Semi-supervised learning (SSL) has tremendous value in practice due to its ability to utilize both labeled data and unlabelled data. An important class of SSL methods is to naturally represent data as graphs such that the label information of unlabelled samples can be inferred from the graphs, which corresponds to graph-based semi-supervised learning (GSSL) methods. GSSL methods have demonstrated their advantages in various domains due to their uniqueness of structure, the universality of applications, and their scalability to large scale data. Focusing on this class of methods, this work aims to provide both researchers and practitioners with a solid and systematic understanding of relevant advances as well as the underlying connections among them. This makes our paper distinct from recent surveys that cover an overall picture of SSL methods while neglecting fundamental understanding of GSSL methods. In particular, a major contribution of this paper lies in a new generalized taxonomy for GSSL, including graph regularization and graph embedding methods, with the most up-to-date references and useful resources such as codes, datasets, and applications. Furthermore, we present several potential research directions as future work with insights into this rapidly growing field.

Graph-based Semi-supervised Learning: A Comprehensive Review.

Graph-based Semi-Supervised Learning (SSL) aims to transfer the labels of a handful of labeled data to the remaining massive unlabeled data via a graph. As one of the most popular graph-based SSL approaches, the recently proposed Graph Convolutional Networks (GCNs) have gained remarkable progress by combining the sound expressiveness of neural networks with graph structure. Nevertheless, the existing graph-based methods do not directly address the core problem of SSL, \emph{i.e.}, the shortage of supervision, and thus their performances are still very limited. To accommodate this issue, this paper presents a novel GCN-based SSL algorithm which aims to enrich the supervision signals by utilizing both data similarities and graph structure. Firstly, by designing a semi-supervised contrastive loss, the improved node representations can be generated via maximizing the agreement between different views of the same data or the data from the same class. Therefore, the rich unlabeled data and the scarce yet valuable labeled data can jointly provide abundant supervision information for learning discriminative node representations, which helps improve the subsequent classification result. Secondly, the underlying determinative relationship between the input graph topology and data features is extracted as supplementary supervision signals for SSL via using a graph generative loss related to input features. Intensive experimental results on a variety of real-world datasets firmly verify the effectiveness of our algorithm when compared with other state-of-the-art methods.

/pdf/contrastive-and-generative-graph-convolutional-networks-for-u97oe278qm.pdf

Contrastive and Generative Graph Convolutional Networks for Graph-based Semi-Supervised Learning.

Graph-based Semi-Supervised Learning (SSL) aims to transfer the labels of a handful of labeled data to the remaining massive unlabeled data via a graph. As one of the most popular graph-based SSL approaches, the recently proposed Graph Convolutional Networks (GCNs) have gained remarkable progress by combining the sound expressiveness of neural networks with graph structure. Nevertheless, the existing graph-based methods do not directly address the core problem of SSL, i.e., the shortage of supervision, and thus their performances are still very limited. To accommodate this issue, a novel GCN-based SSL algorithm is presented in this paper to enrich the supervision signals by utilizing both data similarities and graph structure. Firstly, by designing a semi-supervised contrastive loss, improved node representations can be generated via maximizing the agreement between different views of the same data or the data from the same class. Therefore, the rich unlabeled data and the scarce yet valuable labeled data can jointly provide abundant supervision information for learning discriminative node representations, which helps improve the subsequent classification result. Secondly, the underlying determinative relationship between the data features and input graph topology is extracted as supplementary supervision signals for SSL via using a graph generative loss related to the input features. Intensive experimental results on a variety of real-world datasets firmly verify the effectiveness of our algorithm compared with other state-of-the-art methods.

pdf/contrastive-and-generative-graph-convolutional-networks-for-j6f9mt73v5.pdf

Contrastive and Generative Graph Convolutional Networks for Graph-based Semi-Supervised Learning

