Rapid and massive adoption of mobile/ online payment services has brought new challenges to the service providers as well as regulators in safeguarding the proper uses such services/ systems. In this paper, we leverage recent advances in deep-neural-network-based graph representation learning to detect abnormal/ suspicious financial transactions in real-world e-payment networks. In particular, we propose an end-to-end Graph Convolution Network (GCN)-based algorithm to learn the embeddings of the nodes and edges of a large-scale time-evolving graph. In the context of e-payment transaction graphs, the resultant node and edge embeddings can effectively characterize the user-background as well as the financial transaction patterns of individual account holders. As such, we can use the graph embedding results to drive downstream graph mining tasks such as node-classification to identify illicit accounts within the payment networks. Our algorithm outperforms state-of-the-art schemes including GraphSAGE, Gradient Boosting Decision Tree and Random Forest to deliver considerably higher accuracy (94.62% and 86.98% respectively) in classifying user accounts within 2 practical e-payment transaction datasets. It also achieves outstanding accuracy (97.43%) for another biomedical entity identification task while using only edge-related information.
Graph embedding learning that aims to automatically learn low-dimensional node representations, has drawn increasing attention in recent years. To date, most recent graph embedding methods are evaluated on social and information networks and are not comprehensively studied on biomedical networks under systematic experiments and analyses. On the other hand, for a variety of biomedical network analysis tasks, traditional techniques such as matrix factorization (which can be seen as a type of graph embedding methods) have shown promising results, and hence there is a need to systematically evaluate the more recent graph embedding methods (e.g. random walk-based and neural network-based) in terms of their usability and potential to further the state-of-the-art. We select 11 representative graph embedding methods and conduct a systematic comparison on 3 important biomedical link prediction tasks: drug-disease association (DDA) prediction, drug-drug interaction (DDI) prediction, protein-protein interaction (PPI) prediction; and 2 node classification tasks: medical term semantic type classification, protein function prediction. Our experimental results demonstrate that the recent graph embedding methods achieve promising results and deserve more attention in the future biomedical graph analysis. Compared with three state-of-the-art methods for DDAs, DDIs and protein function predictions, the recent graph embedding methods achieve competitive performance without using any biological features and the learned embeddings can be treated as complementary representations for the biological features. By summarizing the experimental results, we provide general guidelines for properly selecting graph embedding methods and setting their hyper-parameters for different biomedical tasks.
Depression and anxiety are critical public health issues affecting millions of people around the world. To identify individuals who are vulnerable to depression and anxiety, predictive models have been built that typically utilize data from one source. Unlike these traditional models, in this study, we leverage a rich heterogeneous data set from the University of Notre Dame's NetHealth study that collected individuals' (student participants') social interaction data via smartphones, health-related behavioral data via wearables (Fitbit), and trait data from surveys. To integrate the different types of information, we model the NetHealth data as a heterogeneous information network (HIN). Then, we redefine the problem of predicting individuals' mental health conditions (depression or anxiety) in a novel manner, as applying to our HIN a popular paradigm of a recommender system (RS), which is typically used to predict the preference that a person would give to an item (e.g., a movie or book). In our case, the items are the individuals' different mental health states. We evaluate four state-of-the-art RS approaches. Also, we model the prediction of individuals' mental health as another problem type - that of node classification (NC) in our HIN, evaluating in the process four node features under logistic regression as a proof-of-concept classifier. We find that our RS and NC network methods produce more accurate predictions than a logistic regression model using the same NetHealth data in the traditional non-network fashion as well as a random-approach. Also, we find that the best of the considered RS approaches outperforms all considered NC approaches. This is the first study to integrate smartphone, wearable sensor, and survey data in an HIN manner and use RS or NC on the HIN to predict individuals' mental health conditions.
Graph neural networks (GNNs) which apply the deep neural networks to graph data have achieved significant performance for the task of semi-supervised node classification. However, only few work has addressed the adversarial robustness of GNNs. In this paper, we first present a novel gradient-based attack method that facilitates the difficulty of tackling discrete graph data. When comparing to current adversarial attacks on GNNs, the results show that by only perturbing a small number of edge perturbations, including addition and deletion, our optimization-based attack can lead to a noticeable decrease in classification performance. Moreover, leveraging our gradient-based attack, we propose the first optimization-based adversarial training for GNNs. Our method yields higher robustness against both different gradient based and greedy attack methods without sacrificing classification accuracy on original graph.
