The graph convolution network (GCN) is a widely-used facility to realize graph-based semi-supervised learning, which usually integrates node features and graph topologic information to build learning models. However, as for multi-label learning tasks, the supervision part of GCN simply minimizes the cross-entropy loss between the last layer outputs and the ground-truth label distribution, which tends to lose some useful information such as label correlations, so that prevents from obtaining high performance. In this paper, we pro-pose a novel GCN-based semi-supervised learning approach for multi-label classification, namely ML-GCN. ML-GCN first uses a GCN to embed the node features and graph topologic information. Then, it randomly generates a label matrix, where each row (i.e., label vector) represents a kind of labels. The dimension of the label vector is the same as that of the node vector before the last convolution operation of GCN. That is, all labels and nodes are embedded in a uniform vector space. Finally, during the ML-GCN model training, label vectors and node vectors are concatenated to serve as the inputs of the relaxed skip-gram model to detect the node-label correlation as well as the label-label correlation. Experimental results on several graph classification datasets show that the proposed ML-GCN outperforms four state-of-the-art methods.
Comprehensibility of source code is strongly affected by identifier names, therefore software developers need to give good (e.g. meaningful but short) names to identifiers. On the other hand, giving a good name is sometimes a difficult and time-consuming task even for experienced developers. To support naming identifiers, several techniques for recommending identifier name candidates have been proposed. These techniques, however, still have challenges on the goodness of suggested candidates and limitations on applicable situations. This paper proposes a new approach to recommending method names by applying graph embedding techniques to the method call graph. The evaluation experiment confirms that the proposed technique can suggest more appropriate method name candidates in difficult situations than the state of the art approach.
Graph Convolutional Networks (GCNs) are powerful models for learning representations of attributed graphs. To scale GCNs to large graphs, state-of-the-art methods use various layer sampling techniques to alleviate the "neighbor explosion" problem during minibatch training. We propose GraphSAINT, a graph sampling based inductive learning method that improves training efficiency and accuracy in a fundamentally different way. By changing perspective, GraphSAINT constructs minibatches by sampling the training graph, rather than the nodes or edges across GCN layers. Each iteration, a complete GCN is built from the properly sampled subgraph. Thus, we ensure fixed number of well-connected nodes in all layers. We further propose normalization technique to eliminate bias, and sampling algorithms for variance reduction. Importantly, we can decouple the sampling from the forward and backward propagation, and extend GraphSAINT with many architecture variants (e.g., graph attention, jumping connection). GraphSAINT demonstrates superior performance in both accuracy and training time on five large graphs, and achieves new state-of-the-art F1 scores for PPI (0.995) and Reddit (0.970).
Attention operators have been widely applied in various fields, including computer vision, natural language processing, and network embedding learning. Attention operators on graph data enables learnable weights when aggregating information from neighboring nodes. However, graph attention operators (GAOs) consume excessive computational resources, preventing their applications on large graphs. In addition, GAOs belong to the family of soft attention, instead of hard attention, which has been shown to yield better performance. In this work, we propose novel hard graph attention operator (hGAO) and channel-wise graph attention operator (cGAO). hGAO uses the hard attention mechanism by attending to only important nodes. Compared to GAO, hGAO improves performance and saves computational cost by only attending to important nodes. To further reduce the requirements on computational resources, we propose the cGAO that performs attention operations along channels. cGAO avoids the dependency on the adjacency matrix, leading to dramatic reductions in computational resource requirements. Experimental results demonstrate that our proposed deep models with the new operators achieve consistently better performance. Comparison results also indicates that hGAO achieves significantly better performance than GAO on both node and graph embedding tasks. Efficiency comparison shows that our cGAO leads to dramatic savings in computational resources, making them applicable to large graphs.
Recently, network embedding that encodes structural information of graphs into a vector space has become popular for network analysis. Although recent methods show promising performance for various applications, the huge sizes of graphs may hinder a direct application of existing network embedding method to them. This paper presents NECL, a novel efficient Network Embedding method with two goals. 1) Is there an ideal Compression of a network? 2) Will the compression of a network significantly boost the representation Learning of the network? For the first problem, we propose a neighborhood similarity based graph compression method that compresses the input graph to get a smaller graph without losing any/much information about the global structure of the graph and the local proximity of the vertices in the graph. For the second problem, we use the compressed graph for network embedding instead of the original large graph to bring down the embedding cost. NECL is a general meta-strategy to improve the efficiency of all of the state-of-the-art graph embedding algorithms based on random walks, including DeepWalk and Node2vec, without losing their effectiveness. Extensive experiments on large real-world networks validate the efficiency of NECL method that yields an average improvement of 23 - 57% embedding time, including walking and learning time without decreasing classification accuracy as evaluated on single and multi-label classification tasks on real-world graphs such as DBLP, BlogCatalog, Cora and Wiki.
