we introduce an extra Spatial-Temporal Adaptive Module to conquer the heterogeneity lying in cell towers. Our experiments on two real-world cellular traffic datasets show AHSTGNN outperforms the state-of-the-art by a significant margin, illustrating the superior scalability of our method for spatial-temporal cellular traffic prediction.
Tackling unfairness in graph learning models is a challenging task, as the unfairness issues on graphs involve both attributes and topological structures. Existing work on fair graph learning simply assumes that attributes of all nodes are available for model training and then makes fair predictions. In practice, however, the attributes of some nodes might not be accessible due to missing data or privacy concerns, which makes fair graph learning even more challenging. In this paper, we propose FairAC, a fair attribute completion method, to complement missing information and learn fair node embeddings for graphs with missing attributes. FairAC adopts an attention mechanism to deal with the attribute missing problem and meanwhile, it mitigates two types of unfairness, i.e., feature unfairness from attributes and topological unfairness due to attribute completion. FairAC can work on various types of homogeneous graphs and generate fair embeddings for them and thus can be applied to most downstream tasks to improve their fairness performance. To our best knowledge, FairAC is the first method that jointly addresses the graph attribution completion and graph unfairness problems. Experimental results on benchmark datasets show that our method achieves better fairness performance with less sacrifice in accuracy, compared with the state-of-the-art methods of fair graph learning. Code is available at: https://github.com/donglgcn/FairAC.
Graph neural architecture search (NAS) has gained popularity in automatically designing powerful graph neural networks (GNNs) with relieving human efforts. However, existing graph NAS methods mainly work under the homophily assumption and overlook another important graph property, i.e., heterophily, which exists widely in various real-world applications. To date, automated heterophilic graph learning with NAS is still a research blank to be filled in. Due to the complexity and variety of heterophilic graphs, the critical challenge of heterophilic graph NAS mainly lies in developing the heterophily-specific search space and strategy. Therefore, in this paper, we propose a novel automated graph neural network on heterophilic graphs, namely Auto-HeG, to automatically build heterophilic GNN models with expressive learning abilities. Specifically, Auto-HeG incorporates heterophily into all stages of automatic heterophilic graph learning, including search space design, supernet training, and architecture selection. Through the diverse message-passing scheme with joint micro-level and macro-level designs, we first build a comprehensive heterophilic GNN search space, enabling Auto-HeG to integrate complex and various heterophily of graphs. With a progressive supernet training strategy, we dynamically shrink the initial search space according to layer-wise variation of heterophily, resulting in a compact and efficient supernet. Taking a heterophily-aware distance criterion as the guidance, we conduct heterophilic architecture selection in the leave-one-out pattern, so that specialized and expressive heterophilic GNN architectures can be derived. Extensive experiments illustrate the superiority of Auto-HeG in developing excellent heterophilic GNNs to human-designed models and graph NAS models.
Recently, much exertion has been paid to design graph self-supervised methods to obtain generalized pre-trained models, and adapt pre-trained models onto downstream tasks through fine-tuning. However, there exists an inherent gap between pretext and downstream graph tasks, which insufficiently exerts the ability of pre-trained models and even leads to negative transfer. Meanwhile, prompt tuning has seen emerging success in natural language processing by aligning pre-training and fine-tuning with consistent training objectives. In this paper, we identify the challenges for graph prompt tuning: The first is the lack of a strong and universal pre-training task across sundry pre-training methods in graph domain. The second challenge lies in the difficulty of designing a consistent training objective for both pre-training and downstream tasks. To overcome above obstacles, we propose a novel framework named SGL-PT which follows the learning strategy ``Pre-train, Prompt, and Predict''. Specifically, we raise a strong and universal pre-training task coined as SGL that acquires the complementary merits of generative and contrastive self-supervised graph learning. And aiming for graph classification task, we unify pre-training and fine-tuning by designing a novel verbalizer-free prompting function, which reformulates the downstream task in a similar format as pretext task. Empirical results show that our method surpasses other baselines under unsupervised setting, and our prompt tuning method can greatly facilitate models on biological datasets over fine-tuning methods.