A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications

Cai, Hongyun; Zheng, Vincent W.; Chang, Kevin Chen-Chuan

doi:10.48550/arxiv.1709.07604

Cited by 21 publications

(26 citation statements)

References 95 publications

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“…Thus, the number of units in input layer is 𝑑 𝑧 , and the number of units in output layer is 𝑑 𝑜 = 𝑛 𝑔 ×𝑛 𝑚𝑖𝑛 . For better understanding, we convert the output vector ì 𝑜 ∈ 𝑅 𝑑 𝑜 into the matrix form 𝑂 ∈ 𝑅 𝑛 𝑔 ×𝑛 𝑚𝑖𝑛 , and then we apply 𝑠𝑜 𝑓 𝑡𝑚𝑎𝑥 (𝑂 𝑖 ) function to normalize each row in 𝑂 as equation (2):…”

Section: Graphgenerator (G)mentioning

confidence: 99%

“…Network data, consisting of nodes (objects) and edges (objects' relationships), is ubiquitous in many real-world problems, such as social networks, protein-protein interaction networks, citation networks and so on. Recently, network embedding [2,4,42] techniques, which map the nodes of the original networks into the dense and low-dimensional vectors (called node embeddings) and preserve the network structure information as much as possible, have shown promising performance on many network data analysis tasks, such as node classification [19,32], link prediction [11,26], community detection [7] and so on.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, two key challenges of imbalanced network analysis are that: (1) The number of one class examples (minority nodes) is far less than that of other classes (majority nodes) in the network, and the labeling for minority nodes is extremely expensive. (2) The minority nodes are non-separability from the majority nodes, that is, it is difficult to find the support regions of majority and minority nodes in the networks (as shown in Figure 1(a)). To address the above challenges, we propose a semi-supervised generative adversarial graph network model, called ImGAGN.…”

Section: Introductionmentioning

confidence: 99%

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ImGAGN:Imbalanced Network Embedding via Generative Adversarial Graph Networks

Qu,

Zhu,

Zheng

et al. 2021

Preprint

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Imbalanced classification on graphs is ubiquitous yet challenging in many real-world applications, such as fraudulent node detection. Recently, graph neural networks (GNNs) have shown promising performance on many network analysis tasks. However, most existing GNNs have almost exclusively focused on the balanced networks, and would get unappealing performance on the imbalanced networks. To bridge this gap, in this paper, we present a generative adversarial graph network model, called ImGAGN to address the imbalanced classification problem on graphs. It introduces a novel generator for graph structure data, named GraphGenerator, which can simulate both the minority class nodes' attribute distribution and network topological structure distribution by generating a set of synthetic minority nodes such that the number of nodes in different classes can be balanced. Then a graph convolutional network (GCN) discriminator is trained to discriminate between real nodes and fake (i.e., generated) nodes, and also between minority nodes and majority nodes on the synthetic balanced network. To validate the effectiveness of the proposed method, extensive experiments are conducted on four real-world imbalanced network datasets. Experimental results demonstrate that the proposed method Im-GAGN outperforms state-of-the-art algorithms for semi-supervised imbalanced node classification task. CCS CONCEPTS• Computing methodologies → Neural networks.

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Section: Graphgenerator (G)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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ImGAGN:Imbalanced Network Embedding via Generative Adversarial Graph Networks

Qu,

Zhu,

Zheng

et al. 2021

Preprint

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“…A comprehensive survey of knowledge graph embedding models is out of the scope of this paper. Recent surveys such as (Nickel et al, 2016a) and (Cai et al, 2017) summarize recent literature.…”

Section: Related Workmentioning

confidence: 99%

Probability Calibration for Knowledge Graph Embedding Models

Tabacof,

Costabello

2019

Preprint

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Knowledge graph embedding research has overlooked the problem of probability calibration. We show popular embedding models are indeed uncalibrated. That means probability estimates associated to predicted triples are unreliable. We present a novel method to calibrate a model when ground truth negatives are not available, which is the usual case in knowledge graphs. We propose to use Platt scaling and isotonic regression alongside our method. Experiments on three datasets with ground truth negatives show our contribution leads to well calibrated models when compared to the gold standard of using negatives. We get significantly better results than the uncalibrated models from all calibration methods. We show isotonic regression offers the best the performance overall, not without trade-offs. We also show that calibrated models reach state-of-the-art accuracy without the need to define relation-specific decision thresholds. INTRODUCTIONKnowledge graph embedding models are neural architectures that learn vector representations (i.e. embeddings) of nodes and edges of a knowledge graph. Such knowledge graph embeddings have applications in knowledge graph completion, knowledge discovery, entity resolution, and link-based clustering, just to cite a few (Nickel et al., 2016a).Despite burgeoning research, the problem of calibrating such models has been overlooked, and existing knowledge graph embedding models do not offer any guarantee on the probability estimates they assign to predicted facts. Probability calibration is important whenever you need the predictions to make probabilistic sense, i.e., if the model predicts a fact is true with 80% confidence, it should to be correct 80% of the times. Prior art suggests to use a sigmoid layer to turn logits returned by models into probabilities (Nickel et al., 2016a) (also called the expit transform), but we show that this provides poor calibration. Figure 1 shows reliability diagrams for off-the-shelf TransE and ComplEx. The identity function represents perfect calibration. Both models are miscalibrated: all TransE combinations in Figure 1a under-forecast the probabilities (i.e. probabilities are too small), whereas ComplEx under-forecasts or over-forecasts according to which loss is used (Figure1b).Calibration is crucial in high-stakes scenarios such as drug-target discovery from biological networks, where end-users need trustworthy and interpretable decisions. Moreover, since probabilities are not calibrated, when classifying triples (i.e. facts) as true or false, users must define relationspecific thresholds, which can be awkward for graphs with a great number of relation types.

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“…There are also works [8,37] trying to use deep learning techniques to learn node representations. Two recent surveys provide comprehensive overviews on graph representation learning algorithms [7,13]. Recently, there are also some network embedding methods [28,32] designed for multi-dimensional graphs.…”

Section: Related Workmentioning

confidence: 99%

Multi-dimensional Graph Convolutional Networks

Ma¹,

Wang²,

Aggarwal³

et al. 2018

Preprint

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Convolutional neural networks (CNNs) leverage the great power in representation learning on regular grid data such as image and video. Recently, increasing attention has been paid on generalizing CNNs to graph or network data which is highly irregular. Some focus on graph-level representation learning while others aim to learn node-level representations. These methods have been shown to boost the performance of many graph-level tasks such as graph classification and node-level tasks such as node classification. Most of these methods have been designed for single-dimensional graphs where a pair of nodes can only be connected by one type of relation. However, many real-world graphs have multiple types of relations and they can be naturally modeled as multi-dimensional graphs with each type of relation as a dimension. Multi-dimensional graphs bring about richer interactions between dimensions, which poses tremendous challenges to the graph convolutional neural networks designed for single-dimensional graphs. In this paper, we study the problem of graph convolutional networks for multi-dimensional graphs and propose a multi-dimensional convolutional neural network model mGCN aiming to capture rich information in learning node-level representations for multi-dimensional graphs. Comprehensive experiments on real-world multi-dimensional graphs demonstrate the effectiveness of the proposed framework.

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A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications

Cited by 21 publications

References 95 publications

ImGAGN:Imbalanced Network Embedding via Generative Adversarial Graph Networks

ImGAGN:Imbalanced Network Embedding via Generative Adversarial Graph Networks

Probability Calibration for Knowledge Graph Embedding Models

Multi-dimensional Graph Convolutional Networks

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