Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix factorization and random walk-based models. In this paper, we aim to bring together the best of both worlds, towards learning latent node representations. In particular, we propose a weighted matrix factorization model which encodes random walk-based information about the nodes of the graph. The main benefit of this formulation is that it allows to utilize kernel functions on the computation of the embeddings. We perform an empirical evaluation on real-world networks, showing that the proposed model outperforms baseline node embedding algorithms in two downstream machine learning tasks.
Graph Neural Networks (GNNs) have achieved promising performance on a wide range of graph-based tasks. Despite their success, one severe limitation of GNNs is the over-smoothing issue (indistinguishable representations of nodes in different classes). In this work, we present a systematic and quantitative study on the over-smoothing issue of GNNs. First, we introduce two quantitative metrics, MAD and MADGap, to measure the smoothness and over-smoothness of the graph nodes representations, respectively. Then, we verify that smoothing is the nature of GNNs and the critical factor leading to over-smoothness is the low information-to-noise ratio of the message received by the nodes, which is partially determined by the graph topology. Finally, we propose two methods to alleviate the over-smoothing issue from the topological view: (1) MADReg which adds a MADGap-based regularizer to the training objective;(2) AdaGraph which optimizes the graph topology based on the model predictions. Extensive experiments on 7 widely-used graph datasets with 10 typical GNN models show that the two proposed methods are effective for relieving the over-smoothing issue, thus improving the performance of various GNN models.
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph in the low dimensional space. However, real world graphs have a combination of several properties which are difficult to characterize and capture by a single approach. In this work, we introduce the problem of graph representation ensemble learning and provide a first of its kind framework to aggregate multiple graph embedding methods efficiently. We provide analysis of our framework and analyze -- theoretically and empirically -- the dependence between state-of-the-art embedding methods. We test our models on the node classification task on four real world graphs and show that proposed ensemble approaches can outperform the state-of-the-art methods by up to 8% on macro-F1. We further show that the approach is even more beneficial for underrepresented classes providing an improvement of up to 12%.
Graph neural networks (GNNs) have recently made remarkable breakthroughs in the paradigm of learning with graph-structured data. However, most existing GNNs limit the receptive field of the node on each layer to its connected (one-hop) neighbors, which disregards the fact that large receptive field has been proven to be a critical factor in state-of-the-art neural networks. In this paper, we propose a novel approach to appropriately define a variable receptive field for GNNs by incorporating high-order proximity information extracted from the hierarchical topological structure of the input graph. Specifically, multiscale groups obtained from trainable hierarchical semi-nonnegative matrix factorization are used for adjusting the weights when aggregating one-hop neighbors. Integrated with the graph attention mechanism on attributes of neighboring nodes, the learnable parameters within the process of aggregation are optimized in an end-to-end manner. Extensive experiments show that the proposed method (hpGAT) outperforms state-of-the-art methods and demonstrate the importance of exploiting high-order proximity in handling noisy information of local neighborhood.
This paper studies the problem of cross-network node classification to overcome the insufficiency of labeled data in a single network. It aims to leverage the label information in a partially labeled source network to assist node classification in a completely unlabeled or partially labeled target network. Existing methods for single network learning cannot solve this problem due to the domain shift across networks. Some multi-network learning methods heavily rely on the existence of cross-network connections, thus are inapplicable for this problem. To tackle this problem, we propose a novel \textcolor{black}{graph} transfer learning framework AdaGCN by leveraging the techniques of adversarial domain adaptation and graph convolution. It consists of two components: a semi-supervised learning component and an adversarial domain adaptation component. The former aims to learn class discriminative node representations with given label information of the source and target networks, while the latter contributes to mitigating the distribution divergence between the source and target domains to facilitate knowledge transfer. Extensive empirical evaluations on real-world datasets show that AdaGCN can successfully transfer class information with a low label rate on the source network and a substantial divergence between the source and target domains. The source code for reproducing the experimental results is available at https://github.com/daiquanyu/AdaGCN.
Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the computational patterns of GNNs into a few generalized sparse tensor operations suitable for extensive parallelization. By advocating graph as the central programming abstraction, DGL can perform optimizations transparently. By cautiously adopting a framework-neutral design, DGL allows users to easily port and leverage the existing components across multiple deep learning frameworks. Our evaluation shows that DGL significantly outperforms other popular GNN-oriented frameworks in both speed and memory consumption over a variety of benchmarks and has little overhead for small scale workloads.