Graph embedding is a popular algorithmic approach for creating vector representations for individual vertices in networks. Training these algorithms at scale is important for creating embeddings that can be used for classification, ranking, recommendation and other common applications in industry. While industrial systems exist for training graph embeddings on large datasets, many of these distributed architectures are forced to partition copious amounts of data and model logic across many worker nodes. In this paper, we propose a distributed infrastructure that completely avoids graph partitioning, dynamically creates size constrained computational graphs across worker nodes, and uses highly efficient indexing operations for updating embeddings that allow the system to function at scale. We show that our system can scale an existing embeddings algorithm - skip-gram - to train on the open-source Friendster network (68 million vertices) and on an internal heterogeneous graph (50 million vertices). We measure the performance of our system on two key quantitative metrics: link-prediction accuracy and rate of convergence. We conclude this work by analyzing how a greater number of worker nodes actually improves our system's performance on the aforementioned metrics and discuss our next steps for rigorously evaluating the embedding vectors produced by our system.
Detecting communities on graphs has received significant interest in recent literature. Current state-of-the-art community embedding approach called \textit{ComE} tackles this problem by coupling graph embedding with community detection. Considering the success of hyperbolic representations of graph-structured data in last years, an ongoing challenge is to set up a hyperbolic approach for the community detection problem. The present paper meets this challenge by introducing a Riemannian equivalent of \textit{ComE}. Our proposed approach combines hyperbolic embeddings with Riemannian K-means or Riemannian mixture models to perform community detection. We illustrate the usefulness of this framework through several experiments on real-world social networks and comparisons with \textit{ComE} and recent hyperbolic-based classification approaches.
Exploring the effects a chemical compound has on a species takes a considerable experimental effort. Appropriate methods for estimating and suggesting new effects can dramatically reduce the work needed to be done by a laboratory. In this paper we explore the suitability of using a knowledge graph embedding approach for ecotoxicological effect prediction. A knowledge graph has been constructed from publicly available data sets, including a species taxonomy and chemical classification and similarity. The publicly available effect data is integrated to the knowledge graph using ontology alignment techniques. Our experimental results show that the knowledge graph based approach improves the selected baselines.
Graph alignment, also known as network alignment, is a fundamental task in social network analysis. Many recent works have relied on partially labeled cross-graph node correspondences, i.e., anchor links. However, due to the privacy and security issue, the manual labeling of anchor links for diverse scenarios may be prohibitive. Aligning two graphs without any anchor links is a crucial and challenging task. In this paper, we propose an Unsupervised Adversarial Graph Alignment (UAGA) framework to learn a cross-graph alignment between two embedding spaces of different graphs in a fully unsupervised fashion (\emph{i.e.,} no existing anchor links and no users' personal profile or attribute information is available). The proposed framework learns the embedding spaces of each graph, and then attempts to align the two spaces via adversarial training, followed by a refinement procedure. We further extend our UAGA method to incremental UAGA (iUAGA) that iteratively reveals the unobserved user links based on the pseudo anchor links. This can be used to further improve both the embedding quality and the alignment accuracy. Moreover, the proposed methods will benefit some real-world applications, \emph{e.g.,} link prediction in social networks. Comprehensive experiments on real-world data demonstrate the effectiveness of our proposed approaches UAGA and iUAGA for unsupervised graph alignment.
We study the problem of detecting critical structures using a graph embedding model. Existing graph embedding models lack the ability to precisely detect critical structures that are specific to a task at the global scale. In this paper, we propose a novel graph embedding model, called the Ego-CNNs, that employs the ego-convolutions convolutions at each layer and stacks up layers using an ego-centric way to detects precise critical structures efficiently. An Ego-CNN can be jointly trained with a task model and help explain/discover knowledge for the task. We conduct extensive experiments and the results show that Ego-CNNs (1) can lead to comparable task performance as the state-of-the-art graph embedding models, (2) works nicely with CNN visualization techniques to illustrate the detected structures, and (3) is efficient and can incorporate with scale-free priors, which commonly occurs in social network datasets, to further improve the training efficiency.
Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is the Markov Logic Network (MLN), which is able to leverage domain knowledge with first-order logic and meanwhile handle their uncertainty. However, the inference of MLNs is usually very difficult due to the complicated graph structures. Different from MLNs, knowledge graph embedding methods (e.g. TransE, DistMult) learn effective entity and relation embeddings for reasoning, which are much more effective and efficient. However, they are unable to leverage domain knowledge. In this paper, we propose the probabilistic Logic Neural Network (pLogicNet), which combines the advantages of both methods. A pLogicNet defines the joint distribution of all possible triplets by using a Markov logic network with first-order logic, which can be efficiently optimized with the variational EM algorithm. In the E-step, a knowledge graph embedding model is used for inferring the missing triplets, while in the M-step, the weights of logic rules are updated based on both the observed and predicted triplets. Experiments on multiple knowledge graphs prove the effectiveness of pLogicNet over many competitive baselines.