Graph Neural Networks (GNNs) have boosted the performance of many graph related tasks such as node classification and graph classification. Recent researches show that graph neural networks are vulnerable to adversarial attacks, which deliberately add carefully created unnoticeable perturbation to the graph structure. The perturbation is usually created by adding/deleting a few edges, which might be noticeable even when the number of edges modified is small. In this paper, we propose a graph rewiring operation which affects the graph in a less noticeable way compared to adding/deleting edges. We then use reinforcement learning to learn the attack strategy based on the proposed rewiring operation. Experiments on real world graphs demonstrate the effectiveness of the proposed framework. To understand the proposed framework, we further analyze how its generated perturbation to the graph structure affects the output of the target model.
Graph data widely exist in many high-impact applications. Inspired by the success of deep learning in grid-structured data, graph neural network models have been proposed to learn powerful node-level or graph-level representation. However, most of the existing graph neural networks suffer from the following limitations: (1) there is limited analysis regarding the graph convolution properties, such as seed-oriented, degree-aware and order-free; (2) the node's degree-specific graph structure is not explicitly expressed in graph convolution for distinguishing structure-aware node neighborhoods; (3) the theoretical explanation regarding the graph-level pooling schemes is unclear. To address these problems, we propose a generic degree-specific graph neural network named DEMO-Net motivated by Weisfeiler-Lehman graph isomorphism test that recursively identifies 1-hop neighborhood structures. In order to explicitly capture the graph topology integrated with node attributes, we argue that graph convolution should have three properties: seed-oriented, degree-aware, order-free. To this end, we propose multi-task graph convolution where each task represents node representation learning for nodes with a specific degree value, thus leading to preserving the degree-specific graph structure. In particular, we design two multi-task learning methods: degree-specific weight and hashing functions for graph convolution. In addition, we propose a novel graph-level pooling/readout scheme for learning graph representation provably lying in a degree-specific Hilbert kernel space. The experimental results on several node and graph classification benchmark data sets demonstrate the effectiveness and efficiency of our proposed DEMO-Net over state-of-the-art graph neural network models.
Recently, neural network based approaches have achieved significant improvement for solving large, complex, graph-structured problems. However, their bottlenecks still need to be addressed, and the advantages of multi-scale information and deep architectures have not been sufficiently exploited. In this paper, we theoretically analyze how existing Graph Convolutional Networks (GCNs) have limited expressive power due to the constraint of the activation functions and their architectures. We generalize spectral graph convolution and deep GCN in block Krylov subspace forms and devise two architectures, both with the potential to be scaled deeper but each making use of the multi-scale information in different ways. We further show that the equivalence of these two architectures can be established under certain conditions. On several node classification tasks, with or without the help of validation, the two new architectures achieve better performance compared to many state-of-the-art methods.
In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We introduce a scalable optimization algorithm with no correction steps (in contrast to Frank-Wolfe and its variants), a variant of gradient ascent for coreset selection in graphs, that greedily selects a weighted subset of vertices that are deemed most important to sample. Our algorithm estimates the mean of the function by taking a weighted sum only at these vertices, and we provably bound the estimation error in terms of the location and weights of the selected vertices in the graph. In addition, we consider the case where nodes have different selection costs and provide bounds on the quality of the low-cost selected coresets. We demonstrate the benefits of our algorithm on the semi-supervised node classification of graph convolutional neural network, point clouds and structured graphs, as well as sensor placement where the cost of placing sensors depends on the location of the placement. We also elucidate that the empirical convergence of our proposed method is faster than random selection and various clustering methods while still respecting sensor placement cost. The paper concludes with validation of the developed algorithm on both synthetic and real datasets, demonstrating that it outperforms the current state of the art.
Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static relationships. We propose the Graph Learning Network (GLN), a simple yet effective process to learn node embeddings and structure prediction functions. Our model uses graph convolutions to propose expected node features, and predict the best structure based on them. We repeat these steps recursively to enhance the prediction and the embeddings.
In this paper, we present {GraRep}, a novel model for learning vertex representations of weighted graphs. This model learns low dimensional vectors to represent vertices appearing in a graph and, unlike existing work, integrates global structural information of the graph into the learning process. We also formally analyze the connections between our work and several previous research efforts, including the DeepWalk model of Perozzi et al. as well as the skip-gram model with negative sampling of Mikolov et al. We conduct experiments on a language network, a social network as well as a citation network and show that our learned global representations can be effectively used as features in tasks such as clustering, classification and visualization. Empirical results demonstrate that our representation significantly outperforms other state-of-the-art methods in such tasks.
