We examine two fundamental tasks associated with graph representation learning: link prediction and semi-supervised node classification. We present a densely connected autoencoder architecture capable of learning a joint representation of both local graph structure and available external node features for the multi-task learning of link prediction and node classification. To the best of our knowledge, this is the first architecture that can be efficiently trained end-to-end in a single learning stage to simultaneously perform link prediction and node classification. We provide comprehensive empirical evaluation of our models on a range of challenging benchmark graph-structured datasets, and demonstrate significant improvement in accuracy over related methods for graph representation learning. Code implementation is available at this https URL
The field of graph representation learning is seeing a resurgence of research interest in recent years, driven in part by the latest advances in deep learning. The aim is to learn a mapping that encodes the input graph into low-dimensional feature embeddings while preserving its original global structure. @cite_14 succinctly articulate the diverse set of previously proposed approaches for graph representation learning, or graph embedding, as belonging within a unified encoder-decoder framework. In this section, we summarize three classes of encoder-decoder models most related to our work: matrix factorization (MF), autoencoders, and graph convolutional networks (GCNs).
@cite_14
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We propose a novel subgraph image representation for classification of network fragments with the target being their parent networks. The graph image representation is based on 2D image embeddings of adjacency matrices. We use this image representation in two modes. First, as the input to a machine learning algorithm. Second, as the input to a pure transfer learner. Our conclusions from multiple datasets are that 1. deep learning using structured image features performs the best compared to graph kernel and classical features based methods; and, 2. pure transfer learning works effectively with minimum interference from the user and is robust against small data. Celebrated and its fruitful variants are powerful models to achieve excellent performance on the tasks that map sequences to sequences. However, these are many machine learning tasks with inputs naturally represented in a form of graphs, which imposes significant challenges to existing Seq2Seq models for lossless conversion from its graph form to the sequence. In this work, we present a general end-to-end approach to map the input graph to a sequence of vectors, and then another attention-based LSTM to decode the target sequence from these vectors. Specifically, to address inevitable information loss for data conversion, we introduce a novel graph-to-sequence neural network model that follows the encoder-decoder architecture. Our method first uses an improved graph-based neural network to generate the node and graph embeddings by a novel aggregation strategy to incorporate the edge direction information into the node embeddings. We also propose an attention based mechanism that aligns node embeddings and decoding sequence to better cope with large graphs. Experimental results on bAbI task, Shortest Path Task, and Natural Language Generation Task demonstrate that our model achieves the state-of-the-art performance and significantly outperforms other baselines. We also show that with the proposed aggregation strategy, our proposed model is able to quickly converge to good performance. Learning 3D global features by aggregating multiple views has been introduced as a successful strategy for 3D shape analysis. In recent deep learning models with end-to-end training, pooling is a widely adopted procedure for view aggregation. However, pooling merely retains the max or mean value over all views, which disregards the content information of almost all views and also the spatial information among the views. To resolve these issues, we propose Sequential Views To Sequential Labels (SeqViews2SeqLabels) as a novel deep learning model with an encoder–decoder structure based on recurrent neural networks (RNNs) with attention. SeqViews2SeqLabels consists of two connected parts, an encoder-RNN followed by a decoder-RNN, that aim to learn the global features by aggregating sequential views and then performing shape classification from the learned global features, respectively. Specifically, the encoder-RNN learns the global features by simultaneously encoding the spatial and content information of sequential views, which captures the semantics of the view sequence. With the proposed prediction of sequential labels, the decoder-RNN performs more accurate classification using the learned global features by predicting sequential labels step by step. Learning to predict sequential labels provides more and finer discriminative information among shape classes to learn, which alleviates the overfitting problem inherent in training using a limited number of 3D shapes. Moreover, we introduce an attention mechanism to further improve the discriminative ability of SeqViews2SeqLabels. This mechanism increases the weight of views that are distinctive to each shape class, and it dramatically reduces the effect of selecting the first view position. Shape classification and retrieval results under three large-scale benchmarks verify that SeqViews2SeqLabels learns more discriminative global features by more effectively aggregating sequential views than state-of-the-art methods. Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN. Graph-based representations are of broad use and applicability in pattern recognition. They exhibit, however, a major drawback with regards to the processing tools that are available in their domain. Graph embedding into vector spaces is a growing field among the structural pattern recognition community which aims at providing a feature vector representation for every graph, and thus enables classical statistical learning machinery to be used on graph-based input patterns. In this work, we propose a novel embedding methodology for graphs with continuous node attributes and unattributed edges. The approach presented in this paper is based on statistics of the node labels and the edges between them, based on their similarity to a set of representatives. We specifically deal with an important issue of this methodology, namely, the selection of a suitable set of representatives. In an experimental evaluation, we empirically show the advantages of this novel approach in the context of different classification problems using several databases of graphs. Learning low-dimensional representations of networks has proved effective in a variety of tasks such as node classification, link prediction and network visualization. Existing methods can effectively encode different structural properties into the representations, such as neighborhood connectivity patterns, global structural role similarities and other high-order proximities. However, except for objectives to capture network structural properties, most of them suffer from lack of additional constraints for enhancing the robustness of representations. In this paper, we aim to exploit the strengths of generative adversarial networks in capturing latent features, and investigate its contribution in learning stable and robust graph representations. Specifically, we propose an Adversarial Network Embedding (ANE) framework, which leverages the adversarial learning principle to regularize the representation learning. It consists of two components, i.e., a structure preserving component and an adversarial learning component. The former component aims to capture network structural properties, while the latter contributes to learning robust representations by matching the posterior distribution of the latent representations to given priors. As shown by the empirical results, our method is competitive with or superior to state-of-the-art approaches on benchmark network embedding tasks. Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10 accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets. Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10 accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark datasets. Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a low-dimensional vector space, followed by using some scheme to aggregate the node embeddings. In this work, we develop a new approach to learn graph-level representations, which includes a combination of unsupervised and supervised learning components. We start by learning a set of node representations in an unsupervised fashion. Graph nodes are mapped into node sequences sampled from random walk approaches approximated by the Gumbel-Softmax distribution. Recurrent neural network (RNN) units are modified to accommodate both the node representations as well as their neighborhood information. Experiments on standard graph classification benchmarks demonstrate that our proposed approach achieves superior or comparable performance relative to the state-of-the-art algorithms in terms of convergence speed and classification accuracy. We further illustrate the effectiveness of the different components used by our approach. Graph Convolutional Networks (GCNs) have shown significant improvements in semi-supervised learning on graph-structured data. Concurrently, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper, we propose a model: Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-GCN model improves state-of-the-art baselines on all of the challenging node classification tasks we consider: Cora, Citeseer, Pubmed, and PPI. In addition, our proposed method has other desirable properties, including generalization to recently proposed semi-supervised learning methods such as GraphSAGE, allowing us to propose N-SAGE, and resilience to adversarial input perturbations. Learning rich visual representations often require training on datasets of millions of manually annotated examples. This substantially limits the scalability of learning effective representations as labeled data is expensive or scarce. In this paper, we address the problem of unsupervised visual representation learning from a large, unlabeled collection of images. By representing each image as a node and each nearest-neighbor matching pair as an edge, our key idea is to leverage graph-based analysis to discover positive and negative image pairs (i.e., pairs belonging to the same and different visual categories). Specifically, we propose to use a cycle consistency criterion for mining positive pairs and geodesic distance in the graph for hard negative mining. We show that the mined positive and negative image pairs can provide accurate supervisory signals for learning effective representations using Convolutional Neural Networks (CNNs). We demonstrate the effectiveness of the proposed unsupervised constraint mining method in two settings: (1) unsupervised feature learning and (2) semi-supervised learning. For unsupervised feature learning, we obtain competitive performance with several state-of-the-art approaches on the PASCAL VOC 2007 dataset. For semi-supervised learning, we show boosted performance by incorporating the mined constraints on three image classification datasets. Deep learning on graphs has become a popular research topic with many applications. However, past work has concentrated on learning graph embedding tasks only, which is in contrast with advances in generative models for images and text. Is it possible to transfer this progress to the domain of graphs? We propose to sidestep hurdles associated with linearization of such discrete structures by having a decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. Our method is formulated as a variational autoencoder. We evaluate on the challenging task of conditional molecule generation. It is always well believed that modeling relationships between objects would be helpful for representing and eventually describing an image. Nevertheless, there has not been evidence in support of the idea on image description generation. In this paper, we introduce a new design to explore the connections between objects for image captioning under the umbrella of attention-based encoder-decoder framework. Specifically, we present Graph Convolutional Networks plus Long Short-Term Memory (dubbed as GCN-LSTM) architecture that novelly integrates both semantic and spatial object relationships into image encoder. Technically, we build graphs over the detected objects in an image based on their spatial and semantic connections. The representations of each region proposed on objects are then refined by leveraging graph structure through GCN. With the learnt region-level features, our GCN-LSTM capitalizes on LSTM-based captioning framework with attention mechanism for sentence generation. Extensive experiments are conducted on COCO image captioning dataset, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, GCN-LSTM increases CIDEr-D performance from 120.1 to 128.7 on COCO testing set. Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semisupervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires a considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits. First, we show that the graph convolution of the GCN model is actually a special form of Laplacian smoothing, which is the key reason why GCNs work, but it also brings potential concerns of over-smoothing with many convolutional layers. Second, to overcome the limits of the GCN model with shallow architectures, we propose both co-training and self-training approaches to train GCNs. Our approaches significantly improve GCNs in learning with very few labels, and exempt them from requiring additional labels for validation. Extensive experiments on benchmarks have verified our theory and proposals. We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine learning tasks. Unlike previous work, we (1) explicitly model an edge as a function of node embeddings, and we (2) propose a novel objective, the graph likelihood, which contrasts information from sampled random walks with non-existent edges. Individually, both of these contributions improve the learned representations, especially when there are memory constraints on the total size of the embeddings. When combined, our contributions enable us to significantly improve the state-of-the-art by learning more concise representations that better preserve the graph structure. We evaluate our method on a variety of link-prediction task including social networks, collaboration networks, and protein interactions, showing that our proposed method learn representations with error reductions of up to 76 and 55 , on directed and undirected graphs. In addition, we show that the representations learned by our method are quite space efficient, producing embeddings which have higher structure-preserving accuracy but are 10 times smaller. In this paper, we propose a novel model for learning graph representations, which generates a low-dimensional vector representation for each vertex by capturing the graph structural information. Different from other previous research efforts, we adopt a random surfing model to capture graph structural information directly, instead of using the sampling-based method for generating linear sequences proposed by (2014). The advantages of our approach will be illustrated from both theorical and empirical perspectives. We also give a new perspective for the matrix factorization method proposed by Levy and Goldberg (2014), in which the pointwise mutual information (PMI) matrix is considered as an analytical solution to the objective function of the skip-gram model with negative sampling proposed by (2013). Unlike their approach which involves the use of the SVD for finding the low-dimensitonal projections from the PMI matrix, however, the stacked denoising autoencoder is introduced in our model to extract complex features and model non-linearities. To demonstrate the effectiveness of our model, we conduct experiments on clustering and visualization tasks, employing the learned vertex representations as features. Empirical results on datasets of varying sizes show that our model outperforms other stat-of-the-art models in such tasks. We consider learning representations (features) in the setting in which we have access to multiple unlabeled views of the data for representation learning while only one view is available at test time. Previous work on this problem has proposed several techniques based on deep neural networks, typically involving either autoencoder-like networks with a reconstruction objective or paired feedforward networks with a correlation-based objective. We analyze several techniques based on prior work, as well as new variants, and compare them experimentally on visual, speech, and language domains. To our knowledge this is the first head-to-head comparison of a variety of such techniques on multiple tasks. We find an advantage for correlation-based representation learning, while the best results on most tasks are obtained with our new variant, deep canonically correlated autoencoders (DCCAE). 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 as well as the skip-gram model with negative sampling of 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. Modern deep transfer learning approaches have mainly focused on learning generic feature vectors from one task that are transferable to other tasks, such as word embeddings in language and pretrained convolutional features in vision. However, these approaches usually transfer unary features and largely ignore more structured graphical representations. This work explores the possibility of learning generic latent relational graphs that capture dependencies between pairs of data units (e.g., words or pixels) from large-scale unlabeled data and transferring the graphs to downstream tasks. Our proposed transfer learning framework improves performance on various tasks including question answering, natural language inference, sentiment analysis, and image classification. We also show that the learned graphs are generic enough to be transferred to different embeddings on which the graphs have not been trained (including GloVe embeddings, ELMo embeddings, and task-specific RNN hidden unit), or embedding-free units such as image pixels. Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the latent codes from the graphs, which often results in inferior embedding in real-world graph data. In this paper, we propose a novel adversarial graph embedding framework for graph data. The framework encodes the topological structure and node content in a graph to a compact representation, on which a decoder is trained to reconstruct the graph structure. Furthermore, the latent representation is enforced to match a prior distribution via an adversarial training scheme. To learn a robust embedding, two variants of adversarial approaches, adversarially regularized graph autoencoder (ARGA) and adversarially regularized variational graph autoencoder (ARVGA), are developed. Experimental studies on real-world graphs validate our design and demonstrate that our algorithms outperform baselines by a wide margin in link prediction, graph clustering, and graph visualization tasks.