Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and information systems. With the continuous penetration of artificial intelligence technologies, graph learning (i.e., machine learning on graphs) is gaining attention from both researchers and practitioners. Graph learning proves effective for many tasks, such as classification, link prediction, and matching. Generally, graph learning methods extract relevant features of graphs by taking advantage of machine learning algorithms. In this survey, we present a comprehensive overview on the state-of-the-art of graph learning. Special attention is paid to four categories of existing graph learning methods, including graph signal processing, matrix factorization, random walk, and deep learning. Major models and algorithms under these categories are reviewed respectively. We examine graph learning applications in areas such as text, images, science, knowledge graphs, and combinatorial optimization. In addition, we discuss several promising research directions in this field.
Graph neural networks (GNN) have been ubiquitous in graph node classification tasks. Most of GNN methods update the node embedding iteratively by aggregating its neighbors' information. However, they often suffer from negative disturbance, due to edges connecting nodes with different labels. One approach to alleviate this negative disturbance is to use attention to learn the weights of aggregation, but current attention-based GNNs only consider feature similarity and also suffer from the lack of supervision. In this paper, we consider the label dependency of graph nodes and propose a decoupling attention mechanism to learn both hard and soft attention. The hard attention is learned on labels for a refined graph structure with fewer inter-class edges, so that the aggregation's negative disturbance can be reduced. The soft attention aims to learn the aggregation weights based on features over the refined graph structure to enhance information gains during message passing. Particularly, we formulate our model under the EM framework, and the learned attention is used to guide the label propagation in the M-step and the feature propagation in the E-step, respectively. Extensive experiments are performed on six well-known benchmark graph datasets to verify the effectiveness of the proposed method.
Graph Neural Networks have recently become a prevailing paradigm for various high-impact graph analytical problems. Existing efforts can be mainly categorized as spectral-based and spatial-based methods. The major challenge for the former is to find an appropriate graph filter to distill discriminative information from input signals for learning. Recently, myriads of explorations are made to achieve better graph filters, e.g., Graph Convolutional Network (GCN), which leverages Chebyshev polynomial truncation to seek an approximation of graph filters and bridge these two families of methods. Nevertheless, it has been shown in recent studies that GCN and its variants are essentially employing fixed low-pass filters to perform information denoising. Thus their learning capability is rather limited and may over-smooth node representations at deeper layers. To tackle these problems, we develop a novel graph neural network framework AdaGNN with a well-designed adaptive frequency response filter. At its core, AdaGNN leverages a simple but elegant trainable filter that spans across multiple layers to capture the varying importance of different frequency components for node representation learning. The inherent differences among different feature channels are also well captured by the filter. As such, it empowers AdaGNN with stronger expressiveness and naturally alleviates the over-smoothing problem. We empirically validate the effectiveness of the proposed framework on various benchmark datasets. Theoretical analysis is also provided to show the superiority of the proposed AdaGNN. The open-source implementation of AdaGNN can be found here: https://github.com/yushundong/AdaGNN.
Graphs naturally lend themselves to model the complexities of Hyperspectral Image (HSI) data as well as to serve as semi-supervised classifiers by propagating given labels among nearest neighbours. In this work, we present a novel framework for the classification of HSI data in light of a very limited amount of labelled data, inspired by multi-view graph learning and graph signal processing. Given an a priori superpixel-segmented hyperspectral image, we seek a robust and efficient graph construction and label propagation method to conduct semi-supervised learning (SSL). Since the graph is paramount to the success of the subsequent classification task, particularly in light of the intrinsic complexity of HSI data, we consider the problem of finding the optimal graph to model such data. Our contribution is two-fold: firstly, we propose a multi-stage edge-efficient semi-supervised graph learning framework for HSI data which exploits given label information through pseudo-label features embedded in the graph construction. Secondly, we examine and enhance the contribution of multiple superpixel features embedded in the graph on the basis of pseudo-labels in an extension of the previous framework, which is less reliant on excessive parameter tuning. Ultimately, we demonstrate the superiority of our approaches in comparison with state-of-the-art methods through extensive numerical experiments.
