Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by learning the problem-specific solution structure. However, reproducing the results of these publications proves to be difficult. We make three contributions. First, we present an open-source benchmark suite for the NP-hard Maximum Independent Set problem, in both its weighted and unweighted variants. The suite offers a unified interface to various state-of-the-art traditional and machine learning-based solvers. Second, using our benchmark suite, we conduct an in-depth analysis of the popular guided tree search algorithm by Li et al. [NeurIPS 2018], testing various configurations on small and large synthetic and real-world graphs. By re-implementing their algorithm with a focus on code quality and extensibility, we show that the graph convolution network used in the tree search does not learn a meaningful representation of the solution structure, and can in fact be replaced by random values. Instead, the tree search relies on algorithmic techniques like graph kernelization to find good solutions. Thus, the results from the original publication are not reproducible. Third, we extend the analysis to compare the tree search implementations to other solvers, showing that the classical algorithmic solvers often are faster, while providing solutions of similar quality. Additionally, we analyze a recent solver based on reinforcement learning and observe that for this solver, the GNN is responsible for the competitive solution quality.
Power estimation is the basis of many hardware optimization strategies. However, it is still challenging to offer accurate power estimation at an early stage such as high-level synthesis (HLS). In this paper, we propose PowerGear, a graph-learning-assisted power estimation approach for FPGA HLS, which features high accuracy, efficiency and transferability. PowerGear comprises two main components: a graph construction flow and a customized graph neural network (GNN) model. Specifically, in the graph construction flow, we introduce buffer insertion, datapath merging, graph trimming and feature annotation techniques to transform HLS designs into graph-structured data, which encode both intra-operation micro-architectures and inter-operation interconnects annotated with switching activities. Furthermore, we propose a novel power-aware heterogeneous edge-centric GNN model which effectively learns heterogeneous edge semantics and structural properties of the constructed graphs via edge-centric neighborhood aggregation, and fits the formulation of dynamic power. Compared with on-board measurement, PowerGear estimates total and dynamic power for new HLS designs with errors of 3.60% and 8.81%, respectively, which outperforms the prior arts in research and the commercial product Vivado. In addition, PowerGear demonstrates a speedup of 4x over Vivado power estimator. Finally, we present a case study in which PowerGear is exploited to facilitate design space exploration for FPGA HLS, leading to a performance gain of up to 11.2%, compared with methods using state-of-the-art predictive models.
Accurate forecasting of multivariate time series is an extensively studied subject in finance, transportation, and computer science. Fully mining the correlation and causation between the variables in a multivariate time series exhibits noticeable results in improving the performance of a time series model. Recently, some models have explored the dependencies between variables through end-to-end graph structure learning without the need for predefined graphs. However, current models do not incorporate the trade-off between efficiency and flexibility and lack the guidance of domain knowledge in the design of graph structure learning algorithms. This paper alleviates the above issues by proposing Balanced Graph Structure Learning for Forecasting (BGSLF), a novel deep learning model that joins graph structure learning and forecasting. Technically, BGSLF leverages the spatial information into convolutional operations and extracts temporal dynamics using the diffusion convolutional recurrent network. The proposed framework balance the trade-off between efficiency and flexibility by introducing Multi-Graph Generation Network (MGN) and Graph Selection Module. In addition, a method named Smooth Sparse Unit (SSU) is designed to sparse the learned graph structures, which conforms to the sparse spatial correlations in the real world. Extensive experiments on four real-world datasets demonstrate that our model achieves state-of-the-art performances with minor trainable parameters. Code will be made publicly available.
Many real-world networks are inherently decentralized. For example, in social networks, each user maintains a local view of a social graph, such as a list of friends and her profile. It is typical to collect these local views of social graphs and conduct graph learning tasks. However, learning over graphs can raise privacy concerns as these local views often contain sensitive information. In this paper, we seek to ensure private graph learning on a decentralized network graph. Towards this objective, we propose {\em Solitude}, a new privacy-preserving learning framework based on graph neural networks (GNNs), with formal privacy guarantees based on edge local differential privacy. The crux of {\em Solitude} is a set of new delicate mechanisms that can calibrate the introduced noise in the decentralized graph collected from the users. The principle behind the calibration is the intrinsic properties shared by many real-world graphs, such as sparsity. Unlike existing work on locally private GNNs, our new framework can simultaneously protect node feature privacy and edge privacy, and can seamlessly incorporate with any GNN with privacy-utility guarantees. Extensive experiments on benchmarking datasets show that {\em Solitude} can retain the generalization capability of the learned GNN while preserving the users' data privacy under given privacy budgets.