Network embedding is an effective way to solve the network analytics problems such as node classification, link prediction, etc. It represents network elements using low dimensional vectors such that the graph structural information and properties are maximumly preserved. Many prior works focused on embeddings for networks with the same type of edges or vertices, while some works tried to generate embeddings for heterogeneous network using mechanisms like specially designed meta paths. In this paper, we propose two novel algorithms, GHINE (General Heterogeneous Information Network Embedding) and AHINE (Adaptive Heterogeneous Information Network Embedding), to compute distributed representations for elements in heterogeneous networks. Specially, AHINE uses an adaptive deep model to learn network embeddings that maximizes the likelihood of preserving the relationship chains between non-adjacent nodes. We apply our embeddings to a large network of points of interest (POIs) and achieve superior accuracy on some prediction problems on a ride-hailing platform. In addition, we show that AHINE outperforms state-of-the-art methods on a set of learning tasks on public datasets, including node labelling and similarity ranking in bibliographic networks.
Data from many real-world applications can be naturally represented by multi-view networks where the different views encode different types of relationships (e.g., friendship, shared interests in music, etc.) between real-world individuals or entities. There is an urgent need for methods to obtain low-dimensional, information preserving and typically nonlinear embeddings of such multi-view networks. However, most of the work on multi-view learning focuses on data that lack a network structure, and most of the work on network embeddings has focused primarily on single-view networks. Against this background, we consider the multi-view network representation learning problem, i.e., the problem of constructing low-dimensional information preserving embeddings of multi-view networks. Specifically, we investigate a novel Generative Adversarial Network (GAN) framework for Multi-View Network Embedding, namely MEGAN, aimed at preserving the information from the individual network views, while accounting for connectivity across (and hence complementarity of and correlations between) different views. The results of our experiments on two real-world multi-view data sets show that the embeddings obtained using MEGAN outperform the state-of-the-art methods on node classification, link prediction and visualization tasks.
Machine learning techniques for road networks hold the potential to facilitate many important transportation applications. Graph Convolutional Networks (GCNs) are neural networks that are capable of leveraging the structure of a road network by utilizing information of, e.g., adjacent road segments. While state-of-the-art GCNs target node classification tasks in social, citation, and biological networks, machine learning tasks in road networks differ substantially from such tasks. In road networks, prediction tasks concern edges representing road segments, and many tasks involve regression. In addition, road networks differ substantially from the networks assumed in the GCN literature in terms of the attribute information available and the network characteristics. Many implicit assumptions of GCNs do therefore not apply. We introduce the notion of Relational Fusion Network (RFN), a novel type of GCN designed specifically for machine learning on road networks. In particular, we propose methods that outperform state-of-the-art GCNs on both a road segment regression task and a road segment classification task by 32-40% and 21-24%, respectively. In addition, we provide experimental evidence of the short-comings of state-of-the-art GCNs in the context of road networks: unlike our method, they cannot effectively leverage the road network structure for road segment classification and fail to outperform a regular multi-layer perceptron.
Network Embedding is the task of learning continuous node representations for networks, which has been shown effective in a variety of tasks such as link prediction and node classification. Most of existing works aim to preserve different network structures and properties in low-dimensional embedding vectors, while neglecting the existence of noisy information in many real-world networks and the overfitting issue in the embedding learning process. Most recently, generative adversarial networks (GANs) based regularization methods are exploited to regularize embedding learning process, which can encourage a global smoothness of embedding vectors. These methods have very complicated architecture and suffer from the well-recognized non-convergence problem of GANs. In this paper, we aim to introduce a more succinct and effective local regularization method, namely adversarial training, to network embedding so as to achieve model robustness and better generalization performance. Firstly, the adversarial training method is applied by defining adversarial perturbations in the embedding space with an adaptive $L_2$ norm constraint that depends on the connectivity pattern of node pairs. Though effective as a regularizer, it suffers from the interpretability issue which may hinder its application in certain real-world scenarios. To improve this strategy, we further propose an interpretable adversarial training method by enforcing the reconstruction of the adversarial examples in the discrete graph domain. These two regularization methods can be applied to many existing embedding models, and we take DeepWalk as the base model for illustration in the paper. Empirical evaluations in both link prediction and node classification demonstrate the effectiveness of the proposed methods.
Network embedding has been intensively studied in the literature and widely used in various applications, such as link prediction and node classification. While previous work focus on the design of new algorithms or are tailored for various problem settings, the discussion of initialization strategies in the learning process is often missed. In this work, we address this important issue of initialization for network embedding that could dramatically improve the performance of the algorithms on both effectiveness and efficiency. Specifically, we first exploit the graph partition technique that divides the graph into several disjoint subsets, and then construct an abstract graph based on the partitions. We obtain the initialization of the embedding for each node in the graph by computing the network embedding on the abstract graph, which is much smaller than the input graph, and then propagating the embedding among the nodes in the input graph. With extensive experiments on various datasets, we demonstrate that our initialization technique significantly improves the performance of the state-of-the-art algorithms on the evaluations of link prediction and node classification by up to 7.76% and 8.74% respectively. Besides, we show that the technique of initialization reduces the running time of the state-of-the-arts by at least 20%.