Graph neural networks (GNNs) have been demonstrated as a powerful tool for analyzing non-Euclidean graph data. However, the lack of efficient distributed graph learning systems severely hinders applications of GNNs, especially when graphs are big and GNNs are relatively deep. Herein, we present GraphTheta, the first distributed and scalable graph learning system built upon vertex-centric distributed graph processing with neural network operators implemented as user-defined functions. This system supports multiple training strategies and enables efficient and scalable big-graph learning on distributed (virtual) machines with low memory. To facilitate graph convolutions, GraphTheta puts forward a new graph learning abstraction named NN-TGAR to bridge the gap between graph processing and graph deep learning. A distributed graph engine is proposed to conduct the stochastic gradient descent optimization with a hybrid-parallel execution, and a new cluster-batched training strategy is supported. We evaluate GraphTheta using several datasets with network sizes ranging from small-, modest- to large-scale. Experimental results show that GraphTheta can scale well to 1,024 workers for training an in-house developed GNN on an industry-scale Alipay dataset of 1.4 billion nodes and 4.1 billion attributed edges, with a cluster of CPU virtual machines (dockers) of small memory each (5$\sim$12GB). Moreover, GraphTheta can outperform DistDGL by up to $2.02\times$, with better scalability, and GraphLearn by up to $30.56\times$. As for model accuracy, GraphTheta is capable of learning as good GNNs as existing frameworks. To the best of our knowledge, this work presents the largest edge-attributed GNN learning task in the literature.
This work introduces a highly scalable spectral graph densification framework for learning resistor networks with linear measurements, such as node voltages and currents. We prove that given $O(\log N)$ pairs of voltage and current measurements, it is possible to recover ultra-sparse $N$-node resistor networks which can well preserve the effective resistance distances on the graph. Also, the learned graphs preserve the structural (spectral) properties of the original graph, which can potentially be leveraged in many circuit design and optimization tasks. We show that the proposed graph learning approach is equivalent to solving the classical graphical Lasso problems with Laplacian-like precision matrices. Through extensive experiments for a variety of real-world test cases, we show that the proposed approach is highly scalable for learning ultra-sparse resistor networks without sacrificing solution quality.
We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and effect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations' covariance matrix and the so-called graph shift operator (GSO -- a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations' empirical covariance matrix. For streaming data said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.
This paper is concerned with the blind identification of graph filters from graph signals. Our aim is to determine if the graph filter generating the graph signals is first-order lowpass without knowing the graph topology. Notice that lowpass graph filter is a common prerequisite for applying graph signal processing tools for sampling, denoising, and graph learning. Our method is inspired by the Perron Frobenius theorem, which observes that for first-order lowpass graph filter, the top eigenvector of output covariance would be the only eigenvector with elements of the same sign. Utilizing this observation, we develop a simple detector that answers if a given data set is produced by a first-order lowpass graph filter. We analyze the effects of finite-sample, graph size, observation noise, strength of lowpass filter, on the detector's performance. Numerical experiments on synthetic and real data support our findings.
Phasor measurement units (PMUs) are being widely installed on power systems, providing a unique opportunity to enhance wide-area situational awareness. One essential application is the use of PMU data for real-time event identification. However, how to take full advantage of all PMU data in event identification is still an open problem. Thus, we propose a novel method that performs event identification by mining interaction graphs among different PMUs. The proposed interaction graph inference method follows an entirely data-driven manner without knowing the physical topology. Moreover, unlike previous works that treat interactive learning and event identification as two different stages, our method learns interactions jointly with the identification task, thereby improving the accuracy of graph learning and ensuring seamless integration between the two stages. Moreover, to capture multi-scale event patterns, a dilated inception-based method is investigated to perform feature extraction of PMU data. To test the proposed data-driven approach, a large real-world dataset from tens of PMU sources and the corresponding event logs have been utilized in this work. Numerical results validate that our method has higher classification accuracy compared to previous methods.
This paper presents Gem, a model-agnostic approach for providing interpretable explanations for any GNNs on various graph learning tasks. Specifically, we formulate the problem of providing explanations for the decisions of GNNs as a causal learning task. Then we train a causal explanation model equipped with a loss function based on Granger causality. Different from existing explainers for GNNs, Gem explains GNNs on graph-structured data from a causal perspective. It has better generalization ability as it has no requirements on the internal structure of the GNNs or prior knowledge on the graph learning tasks. In addition, Gem, once trained, can be used to explain the target GNN very quickly. Our theoretical analysis shows that several recent explainers fall into a unified framework of additive feature attribution methods. Experimental results on synthetic and real-world datasets show that Gem achieves a relative increase of the explanation accuracy by up to $30\%$ and speeds up the explanation process by up to $110\times$ as compared to its state-of-the-art alternatives.
In this paper, we propose a novel graph learning framework for phrase grounding in the image. Developing from the sequential to the dense graph model, existing works capture coarse-grained context but fail to distinguish the diversity of context among phrases and image regions. In contrast, we pay special attention to different motifs implied in the context of the scene graph and devise the disentangled graph network to integrate the motif-aware contextual information into representations. Besides, we adopt interventional strategies at the feature and the structure levels to consolidate and generalize representations. Finally, the cross-modal attention network is utilized to fuse intra-modal features, where each phrase can be computed similarity with regions to select the best-grounded one. We validate the efficiency of disentangled and interventional graph network (DIGN) through a series of ablation studies, and our model achieves state-of-the-art performance on Flickr30K Entities and ReferIt Game benchmarks.