Weather Forecasting is an attractive challengeable task due to its influence on human life and complexity in atmospheric motion. Supported by massive historical observed time series data, the task is suitable for data-driven approaches, especially deep neural networks. Recently, the Graph Neural Networks (GNNs) based methods have achieved excellent performance for spatio-temporal forecasting. However, the canonical GNNs-based methods only individually model the local graph of meteorological variables per station or the global graph of whole stations, lacking information interaction between meteorological variables in different stations. In this paper, we propose a novel Hierarchical Spatio-Temporal Graph Neural Network (HiSTGNN) to model cross-regional spatio-temporal correlations among meteorological variables in multiple stations. An adaptive graph learning layer and spatial graph convolution are employed to construct self-learning graph and study hidden dependency among nodes of variable-level and station-level graph. For capturing temporal pattern, the dilated inception as the backbone of gate temporal convolution is designed to model long and various meteorological trends. Moreover, a dynamic interaction learning is proposed to build bidirectional information passing in hierarchical graph. Experimental results on three real-world meteorological datasets demonstrate the superior performance of HiSTGNN beyond 7 baselines and it reduces the errors by 4.2% to 11.6% especially compared to state-of-the-art weather forecasting method.
Recent studies have revealed that GNNs are vulnerable to adversarial attacks. Most existing robust graph learning methods measure model robustness based on label information, rendering them infeasible when label information is not available. A straightforward direction is to employ the widely used Infomax technique from typical Unsupervised Graph Representation Learning (UGRL) to learn robust unsupervised representations. Nonetheless, directly transplanting the Infomax technique from typical UGRL to robust UGRL may involve a biased assumption. In light of the limitation of Infomax, we propose a novel unbiased robust UGRL method called Robust Graph Information Bottleneck (RGIB), which is grounded in the Information Bottleneck (IB) principle. Our RGIB attempts to learn robust node representations against adversarial perturbations by preserving the original information in the benign graph while eliminating the adversarial information in the adversarial graph. There are mainly two challenges to optimize RGIB: 1) high complexity of adversarial attack to perturb node features and graph structure jointly in the training procedure; 2) mutual information estimation upon adversarially attacked graphs. To tackle these problems, we further propose an efficient adversarial training strategy with only feature perturbations and an effective mutual information estimator with subgraph-level summary. Moreover, we theoretically establish a connection between our proposed RGIB and the robustness of downstream classifiers, revealing that RGIB can provide a lower bound on the adversarial risk of downstream classifiers. Extensive experiments over several benchmarks and downstream tasks demonstrate the effectiveness and superiority of our proposed method.
Because of its wide application, critical nodes identification has become an important research topic at the micro level of network science. Influence maximization is one of the main problems in critical nodes mining and is usually handled with heuristics. In this paper, a deep graph learning framework IMGNN is proposed and the corresponding training sample generation scheme is designed. The framework takes centralities of nodes in a network as input and the probability that nodes in the optimal initial spreaders as output. By training on a large number of small synthetic networks, IMGNN is more efficient than human-based heuristics in minimizing the size of initial spreaders under the fixed infection scale. The experimental results on one synthetic and five real networks show that, compared with traditional non-iterative node ranking algorithms, IMGNN has the smallest proportion of initial spreaders under different infection probabilities when the final infection scale is fixed. And the reordered version of IMGNN outperforms all the latest critical nodes mining algorithms.
