# Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels

19 Apr 2021-pp 1204-1214

TL;DR: GSKN1 as mentioned in this paper is a GNN model with a theoretically stronger ability to distinguish graph structures, based on anonymous walks (AWs), flexible substructure units, and derive it upon feature mappings of graph kernels (GKs).

Abstract: Graph neural networks (GNNs) have achieved tremendous success in graph mining. However, the inability of GNNs to model substructures in graphs remains a significant drawback. Specifically, message-passing GNNs (MPGNNs), as the prevailing type of GNNs, have been theoretically shown unable to distinguish, detect or count many graph substructures. While efforts have been paid to complement the inability, existing works either rely on pre-defined substructure sets, thus being less flexible, or are lacking in theoretical insights. In this paper, we propose GSKN1, a GNN model with a theoretically stronger ability to distinguish graph structures. Specifically, we design GSKN based on anonymous walks (AWs), flexible substructure units, and derive it upon feature mappings of graph kernels (GKs). We theoretically show that GSKN provably extends the 1-WL test, and hence the maximally powerful MPGNNs from both graph-level and node-level viewpoints. Correspondingly, various experiments are leveraged to evaluate GSKN, where GSKN outperforms a wide range of baselines, endorsing the analysis.

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TL;DR: In this article , a graph harmonic neural network (GHNN) is proposed to combine the advantages of both graph convolutional networks and graph kernels to leverage the unlabeled data, and thus overcomes label scarcity in semi-supervised scenarios.

14 citations

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TL;DR: An overview of non-GNN graph embedding methods, which are based on techniques such as random walks, temporal point processes and neural network learning methods, and GNN-based methods which are the application of deep learning on graph data are provided.

Abstract: Graphs representation learning has been a very active research area in recent years. The goal of graph representation learning is to generate graph representation vectors that capture the structure and features of large graphs accurately. This is especially important because the quality of the graph representation vectors will affect the performance of these vectors in downstream tasks such as node classification, link prediction and anomaly detection. Many techniques are proposed for generating effective graph representation vectors. Two of the most prevalent categories of graph representation learning are graph embedding methods without using graph neural nets (GNN), which we denote as non-GNN based graph embedding methods, and graph neural nets (GNN) based methods. Non-GNN graph embedding methods are based on techniques such as random walks, temporal point processes and neural network learning methods. GNN-based methods, on the other hand, are the application of deep learning on graph data. In this survey, we provide an overview of these two categories and cover the current state-of-the-art methods for both static and dynamic graphs. Finally, we explore some open and ongoing research directions for future work.

11 citations

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25 Apr 2022

TL;DR: Inspired by the idea of attitude polarization in social psychology, that people tend to be more extreme when exposed to an opposite opinion, Polarized Graph Neural Network (Polar-GNN) is proposed, which effectively exploits both similarities and dissimilarities.

Abstract: Despite the recent success of Message-passing Graph Neural Networks (MP-GNNs), the strong inductive bias of homophily limits their ability to generalize to heterophilic graphs and leads to the over-smoothing problem. Most existing works attempt to mitigate this issue in the spirit of emphasizing the contribution from similar neighbors and reducing those from dissimilar ones when performing aggregation, where the dissimilarities are utilized passively and their positive effects are ignored, leading to suboptimal performances. Inspired by the idea of attitude polarization in social psychology, that people tend to be more extreme when exposed to an opposite opinion, we propose Polarized Graph Neural Network (Polar-GNN). Specifically, pairwise similarities and dissimilarities of nodes are firstly modeled with node features and topological structure information. And specially, we assign negative weights for those dissimilar ones. Then nodes aggregate the messages on a hyper-sphere through a polarization operation, which effectively exploits both similarities and dissimilarities. Furthermore, we theoretically demonstrate the validity of the proposed operation. Lastly, an elaborately designed loss function is introduced for the hyper-spherical embedding space. Extensive experiments on real-world datasets verify the effectiveness of our model.