Graph embedding techniques allow to learn high-quality feature vectors from graph structures and are useful in a variety of tasks, from node classification to clustering. Existing approaches have only focused on learning feature vectors for the nodes in a (knowledge) graph. To the best of our knowledge, none of them has tackled the problem of embedding of graph edges, that is, knowledge graph triples. The approaches that are closer to this task have focused on homogeneous graphs involving only one type of edge and obtain edge embeddings by applying some operation (e.g., average) on the embeddings of the endpoint nodes. The goal of this paper is to introduce Triple2Vec, a new technique to directly embed edges in (knowledge) graphs. Trple2Vec builds upon three main ingredients. The first is the notion of line graph. The line graph of a graph is another graph representing the adjacency between edges of the original graph. In particular, the nodes of the line graph are the edges of the original graph. We show that directly applying existing embedding techniques on the nodes of the line graph to learn edge embeddings is not enough in the context of knowledge graphs. Thus, we introduce the notion of triple line graph. The second is an edge weighting mechanism both for line graphs derived from knowledge graphs and homogeneous graphs. The third is a strategy based on graph walks on the weighted triple line graph that can preserve proximity between nodes. Embeddings are finally generated by adopting the SkipGram model, where sentences are replaced with graph walks. We evaluate our approach on different real world (knowledge) graphs and compared it with related work.
Graph Neural Networks (graph NNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up many layers and add non-lineality. To tackle this problem, we investigate the expressive power of graph NNs via their asymptotic behaviors as the layer size tends to infinity. Our strategy is to generalize the forward propagation of a Graph Convolutional Network (GCN), which is a popular graph NN variant, as a specific dynamical system. In the case of a GCN, we show that when its weights satisfy the conditions determined by the spectra of the (augmented) normalized Laplacian, its output exponentially approaches the set of signals that carry information of the connected components and node degrees only for distinguishing nodes. Our theory enables us to relate the expressive power of GCNs with the topological information of the underlying graphs inherent in the graph spectra. To demonstrate this, we characterize the asymptotic behavior of GCNs on the Erd\H{o}s -- R\'{e}nyi graph. We show that when the Erd\H{o}s -- R\'{e}nyi graph is sufficiently dense and large, a broad range of GCNs on it suffers from the "information loss" in the limit of infinite layers with high probability. Based on the theory, we provide a principled guideline for weight normalization of graph NNs. We experimentally confirm that the proposed weight scaling enhances the predictive performance of GCNs in real data. Code is available at https://github.com/delta2323/gnn-asymptotics.
Auto-encoders have emerged as a successful framework for unsupervised learning. However, conventional auto-encoders are incapable of utilizing explicit relations in structured data. To take advantage of relations in graph-structured data, several graph auto-encoders have recently been proposed, but they neglect to reconstruct either the graph structure or node attributes. In this paper, we present the graph attention auto-encoder (GATE), a neural network architecture for unsupervised representation learning on graph-structured data. Our architecture is able to reconstruct graph-structured inputs, including both node attributes and the graph structure, through stacked encoder/decoder layers equipped with self-attention mechanisms. In the encoder, by considering node attributes as initial node representations, each layer generates new representations of nodes by attending over their neighbors' representations. In the decoder, we attempt to reverse the encoding process to reconstruct node attributes. Moreover, node representations are regularized to reconstruct the graph structure. Our proposed architecture does not need to know the graph structure upfront, and thus it can be applied to inductive learning. Our experiments demonstrate competitive performance on several node classification benchmark datasets for transductive and inductive tasks, even exceeding the performance of supervised learning baselines in most cases.
Meta-learning has received a tremendous recent attention as a possible approach for mimicking human intelligence, i.e., acquiring new knowledge and skills with little or even no demonstration. Most of the existing meta-learning methods are proposed to tackle few-shot learning problems such as image and text, in rather Euclidean domain. However, there are very few works applying meta-learning to non-Euclidean domains, and the recently proposed graph neural networks (GNNs) models do not perform effectively on graph few-shot learning problems. Towards this, we propose a novel graph meta-learning framework -- Meta-GNN -- to tackle the few-shot node classification problem in graph meta-learning settings. It obtains the prior knowledge of classifiers by training on many similar few-shot learning tasks and then classifies the nodes from new classes with only few labeled samples. Additionally, Meta-GNN is a general model that can be straightforwardly incorporated into any existing state-of-the-art GNN. Our experiments conducted on three benchmark datasets demonstrate that our proposed approach not only improves the node classification performance by a large margin on few-shot learning problems in meta-learning paradigm, but also learns a more general and flexible model for task adaption.