Unsupervised graph representation learning has emerged as a powerful tool to address real-world problems and achieves huge success in the graph learning domain. Graph contrastive learning is one of the unsupervised graph representation learning methods, which recently attracts attention from researchers and has achieved state-of-the-art performances on various tasks. The key to the success of graph contrastive learning is to construct proper contrasting pairs to acquire the underlying structural semantics of the graph. However, this key part is not fully explored currently, most of the ways generating contrasting pairs focus on augmenting or perturbating graph structures to obtain different views of the input graph. But such strategies could degrade the performances via adding noise into the graph, which may narrow down the field of the applications of graph contrastive learning. In this paper, we propose a novel graph contrastive learning method, namely \textbf{D}ual \textbf{S}pace \textbf{G}raph \textbf{C}ontrastive (DSGC) Learning, to conduct graph contrastive learning among views generated in different spaces including the hyperbolic space and the Euclidean space. Since both spaces have their own advantages to represent graph data in the embedding spaces, we hope to utilize graph contrastive learning to bridge the spaces and leverage advantages from both sides. The comparison experiment results show that DSGC achieves competitive or better performances among all the datasets. In addition, we conduct extensive experiments to analyze the impact of different graph encoders on DSGC, giving insights about how to better leverage the advantages of contrastive learning between different spaces.
Quantum machine learning is a fast-emerging field that aims to tackle machine learning using quantum algorithms and quantum computing. Due to the lack of physical qubits and an effective means to map real-world data from Euclidean space to Hilbert space, most of these methods focus on quantum analogies or process simulations rather than devising concrete architectures based on qubits. In this paper, we propose a novel hybrid quantum-classical algorithm for graph-structured data, which we refer to as the Ego-graph based Quantum Graph Neural Network (egoQGNN). egoQGNN implements the GNN theoretical framework using the tensor product and unity matrix representation, which greatly reduces the number of model parameters required. When controlled by a classical computer, egoQGNN can accommodate arbitrarily sized graphs by processing ego-graphs from the input graph using a modestly-sized quantum device. The architecture is based on a novel mapping from real-world data to Hilbert space. This mapping maintains the distance relations present in the data and reduces information loss. Experimental results show that the proposed method outperforms competitive state-of-the-art models with only 1.68\% parameters compared to those models.
Multivariate time series (MTS) forecasting plays an important role in the automation and optimization of intelligent applications. It is a challenging task, as we need to consider both complex intra-variable dependencies and inter-variable dependencies. Existing works only learn temporal patterns with the help of single inter-variable dependencies. However, there are multi-scale temporal patterns in many real-world MTS. Single inter-variable dependencies make the model prefer to learn one type of prominent and shared temporal patterns. In this paper, we propose a multi-scale adaptive graph neural network (MAGNN) to address the above issue. MAGNN exploits a multi-scale pyramid network to preserve the underlying temporal dependencies at different time scales. Since the inter-variable dependencies may be different under distinct time scales, an adaptive graph learning module is designed to infer the scale-specific inter-variable dependencies without pre-defined priors. Given the multi-scale feature representations and scale-specific inter-variable dependencies, a multi-scale temporal graph neural network is introduced to jointly model intra-variable dependencies and inter-variable dependencies. After that, we develop a scale-wise fusion module to effectively promote the collaboration across different time scales, and automatically capture the importance of contributed temporal patterns. Experiments on four real-world datasets demonstrate that MAGNN outperforms the state-of-the-art methods across various settings.
This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to noisy, incomplete, or perturbed graph signals, making them fragile in such conditions. Our newly proposed framelet convolution addresses these limitations by decomposing graph data into low-pass and high-pass spectra through a finely-tuned multiscale approach. Our approach directly designs filtering functions within the spectral domain, allowing for precise control over the spectral components. The proposed design excels in filtering out unwanted spectral information and significantly reduces the adverse effects of noisy graph signals. Our approach not only enhances the robustness of GNNs but also preserves crucial graph features and structures. Through extensive experiments on diverse, real-world graph datasets, we demonstrate that our framelet convolution achieves superior performance in node classification tasks. It exhibits remarkable resilience to noisy data and adversarial attacks, highlighting its potential as a robust solution for real-world graph applications. This advancement opens new avenues for more adaptive and reliable spectral GNN architectures.
Multi-view subspace clustering (MSC) is a popular unsupervised method by integrating heterogeneous information to reveal the intrinsic clustering structure hidden across views. Usually, MSC methods use graphs (or affinity matrices) fusion to learn a common structure, and further apply graph-based approaches to clustering. Despite progress, most of the methods do not establish the connection between graph learning and clustering. Meanwhile, conventional graph fusion strategies assign coarse-grained weights to combine multi-graph, ignoring the importance of local structure. In this paper, we propose a fine-grained graph learning framework for multi-view subspace clustering (FGL-MSC) to address these issues. To utilize the multi-view information sufficiently, we design a specific graph learning method by introducing graph regularization and a local structure fusion pattern. The main challenge is how to optimize the fine-grained fusion weights while generating the learned graph that fits the clustering task, thus making the clustering representation meaningful and competitive. Accordingly, an iterative algorithm is proposed to solve the above joint optimization problem, which obtains the learned graph, the clustering representation, and the fusion weights simultaneously. Extensive experiments on eight real-world datasets show that the proposed framework has comparable performance to the state-of-the-art methods. The source code of the proposed method is available at https://github.com/siriuslay/FGL-MSC.