Graph clustering is a fundamental task which discovers communities or groups in networks. Recent studies have mostly focused on developing deep learning approaches to learn a compact graph embedding, upon which classic clustering methods like k-means or spectral clustering algorithms are applied. These two-step frameworks are difficult to manipulate and usually lead to suboptimal performance, mainly because the graph embedding is not goal-directed, i.e., designed for the specific clustering task. In this paper, we propose a goal-directed deep learning approach, Deep Attentional Embedded Graph Clustering (DAEGC for short). Our method focuses on attributed graphs to sufficiently explore the two sides of information in graphs. By employing an attention network to capture the importance of the neighboring nodes to a target node, our DAEGC algorithm encodes the topological structure and node content in a graph to a compact representation, on which an inner product decoder is trained to reconstruct the graph structure. Furthermore, soft labels from the graph embedding itself are generated to supervise a self-training graph clustering process, which iteratively refines the clustering results. The self-training process is jointly learned and optimized with the graph embedding in a unified framework, to mutually benefit both components. Experimental results compared with state-of-the-art algorithms demonstrate the superiority of our method.
We introduce a nonlinear method for directly embedding large, sparse, stochastic graphs into low-dimensional spaces, without requiring vertex features to reside in, or be transformed into, a metric space. Graph data and models are prevalent in real-world applications. Direct graph embedding is fundamental to many graph analysis tasks, in addition to graph visualization. We name the novel approach SG-t-SNE, as it is inspired by and builds upon the core principle of t-SNE, a widely used method for nonlinear dimensionality reduction and data visualization. We also introduce t-SNE-$\Pi$, a high-performance software for 2D, 3D embedding of large sparse graphs on personal computers with superior efficiency. It empowers SG-t-SNE with modern computing techniques for exploiting in tandem both matrix structures and memory architectures. We present elucidating embedding results on one synthetic graph and four real-world networks.
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.
Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these objectives are achieved, they are meaningful, understandable, and compressed representations of networks. They also provide more options and tools for data scientists as machine learning on graphs is still quite limited. Finally, vector operations are simpler and faster than comparable operations on graphs. The main challenge is that one needs to make sure that embeddings well describe the properties of the graphs. In particular, the decision has to be made on the embedding dimensionality which highly impacts the quality of an embedding. As a result, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we propose a ``divergence score'' that can be assign to various embeddings to distinguish good ones from bad ones. This general framework provides a tool for an unsupervised graph embedding comparison. In order to achieve it, we needed to generalize the well-known Chung-Lu model to incorporate geometry which is interesting on its own rights. In order to test our framework, we did a number of experiments with synthetic networks as well as real-world networks, and various embedding algorithms.
With the tide of artificial intelligence, we try to apply deep learning to understand 3D data. Point cloud is an important 3D data structure, which can accurately and directly reflect the real world. In this paper, we propose a simple and effective network, which is named PyramNet, suites for point cloud object classification and semantic segmentation in 3D scene. We design two new operators: Graph Embedding Module(GEM) and Pyramid Attention Network(PAN). Specifically, GEM projects point cloud onto the graph and practices the covariance matrix to explore the relationship between points, so as to improve the local feature expression ability of the model. PAN assigns some strong semantic features to each point to retain fine geometric features as much as possible. Furthermore, we provide extensive evaluation and analysis for the effectiveness of PyramNet. Empirically, we evaluate our model on ModelNet40, ShapeNet and S3DIS.
Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs is an ongoing research problem. The objective of this survey is to summarize and discuss the latest advances in methods to Learn Representations of Graph Data. We start by identifying commonly used types of graph data and review basics of graph theory. This is followed by a discussion of the relationships between graph kernel methods and neural networks. Next we identify the major approaches used for learning representations of graph data namely: Kernel approaches, Convolutional approaches, Graph neural networks approaches, Graph embedding approaches and Probabilistic approaches. A variety of methods under each of the approaches are discussed and the survey is concluded with a brief discussion of the future of learning representation of graph data.
Recently, neural models for information retrieval are becoming increasingly popular. They provide effective approaches for product search due to their competitive advantages in semantic matching. However, it is challenging to use graph-based features, though proved very useful in IR literature, in these neural approaches. In this paper, we leverage the recent advances in graph embedding techniques to enable neural retrieval models to exploit graph-structured data for automatic feature extraction. The proposed approach can not only help to overcome the long-tail problem of click-through data, but also incorporate external heterogeneous information to improve search results. Extensive experiments on a real-world e-commerce dataset demonstrate significant improvement achieved by our proposed approach over multiple strong baselines both as an individual retrieval model and as a feature used in learning-to-rank frameworks.