5 citations

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01 Jul 2022

TL;DR: This paper proposes a novel semi-supervised graph classification framework called Twin Graph Neural Network (TGNN), which has two twin modules that collaborate with each other by exchanging instance similarity knowledge to fully explore the structure information of both labeled and unlabeled data.

Abstract: This paper studies semi-supervised graph classification, a crucial task with a wide range of applications in social network analysis and bioinformatics. Recent works typically adopt graph neural networks to learn graph-level representations for classification, failing to explicitly leverage features derived from graph topology (e.g., paths). Moreover, when labeled data is scarce, these methods are far from satisfactory due to their insufficient topology exploration of unlabeled data. We address the challenge by proposing a novel semi-supervised framework called Twin Graph Neural Network (TGNN). To explore graph structural information from complementary views, our TGNN has a message passing module and a graph kernel module. To fully utilize unlabeled data, for each module, we calculate the similarity of each unlabeled graph to other labeled graphs in the memory bank and our consistency loss encourages consistency between two similarity distributions in different embedding spaces. The two twin modules collaborate with each other by exchanging instance similarity knowledge to fully explore the structure information of both labeled and unlabeled data. We evaluate our TGNN on various public datasets and show that it achieves strong performance.

4 citations

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TL;DR: Graph-level learning has been widely applied in many tasks including comparison, regression, classiﬁcation, and more as discussed by the authors , however, there is no comprehensive survey that reviews graph level learning starting with traditional learning and moving through to the deep learning approaches.

Abstract: —Graphs have a superior ability to represent re- lational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison, regression, classiﬁcation, and more. Traditional approaches to learning a set of graphs tend to rely on hand-crafted features, such as substructures. But while these methods beneﬁt from good interpretability, they often suffer from computational bottlenecks as they cannot skirt the graph isomorphism problem. Conversely, deep learning has helped graph-level learning adapt to the growing scale of graphs by extracting features automatically and decoding graphs into low-dimensional representations. As a result, these deep graph learning methods have been responsible for many successes. Yet, there is no comprehensive survey that reviews graph-level learning starting with traditional learning and moving through to the deep learning approaches. This article ﬁlls this gap and frames the representative algorithms into a systematic taxonomy covering traditional learning, graph-level deep neural networks, graph-level graph neural networks, and graph pooling. To ensure a thoroughly comprehensive survey, the evolutions, interactions, and communications between methods from four different branches of development are also examined. This is followed by a brief review of the benchmark data sets, evaluation metrics, and common downstream applications. The survey concludes with 13 future directions of necessary research that will help to overcome the challenges facing this booming ﬁeld.

1 citations

##### References

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TL;DR: GraphSAGE is presented, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data and outperforms strong baselines on three inductive node-classification benchmarks.

Abstract: Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.

7,926 citations

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03 Dec 1996TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness

Abstract: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigenvalues and quasi-randomness Expanders and explicit constructions Eigenvalues of symmetrical graphs Eigenvalues of subgraphs with boundary conditions Harnack inequalities Heat kernels Sobolev inequalities Advanced techniques for random walks on graphs Bibliography Index.

6,948 citations

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TL;DR: A new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains, and implements a function tau(G,n) isin IRm that maps a graph G and one of its nodes n into an m-dimensional Euclidean space.

Abstract: Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) isin IRm that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

5,701 citations

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TL;DR: This article provides a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields and proposes a new taxonomy to divide the state-of-the-art GNNs into four categories, namely, recurrent GNNS, convolutional GNN’s, graph autoencoders, and spatial–temporal Gnns.

Abstract: 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 the existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this article, 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 GNNs into four categories, namely, recurrent GNNs, convolutional GNNs, graph autoencoders, and spatial–temporal GNNs. We further discuss the applications of GNNs across various domains and summarize the open-source codes, benchmark data sets, and model evaluation of GNNs. Finally, we propose potential research directions in this rapidly growing field.

4,584 citations

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TL;DR: In this article, a spectral graph theory formulation of convolutional neural networks (CNNs) was proposed to learn local, stationary, and compositional features on graphs, and the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs while being universal to any graph structure.

Abstract: In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

4,562 citations