Human actions are typically of combinatorial structures or patterns, i.e., subjects, objects, plus spatio-temporal interactions in between. Discovering such structures is therefore a rewarding way to reason about the dynamics of interactions and recognize the actions. In this paper, we introduce a new design of sub-graphs to represent and encode the discriminative patterns of each action in the videos. Specifically, we present MUlti-scale Sub-graph LEarning (MUSLE) framework that novelly builds space-time graphs and clusters the graphs into compact sub-graphs on each scale with respect to the number of nodes. Technically, MUSLE produces 3D bounding boxes, i.e., tubelets, in each video clip, as graph nodes and takes dense connectivity as graph edges between tubelets. For each action category, we execute online clustering to decompose the graph into sub-graphs on each scale through learning Gaussian Mixture Layer and select the discriminative sub-graphs as action prototypes for recognition. Extensive experiments are conducted on both Something-Something V1 & V2 and Kinetics-400 datasets, and superior results are reported when comparing to state-of-the-art methods. More remarkably, our MUSLE achieves to-date the best reported accuracy of 65.0% on Something-Something V2 validation set.
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this definition is not mathematically valid in the cases of vector-valued graph signals which however are typical operands in the state-of-the-art graph learning modeling and analyses. Seeking a generalized transformation decoding the magnitudes of eigencomponents from vector-valued signals is thus the main objective of this paper. Several attempts are explored, and also it is found that performing the transformation at hierarchical levels of adjacency help profile the spectral characteristics of signals more insightfully. The proposed methods are introduced as a new tool assisting on diagnosing and profiling behaviors of graph learning models.
An unfocused plenoptic light field (LF) camera places an array of microlenses in front of an image sensor in order to separately capture different directional rays arriving at an image pixel. Using a conventional Bayer pattern, data captured at each pixel is a single color component (R, G or B).The sensed data then undergoes demosaicking (interpolation of RGB components per pixel) and conversion to an array of sub-aperture images (SAIs). In this paper, we propose a new LF image coding scheme based on graph lifting transform (GLT), where the acquired sensor data are coded in the original captured form without pre-processing. Specifically, we directly map raw sensed color data to the SAIs, resulting in sparsely distributed color pixels on 2D grids, and perform demosaicking at the receiver after decoding. To exploit spatial correlation among the sparse pixels, we propose a novel intra-prediction scheme, where the prediction kernel is determined according to the local gradient estimated from already coded neighboring pixel blocks. We then connect the pixels by forming a graph, modeling the prediction residuals statistically as a Gaussian Markov Random Field (GMRF). The optimal edge weights are computed via a graph learning method using a set of training SAIs. The residual data is encoded via low-complexity GLT. Experiments show that at high PSNRs -- important for archiving and instant storage scenarios -- our method outperformed significantly a conventional light field image coding scheme with demosaicking followed by High Efficiency Video Coding (HEVC).
Self-supervision is recently surging at its new frontier of graph learning. It facilitates graph representations beneficial to downstream tasks; but its success could hinge on domain knowledge for handcraft or the often expensive trials and errors. Even its state-of-the-art representative, graph contrastive learning (GraphCL), is not completely free of those needs as GraphCL uses a prefabricated prior reflected by the ad-hoc manual selection of graph data augmentations. Our work aims at advancing GraphCL by answering the following questions: How to represent the space of graph augmented views? What principle can be relied upon to learn a prior in that space? And what framework can be constructed to learn the prior in tandem with contrastive learning? Accordingly, we have extended the prefabricated discrete prior in the augmentation set, to a learnable continuous prior in the parameter space of graph generators, assuming that graph priors per se, similar to the concept of image manifolds, can be learned by data generation. Furthermore, to form contrastive views without collapsing to trivial solutions due to the prior learnability, we have leveraged both principles of information minimization (InfoMin) and information bottleneck (InfoBN) to regularize the learned priors. Eventually, contrastive learning, InfoMin, and InfoBN are incorporated organically into one framework of bi-level optimization. Our principled and automated approach has proven to be competitive against the state-of-the-art graph self-supervision methods, including GraphCL, on benchmarks of small graphs; and shown even better generalizability on large-scale graphs, without resorting to human expertise or downstream validation. Our code is publicly released at https://github.com/Shen-Lab/GraphCL_Automated.