Low-dimensional embeddings of knowledge graphs and behavior graphs have proved remarkably powerful in varieties of tasks, from predicting unobserved edges between entities to content recommendation. The two types of graphs can contain distinct and complementary information for the same entities/nodes. However, previous works focus either on knowledge graph embedding or behavior graph embedding while few works consider both in a unified way. Here we present BEM , a Bayesian framework that incorporates the information from knowledge graphs and behavior graphs. To be more specific, BEM takes as prior the pre-trained embeddings from the knowledge graph, and integrates them with the pre-trained embeddings from the behavior graphs via a Bayesian generative model. BEM is able to mutually refine the embeddings from both sides while preserving their own topological structures. To show the superiority of our method, we conduct a range of experiments on three benchmark datasets: node classification, link prediction, triplet classification on two small datasets related to Freebase, and item recommendation on a large-scale e-commerce dataset.
Latent factor models (LFMs) such as matrix factorization have achieved the state-of-the-art performance among various collaborative filtering approaches for recommendation. Despite the high recommendation accuracy of LFMs, a critical issue to be resolved is their lack of interpretability. Extensive efforts have been devoted to interpreting the prediction results of LFMs. However, they either rely on auxiliary information which may not be available in practice, or sacrifice recommendation accuracy for interpretability. Influence functions, stemming from robust statistics, have been developed to understand the effect of training points on the predictions of black-box models. Inspired by this, we propose a novel explanation method named FIA (Fast Influence Analysis) to understand the prediction of trained LFMs by tracing back to the training data with influence functions. We present how to employ influence functions to measure the impact of historical user-item interactions on the prediction results of LFMs and provide intuitive neighbor-style explanations based on the most influential interactions. Our proposed FIA exploits the characteristics of two important LFMs, matrix factorization and neural collaborative filtering, and is capable of accelerating the overall influence analysis process. We provide a detailed complexity analysis for FIA over LFMs and conduct extensive experiments to evaluate its performance using real-world datasets. The results demonstrate the effectiveness and efficiency of FIA, and the usefulness of the generated explanations for the recommendation results.
Recent years have witnessed a surge of interest in machine learning on graphs and networks with applications ranging from vehicular network design to IoT traffic management to social network recommendations. Supervised machine learning tasks in networks such as node classification and link prediction require us to perform feature engineering that is known and agreed to be the key to success in applied machine learning. Research efforts dedicated to representation learning, especially representation learning using deep learning, has shown us ways to automatically learn relevant features from vast amounts of potentially noisy, raw data. However, most of the methods are not adequate to handle heterogeneous information networks which pretty much represents most real-world data today. The methods cannot preserve the structure and semantic of multiple types of nodes and links well enough, capture higher-order heterogeneous connectivity patterns, and ensure coverage of nodes for which representations are generated. We propose a novel efficient algorithm, motif2vec that learns node representations or embeddings for heterogeneous networks. Specifically, we leverage higher-order, recurring, and statistically significant network connectivity patterns in the form of motifs to transform the original graph to motif graph(s), conduct biased random walk to efficiently explore higher order neighborhoods, and then employ heterogeneous skip-gram model to generate the embeddings. Unlike previous efforts that uses different graph meta-structures to guide the random walk, we use graph motifs to transform the original network and preserve the heterogeneity. We evaluate the proposed algorithm on multiple real-world networks from diverse domains and against existing state-of-the-art methods on multi-class node classification and link prediction tasks, and demonstrate its consistent superiority over prior work.
Many researchers both in academia and industry have long been interested in the stock market. Numerous approaches were developed to accurately predict future trends in stock prices. Recently, there has been a growing interest in utilizing graph-structured data in computer science research communities. Methods that use relational data for stock market prediction have been recently proposed, but they are still in their infancy. First, the quality of collected information from different types of relations can vary considerably. No existing work has focused on the effect of using different types of relations on stock market prediction or finding an effective way to selectively aggregate information on different relation types. Furthermore, existing works have focused on only individual stock prediction which is similar to the node classification task. To address this, we propose a hierarchical attention network for stock prediction (HATS) which uses relational data for stock market prediction. Our HATS method selectively aggregates information on different relation types and adds the information to the representations of each company. Specifically, node representations are initialized with features extracted from a feature extraction module. HATS is used as a relational modeling module with initialized node representations. Then, node representations with the added information are fed into a task-specific layer. Our method is used for predicting not only individual stock prices but also market index movements, which is similar to the graph classification task. The experimental results show that performance can change depending on the relational data used. HATS which can automatically select information outperformed all the existing methods.
