The over-smoothing problem is an obstacle of developing deep graph neural network (GNN). Although many approaches to improve the over-smoothing problem have been proposed, there is still a lack of comprehensive understanding and conclusion of this problem. In this work, we analyze the over-smoothing problem from the Markov chain perspective. We focus on message passing of GNN and first establish a connection between GNNs and Markov chains on the graph. GNNs are divided into two classes of operator-consistent and operator-inconsistent based on whether the corresponding Markov chains are time-homogeneous. Next we attribute the over-smoothing problem to the convergence of an arbitrary initial distribution to a stationary distribution. Based on this, we prove that although the previously proposed methods can alleviate over-smoothing, but these methods cannot avoid the over-smoothing problem. In addition, we give the conclusion of the over-smoothing problem in two types of GNNs in the Markovian sense. On the one hand, operator-consistent GNN cannot avoid over-smoothing at an exponential rate. On the other hand, operator-inconsistent GNN is not always over-smoothing. Further, we investigate the existence of the limiting distribution of the time-inhomogeneous Markov chain, from which we derive a sufficient condition for operator-inconsistent GNN to avoid over-smoothing. Finally, we design experiments to verify our findings. Results show that our proposed sufficient condition can effectively improve over-smoothing problem in operator-inconsistent GNN and enhance the performance of the model.
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Graph clustering, which aims to divide the nodes in the graph into several distinct clusters, is a fundamental and challenging task. In recent years, deep graph clustering methods have been increasingly proposed and achieved promising performance. However, the corresponding survey paper is scarce and it is imminent to make a summary in this field. From this motivation, this paper makes the first comprehensive survey of deep graph clustering. Firstly, the detailed definition of deep graph clustering and the important baseline methods are introduced. Besides, the taxonomy of deep graph clustering methods is proposed based on four different criteria including graph type, network architecture, learning paradigm, and clustering method. In addition, through the careful analysis of the existing works, the challenges and opportunities from five perspectives are summarized. At last, the applications of deep graph clustering in four domains are presented. It is worth mentioning that a collection of state-of-the-art deep graph clustering methods including papers, codes, and datasets is available on GitHub. We hope this work will serve as a quick guide and help researchers to overcome challenges in this vibrant field.
Clustering is a fundamental machine learning task which has been widely studied in the literature. Classic clustering methods follow the assumption that data are represented as features in a vectorized form through various representation learning techniques. As the data become increasingly complicated and complex, the shallow (traditional) clustering methods can no longer handle the high-dimensional data type. With the huge success of deep learning, especially the deep unsupervised learning, many representation learning techniques with deep architectures have been proposed in the past decade. Recently, the concept of Deep Clustering, i.e., jointly optimizing the representation learning and clustering, has been proposed and hence attracted growing attention in the community. Motivated by the tremendous success of deep learning in clustering, one of the most fundamental machine learning tasks, and the large number of recent advances in this direction, in this paper we conduct a comprehensive survey on deep clustering by proposing a new taxonomy of different state-of-the-art approaches. We summarize the essential components of deep clustering and categorize existing methods by the ways they design interactions between deep representation learning and clustering. Moreover, this survey also provides the popular benchmark datasets, evaluation metrics and open-source implementations to clearly illustrate various experimental settings. Last but not least, we discuss the practical applications of deep clustering and suggest challenging topics deserving further investigations as future directions.
Graph neural networks generalize conventional neural networks to graph-structured data and have received widespread attention due to their impressive representation ability. In spite of the remarkable achievements, the performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry, especially for datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution, owing to its exponential growth property. In this survey, we comprehensively revisit the technical details of the current hyperbolic graph neural networks, unifying them into a general framework and summarizing the variants of each component. More importantly, we present various HGNN-related applications. Last, we also identify several challenges, which potentially serve as guidelines for further flourishing the achievements of graph learning in hyperbolic spaces.
Graph neural networks (GNNs) have been a hot spot of recent research and are widely utilized in diverse applications. However, with the use of huger data and deeper models, an urgent demand is unsurprisingly made to accelerate GNNs for more efficient execution. In this paper, we provide a comprehensive survey on acceleration methods for GNNs from an algorithmic perspective. We first present a new taxonomy to classify existing acceleration methods into five categories. Based on the classification, we systematically discuss these methods and highlight their correlations. Next, we provide comparisons from aspects of the efficiency and characteristics of these methods. Finally, we suggest some promising prospects for future research.
Recently, graph neural networks (GNNs) have been widely used for document classification. However, most existing methods are based on static word co-occurrence graphs without sentence-level information, which poses three challenges:(1) word ambiguity, (2) word synonymity, and (3) dynamic contextual dependency. To address these challenges, we propose a novel GNN-based sparse structure learning model for inductive document classification. Specifically, a document-level graph is initially generated by a disjoint union of sentence-level word co-occurrence graphs. Our model collects a set of trainable edges connecting disjoint words between sentences and employs structure learning to sparsely select edges with dynamic contextual dependencies. Graphs with sparse structures can jointly exploit local and global contextual information in documents through GNNs. For inductive learning, the refined document graph is further fed into a general readout function for graph-level classification and optimization in an end-to-end manner. Extensive experiments on several real-world datasets demonstrate that the proposed model outperforms most state-of-the-art results, and reveal the necessity to learn sparse structures for each document.
Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: \url{//github.com/shivram1987/ActivationFunctions}.
Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.
Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction and graph clustering. However, they expose uncertainty and unreliability against the well-designed inputs, i.e., adversarial examples. Accordingly, various studies have emerged for both attack and defense addressed in different graph analysis tasks, leading to the arms race in graph adversarial learning. For instance, the attacker has poisoning and evasion attack, and the defense group correspondingly has preprocessing- and adversarial- based methods. Despite the booming works, there still lacks a unified problem definition and a comprehensive review. To bridge this gap, we investigate and summarize the existing works on graph adversarial learning tasks systemically. Specifically, we survey and unify the existing works w.r.t. attack and defense in graph analysis tasks, and give proper definitions and taxonomies at the same time. Besides, we emphasize the importance of related evaluation metrics, and investigate and summarize them comprehensively. Hopefully, our works can serve as a reference for the relevant researchers, thus providing assistance for their studies. More details of our works are available at //github.com/gitgiter/Graph-Adversarial-Learning.
Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prospects, transfer learning has become a popular and promising area in machine learning. Although there are already some valuable and impressive surveys on transfer learning, these surveys introduce approaches in a relatively isolated way and lack the recent advances in transfer learning. As the rapid expansion of the transfer learning area, it is both necessary and challenging to comprehensively review the relevant studies. This survey attempts to connect and systematize the existing transfer learning researches, as well as to summarize and interpret the mechanisms and the strategies in a comprehensive way, which may help readers have a better understanding of the current research status and ideas. Different from previous surveys, this survey paper reviews over forty representative transfer learning approaches from the perspectives of data and model. The applications of transfer learning are also briefly introduced. In order to show the performance of different transfer learning models, twenty representative transfer learning models are used for experiments. The models are performed on three different datasets, i.e., Amazon Reviews, Reuters-21578, and Office-31. And the experimental results demonstrate the importance of selecting appropriate transfer learning models for different applications in practice.
Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into different categories. With a focus on graph convolutional networks, we review alternative architectures that have recently been developed; these learning paradigms include graph attention networks, graph autoencoders, graph generative networks, and graph spatial-temporal networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes and benchmarks of the existing algorithms on different learning tasks. Finally, we propose potential research directions in this fast-growing field.
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