Recent years have witnessed an upsurge in research interests and applications of machine learning on graphs. However, manually designing the optimal machine learning algorithms for different graph datasets and tasks is inflexible, labor-intensive, and requires expert knowledge, limiting its adaptivity and applicability. Automated machine learning (AutoML) on graphs, aiming to automatically design the optimal machine learning algorithm for a given graph dataset and task, has received considerable attention. However, none of the existing libraries can fully support AutoML on graphs. To fill this gap, we present Automated Graph Learning (AutoGL), the first dedicated library for automated machine learning on graphs. AutoGL is open-source, easy to use, and flexible to be extended. Specifically, we propose a three-layer architecture, consisting of backends to interface with devices, a complete automated graph learning pipeline, and supported graph applications. The automated machine learning pipeline further contains five functional modules: auto feature engineering, neural architecture search, hyper-parameter optimization, model training, and auto ensemble, covering the majority of existing AutoML methods on graphs. For each module, we provide numerous state-of-the-art methods and flexible base classes and APIs, which allow easy usage and customization. We further provide experimental results to showcase the usage of our AutoGL library. We also present AutoGL-light, a lightweight version of AutoGL to facilitate customizing pipelines and enriching applications, as well as benchmarks for graph neural architecture search. The codes of AutoGL are publicly available at https://github.com/THUMNLab/AutoGL.
In this paper, we focus on the unsupervised multi-view feature selection which tries to handle high dimensional data in the field of multi-view learning. Although some graph-based methods have achieved satisfactory performance, they ignore the underlying data structure across different views. Besides, their pre-defined laplacian graphs are sensitive to the noises in the original data space, and fail to get the optimal neighbor assignment. To address the above problems, we propose a novel unsupervised multi-view feature selection model based on graph learning, and the contributions are threefold: (1) during the feature selection procedure, the consensus similarity graph shared by different views is learned. Therefore, the proposed model can reveal the data relationship from the feature subset. (2) a reasonable rank constraint is added to optimize the similarity matrix to obtain more accurate information; (3) an auto-weighted framework is presented to assign view weights adaptively, and an effective alternative iterative algorithm is proposed to optimize the problem. Experiments on various datasets demonstrate the superiority of the proposed method compared with the state-of-the-art methods.
Automatically detecting/segmenting object(s) that blend in with their surroundings is difficult for current models. A major challenge is that the intrinsic similarities between such foreground objects and background surroundings make the features extracted by deep model indistinguishable. To overcome this challenge, an ideal model should be able to seek valuable, extra clues from the given scene and incorporate them into a joint learning framework for representation co-enhancement. With this inspiration, we design a novel Mutual Graph Learning (MGL) model, which generalizes the idea of conventional mutual learning from regular grids to the graph domain. Specifically, MGL decouples an image into two task-specific feature maps -- one for roughly locating the target and the other for accurately capturing its boundary details -- and fully exploits the mutual benefits by recurrently reasoning their high-order relations through graphs. Importantly, in contrast to most mutual learning approaches that use a shared function to model all between-task interactions, MGL is equipped with typed functions for handling different complementary relations to maximize information interactions. Experiments on challenging datasets, including CHAMELEON, CAMO and COD10K, demonstrate the effectiveness of our MGL with superior performance to existing state-of-the-art methods.
Knowledge is captured in the form of entities and their relationships and stored in knowledge graphs. Knowledge graphs enhance the capabilities of applications in many different areas including Web search, recommendation, and natural language understanding. This is mainly because, entities enable machines to understand things that go beyond simple tokens. Many modern algorithms use learned entity embeddings from these structured representations. However, building a knowledge graph takes time and effort, hence very costly and nontrivial. On the other hand, many Web sources describe entities in some structured format and therefore, finding ways to get them into useful entity knowledge is advantageous. We propose an approach that processes entity centric textual knowledge sources to learn entity embeddings and in turn avoids the need for a traditional knowledge graph. We first extract triples into the new representation format that does not use traditional complex triple extraction methods defined by pre-determined relationship labels. Then we learn entity embeddings through this new type of triples. We show that the embeddings learned from our approach are: (i) high quality and comparable to a known knowledge graph-based embeddings and can be used to improve them further, (ii) better than a contextual language model-based entity embeddings, and (iii) easy to compute and versatile in domain-specific applications where a knowledge graph is not readily available
Estimating click-through rate (CTR) accurately has an essential impact on improving user experience and revenue in sponsored search. For CTR prediction model, it is necessary to make out user real-time search intention. Most of the current work is to mine their intentions based on user real-time behaviors. However, it is difficult to capture the intention when user behaviors are sparse, causing the behavior sparsity problem. Moreover, it is difficult for user to jump out of their specific historical behaviors for possible interest exploration, namely weak generalization problem. We propose a new approach Graph Intention Network (GIN) based on co-occurrence commodity graph to mine user intention. By adopting multi-layered graph diffusion, GIN enriches user behaviors to solve the behavior sparsity problem. By introducing co-occurrence relationship of commodities to explore the potential preferences, the weak generalization problem is also alleviated. To the best of our knowledge, the GIN method is the first to introduce graph learning for user intention mining in CTR prediction and propose end-to-end joint training of graph learning and CTR prediction tasks in sponsored search. At present, GIN has achieved excellent offline results on the real-world data of the e-commerce platform outperforming existing deep learning models, and has been running stable tests online and achieved significant CTR improvements.