Graph neural networks (GNNs) are widely used in many applications. However, their robustness against adversarial attacks is criticized. Prior studies show that using unnoticeable modifications on graph topology or nodal features can significantly reduce the performances of GNNs. It is very challenging to design robust graph neural networks against poisoning attack and several efforts have been taken. Existing work aims at reducing the negative impact from adversarial edges only with the poisoned graph, which is sub-optimal since they fail to discriminate adversarial edges from normal ones. On the other hand, clean graphs from similar domains as the target poisoned graph are usually available in the real world. By perturbing these clean graphs, we create supervised knowledge to train the ability to detect adversarial edges so that the robustness of GNNs is elevated. However, such potential for clean graphs is neglected by existing work. To this end, we investigate a novel problem of improving the robustness of GNNs against poisoning attacks by exploring clean graphs. Specifically, we propose PA-GNN, which relies on a penalized aggregation mechanism that directly restrict the negative impact of adversarial edges by assigning them lower attention coefficients. To optimize PA-GNN for a poisoned graph, we design a meta-optimization algorithm that trains PA-GNN to penalize perturbations using clean graphs and their adversarial counterparts, and transfers such ability to improve the robustness of PA-GNN on the poisoned graph. Experimental results on four real-world datasets demonstrate the robustness of PA-GNN against poisoning attacks on graphs. Code and data are available here: https://github.com/tangxianfeng/PA-GNN.
Representation learning on networks offers a powerful alternative to the oft painstaking process of manual feature engineering, and as a result, has enjoyed considerable success in recent years. However, all the existing representation learning methods are based on the first-order network (FON), that is, the network that only captures the pairwise interactions between the nodes. As a result, these methods may fail to incorporate non-Markovian higher-order dependencies in the network. Thus, the embeddings that are generated may not accurately represent of the underlying phenomena in a network, resulting in inferior performance in different inductive or transductive learning tasks. To address this challenge, this paper presents HONEM, a higher-order network embedding method that captures the non-Markovian higher-order dependencies in a network. HONEM is specifically designed for the higher-order network structure (HON) and outperforms other state-of-the-art methods in node classification, network re-construction, link prediction, and visualization for networks that contain non-Markovian higher-order dependencies.
We study the problem of end-to-end learning from complex multigraphs with potentially very large numbers of edges between two vertices, each edge labeled with rich information. Examples range from communication networks to flights between airports or financial transaction graphs. We propose Latent-Graph Convolutional Networks (L-GCNs), which propagate information from these complex edges to a latent adjacency tensor, after which further downstream tasks can be performed, such as node classification. We evaluate the performance of several variations of the model on two synthetic datasets simulating fraud in financial transaction networks, ensuring the model must make use of edge labels in order to achieve good classification performance. We find that allowing for nonlinear interactions on a per-neighbor basis boosts performance significantly, while showing promising results in an inductive setting. Finally, we demonstrate the use of L-GCNs on real-world data in the form of an urban transportation network.
The design of deep graph models still remains to be investigated and the crucial part is how to explore and exploit the knowledge from different hops of neighbors in an efficient way. In this paper, we propose a novel RNN-like deep graph neural network architecture by incorporating AdaBoost into the computation of network; and the proposed graph convolutional network called AdaGCN~(Adaboosting Graph Convolutional Network) has the ability to efficiently extract knowledge from high-order neighbors of current nodes and then integrates knowledge from different hops of neighbors into the network in an Adaboost way. Different from other graph neural networks that directly stack many graph convolution layers, AdaGCN shares the same base neural network architecture among all ``layers'' and is recursively optimized, which is similar to an RNN. Besides, We also theoretically established the connection between AdaGCN and existing graph convolutional methods, presenting the benefits of our proposal. Finally, extensive experiments demonstrate the consistent state-of-the-art prediction performance on graphs across different label rates and the computational advantage of our approach AdaGCN~\footnote{Code is available at \url{https://github.com/datake/AdaGCN}.}
Network embedding is a promising way of network representation, facilitating many signed social network processing and analysis tasks such as link prediction and node classification. Recently, feature hashing has been adopted in several existing embedding algorithms to improve the efficiency, which has obtained a great success. However, the existing feature hashing based embedding algorithms only consider the positive links in signed social networks. Intuitively, negative links can also help improve the performance. Thus, in this paper, we propose a novel deep hashing method for signed social network embedding by considering simultaneously positive and negative links. Extensive experiments show that the proposed method performs better than several state-of-the-art baselines through link prediction task over two real-world signed social networks.