Graph machine learning has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To tackle the challenge, automated graph machine learning, which aims at discovering the best hyper-parameter and neural architecture configuration for different graph tasks/data without manual design, is gaining an increasing number of attentions from the research community. In this paper, we extensively discuss automated graph machine learning approaches, covering hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We briefly overview existing libraries designed for either graph machine learning or automated machine learning respectively, and further in depth introduce AutoGL, our dedicated and the world's first open-source library for automated graph machine learning. Also, we describe a tailored benchmark that supports unified, reproducible, and efficient evaluations. Last but not least, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive discussion of approaches, libraries as well as directions for automated graph machine learning.
In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected. The Graph Neural Network (GNN) has proven to be a very useful tool in a variety of graph learning tasks including node classification, link prediction, and edge classification. However, in most of these tasks, the graph data we are working with may be noisy and may contain spurious edges. That is, there is a lot of uncertainty associated with the underlying graph structure. Recent approaches to modeling uncertainty have been to use a Bayesian framework and view the graph as a random variable with probabilities associated with model parameters. Introducing the Bayesian paradigm to graph-based models, specifically for semi-supervised node classification, has been shown to yield higher classification accuracies. However, the method of graph inference proposed in recent work does not take into account the structure of the graph. In this paper, we propose a novel algorithm called Bayesian Graph Convolutional Network using Neighborhood Random Walk Sampling (BGCN-NRWS), which uses a Markov Chain Monte Carlo (MCMC) based graph sampling algorithm utilizing graph structure, reduces overfitting by using a variational inference layer, and yields consistently competitive classification results compared to the state-of-the-art in semi-supervised node classification.
Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional graph representations. Graph neural networks (GNNs) are currently the most popular model in graph embedding approaches. However, standard GNNs in the neighborhood aggregation paradigm suffer from limited discriminative power in distinguishing \emph{high-order} graph structures as opposed to \emph{low-order} structures. To capture high-order structures, researchers have resorted to motifs and developed motif-based GNNs. However, existing motif-based GNNs still often suffer from less discriminative power on high-order structures. To overcome the above limitations, we propose Motif Graph Neural Network (MGNN), a novel framework to better capture high-order structures, hinging on our proposed motif redundancy minimization operator and injective motif combination. First, MGNN produces a set of node representations w.r.t. each motif. The next phase is our proposed redundancy minimization among motifs which compares the motifs with each other and distills the features unique to each motif. Finally, MGNN performs the updating of node representations by combining multiple representations from different motifs. In particular, to enhance the discriminative power, MGNN utilizes an injective function to combine the representations w.r.t. different motifs. We further show that our proposed architecture increases the expressive power of GNNs with a theoretical analysis. We demonstrate that MGNN outperforms state-of-the-art methods on seven public benchmarks on both node classification and graph classification tasks.
Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various prediction tasks, such as link prediction, node classification, clustering, and visualization. The collective effort of the graph learning community has delivered hundreds of methods, but no single method excels under all evaluation metrics such as prediction accuracy, running time, scalability, etc. This survey aims to evaluate all major classes of graph embedding methods by considering algorithmic variations, parameter selections, scalability, hardware and software platforms, downstream ML tasks, and diverse datasets. We organized graph embedding techniques using a taxonomy that includes methods from manual feature engineering, matrix factorization, shallow neural networks, and deep graph convolutional networks. We evaluated these classes of algorithms for node classification, link prediction, clustering, and visualization tasks using widely used benchmark graphs. We designed our experiments on top of PyTorch Geometric and DGL libraries and run experiments on different multicore CPU and GPU platforms. We rigorously scrutinize the performance of embedding methods under various performance metrics and summarize the results. Thus, this paper may serve as a comparative guide to help users select methods that are most suitable for their tasks.