The complete characterization of enzymatic activities between molecules remains incomplete, hindering biological engineering and limiting biological discovery. We develop in this work a technique, Enzymatic Link Prediction (ELP), for predicting the likelihood of an enzymatic transformation between two molecules. ELP models enzymatic reactions catalogued in the KEGG database as a graph. ELP is innovative over prior works in using graph embedding to learn molecular representations that capture not only molecular and enzymatic attributes but also graph connectivity. We explore both transductive (test nodes included in the training graph) and inductive (test nodes not part of the training graph) learning models. We show that ELP achieves high AUC when learning node embeddings using both graph connectivity and node attributes. Further, we show that graph embedding for predicting enzymatic links improves link prediction by 24% over fingerprint-similarity-based approaches. To emphasize the importance of graph embedding in the context of biochemical networks, we illustrate how graph embedding can also guide visualization. The code and datasets are available through https://github.com/HassounLab/ELP.
Interpretability in Graph Convolutional Networks (GCNs) has been explored to some extent in computer vision in general, yet, in the medical domain, it requires further examination. Moreover, most of the interpretability approaches for GCNs, especially in the medical domain, focus on interpreting the model in a post hoc fashion. In this paper, we propose an interpretable graph learning-based model which 1) interprets the clinical relevance of the input features towards the task, 2) uses the explanation to improve the model performance and, 3) learns a population level latent graph that may be used to interpret the cohort's behavior. In a clinical scenario, such a model can assist the clinical experts in better decision-making for diagnosis and treatment planning. The main novelty lies in the interpretable attention module (IAM), which directly operates on multi-modal features. Our IAM learns the attention for each feature based on the unique interpretability-specific losses. We show the application on two publicly available datasets, Tadpole and UKBB, for three tasks of disease, age, and gender prediction. Our proposed model shows superior performance with respect to compared methods with an increase in an average accuracy of 3.2% for Tadpole, 1.6% for UKBB Gender, and 2% for the UKBB Age prediction task. Further, we show exhaustive validation and clinical interpretation of our results.
Leveraging domain knowledge including fingerprints and functional groups in molecular representation learning is crucial for chemical property prediction and drug discovery. When modeling the relation between graph structure and molecular properties implicitly, existing works can hardly capture structural or property changes and complex structure, with much smaller atom vocabulary and highly frequent atoms. In this paper, we propose the Contrastive Knowledge-aware GNN (CKGNN) for self-supervised molecular representation learning to fuse domain knowledge into molecular graph representation. We explicitly encode domain knowledge via knowledge-aware molecular encoder under the contrastive learning framework, ensuring that the generated molecular embeddings equipped with chemical domain knowledge to distinguish molecules with similar chemical formula but dissimilar functions. Extensive experiments on 8 public datasets demonstrate the effectiveness of our model with a 6\% absolute improvement on average against strong competitors. Ablation study and further investigation also verify the best of both worlds: incorporation of chemical domain knowledge into self-supervised learning.
Zero-shot graph embedding is a major challenge for supervised graph learning. Although a recent method RECT has shown promising performance, its working mechanisms are not clear and still needs lots of training data. In this paper, we give deep insights into RECT, and address its fundamental limits. We show that its core part is a GNN prototypical model in which a class prototype is described by its mean feature vector. As such, RECT maps nodes from the raw-input feature space into an intermediate-level semantic space that connects the raw-input features to both seen and unseen classes. This mechanism makes RECT work well on both seen and unseen classes, which however also reduces the discrimination. To realize its full potentials, we propose two label expansion strategies. Specifically, besides expanding the labeled node set of seen classes, we can also expand that of unseen classes. Experiments on real-world datasets validate the superiority of our methods.