Heterogeneous information network (HIN) embedding aims to embed multiple types of nodes into a low-dimensional space. Although most existing HIN embedding methods consider heterogeneous relations in HINs, they usually employ one single model for all relations without distinction, which inevitably restricts the capability of network embedding. In this paper, we take the structural characteristics of heterogeneous relations into consideration and propose a novel Relation structure-aware Heterogeneous Information Network Embedding model (RHINE). By exploring the real-world networks with thorough mathematical analysis, we present two structure-related measures which can consistently distinguish heterogeneous relations into two categories: Affiliation Relations (ARs) and Interaction Relations (IRs). To respect the distinctive characteristics of relations, in our RHINE, we propose different models specifically tailored to handle ARs and IRs, which can better capture the structures and semantics of the networks. At last, we combine and optimize these models in a unified and elegant manner. Extensive experiments on three real-world datasets demonstrate that our model significantly outperforms the state-of-the-art methods in various tasks, including node clustering, link prediction, and node classification.
Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at https://github.com/google-research/google-research/tree/master/cluster_gcn.
We consider the problem of representation learning for graph data. Convolutional neural networks can naturally operate on images, but have significant challenges in dealing with graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied on many image pixel-wise prediction tasks, similar methods are lacking for graph data. This is due to the fact that pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling (gPool) and unpooling (gUnpool) operations in this work. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. We further propose the gUnpool layer as the inverse operation of the gPool layer. The gUnpool layer restores the graph into its original structure using the position information of nodes selected in the corresponding gPool layer. Based on our proposed gPool and gUnpool layers, we develop an encoder-decoder model on graph, known as the graph U-Nets. Our experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.
Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for non-linear dimensionality reduction in a manner akin to previous efforts based on manifold learning with uses for downstream database processing, machine learning and visualization. In this systematic yet comprehensive experimental survey, we benchmark several popular network representation learning methods operating on two key tasks: link prediction and node classification. We examine the performance of 12 unsupervised embedding methods on 15 datasets. To the best of our knowledge, the scale of our study -- both in terms of the number of methods and number of datasets -- is the largest to date. Our results reveal several key insights about work-to-date in this space. First, we find that certain baseline methods (task-specific heuristics, as well as classic manifold methods) that have often been dismissed or are not considered by previous efforts can compete on certain types of datasets if they are tuned appropriately. Second, we find that recent methods based on matrix factorization offer a small but relatively consistent advantage over alternative methods (e.g., random-walk based methods) from a qualitative standpoint. Specifically, we find that MNMF, a community preserving embedding method, is the most competitive method for the link prediction task. While NetMF is the most competitive baseline for node classification. Third, no single method completely outperforms other embedding methods on both node classification and link prediction tasks. We also present several drill-down analysis that reveals settings under which certain algorithms perform well (e.g., the role of neighborhood context on performance) -- guiding the end-user.
Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operators, by repeatedly mixing feature representations of neighbors at various distances. Mixhop requires no additional memory or computational complexity, and outperforms on challenging baselines. In addition, we propose sparsity regularization that allows us to visualize how the network prioritizes neighborhood information across different graph datasets. Our analysis of the learned architectures reveals that neighborhood mixing varies per datasets.
Graph neural networks, which generalize deep neural network models to graph structured data, have attracted increasing attention in recent years. They usually learn node representations by transforming, propagating and aggregating node features and have been proven to improve the performance of many graph related tasks such as node classification and link prediction. To apply graph neural networks for the graph classification task, approaches to generate the \textit{graph representation} from node representations are demanded. A common way is to globally combine the node representations. However, rich structural information is overlooked. Thus a hierarchical pooling procedure is desired to preserve the graph structure during the graph representation learning. There are some recent works on hierarchically learning graph representation analogous to the pooling step in conventional convolutional neural (CNN) networks. However, the local structural information is still largely neglected during the pooling process. In this paper, we introduce a pooling operator $\pooling$ based on graph Fourier transform, which can utilize the node features and local structures during the pooling process. We then design pooling layers based on the pooling operator, which are further combined with traditional GCN convolutional layers to form a graph neural network framework $\m$ for graph classification. Theoretical analysis is provided to understand $\pooling$ from both local and global perspectives. Experimental results of the graph classification task on $6$ commonly used benchmarks demonstrate the effectiveness of the proposed framework.