Graph Convolutional Network (GCN) is an emerging technique for information retrieval (IR) applications. While GCN assumes the homophily property of a graph, real-world graphs are never perfect: the local structure of a node may contain discrepancy, e.g., the labels of a node's neighbors could vary. This pushes us to consider the discrepancy of local structure in GCN modeling. Existing work approaches this issue by introducing an additional module such as graph attention, which is expected to learn the contribution of each neighbor. However, such module may not work reliably as expected, especially when there lacks supervision signal, e.g., when the labeled data is small. Moreover, existing methods focus on modeling the nodes in the training data, and never consider the local structure discrepancy of testing nodes. 
This work focuses on the local structure discrepancy issue for testing nodes, which has received little scrutiny. From a novel perspective of causality, we investigate whether a GCN should trust the local structure of a testing node when predicting its label. To this end, we analyze the working mechanism of GCN with causal graph, estimating the causal effect of a node's local structure for the prediction. The idea is simple yet effective: given a trained GCN model, we first intervene the prediction by blocking the graph structure; we then compare the original prediction with the intervened prediction to assess the causal effect of the local structure on the prediction. Through this way, we can eliminate the impact of local structure discrepancy and make more accurate prediction. Extensive experiments on seven node classification datasets show that our method effectively enhances the inference stage of GCN.

pdf/should-graph-convolution-trust-neighbors-a-simple-causal-49yac6gf4m.pdf

Should Graph Convolution Trust Neighbors? A Simple Causal Inference Method

Node classification is an important problem on graphs. While recent advances in graph neural networks achieve promising performance, they require abundant labeled nodes for training. However, in many practical scenarios, there often exist novel classes in which only one or a few labeled nodes are available as supervision, known as few-shot node classification. Although meta-learning has been widely used in vision and language domains to address few-shot learning, its adoption on graphs has been limited. In particular, graph nodes in a few-shot task are not independent and relate to each other. To deal with this, we propose a novel model called Relative and Absolute Location Embedding (RALE) hinged on the concept of hub nodes. Specifically, RALE captures the task-level dependency by assigning each node a relative location within a task, as well as the graph-level dependency by assigning each node an absolute location on the graph to further align different tasks toward learning a transferable prior. Finally, extensive experiments on three public datasets demonstrate the state-of-the-art performance of RALE.

/pdf/relative-and-absolute-location-embedding-for-few-shot-node-d5tkb79t2i.pdf

Relative and absolute location embedding for few-shot node classification on graph

In this work, we address semi-supervised classification of graph data, where the categories of those unlabeled nodes are inferred from labeled nodes as well as graph structures. Recent works often solve this problem via advanced graph convolution in a conventionally supervised manner, but the performance could degrade significantly when labeled data is scarce. To this end, we propose a Graph Inference Learning (GIL) framework to boost the performance of semi-supervised node classification by learning the inference of node labels on graph topology. To bridge the connection between two nodes, we formally define a structure relation by encapsulating node attributes, between-node paths, and local topological structures together, which can make the inference conveniently deduced from one node to another node. For learning the inference process, we further introduce meta-optimization on structure relations from training nodes to validation nodes, such that the learnt graph inference capability can be better self-adapted to testing nodes. Comprehensive evaluations on four benchmark datasets (including Cora, Citeseer, Pubmed, and NELL) demonstrate the superiority of our proposed GIL when compared against state-of-the-art methods on the semi-supervised node classification task.

Graph Inference Learning for Semi-supervised Classification

The existing graph convolution methods usually suffer high computational burdens, large memory requirements, and intractable batch-processing. In this paper, we propose a high-efficient variational gridded graph convolution network (VG-GCN) to encode non-regular graph data, which overcomes all these aforementioned problems. To capture graph topology structures efficiently, in the proposed framework, we propose a hierarchically-coarsened random walk (hcr-walk) by taking advantage of the classic random walk and node/edge encapsulation. The hcr-walk greatly mitigates the problem of exponentially explosive sampling times which occur in the classic version, while preserving graph structures well. To efficiently encode local hcr-walk around one reference node, we project hcr-walk into an ordered space to form image-like grid data, which favors those conventional convolution networks. Instead of the direct 2-D convolution filtering, a variational convolution block (VCB) is designed to model the distribution of the random-sampling hcr-walk inspired by the well-formulated variational inference. We experimentally validate the efficiency and effectiveness of our proposed VG-GCN, which has high computation speed, and the comparable or even better performance when compared with baseline GCNs.

Variational Gridded Graph Convolution Network for Node Classification

Movie graphs play an important role to bridge heterogenous modalities of videos and texts in human-centric retrieval. In this work, we propose Graph Wasserstein Correlation Analysis (GWCA) to deal with the core issue therein, i.e, cross heterogeneous graph comparison. Spectral graph filtering is introduced to encode graph signals, which are then embedded as probability distributions in a Wasserstein space, called graph Wasserstein metric learning. Such a seamless integration of graph signal filtering together with metric learning results in a surprise consistency on both learning processes, in which the goal of metric learning is just to optimize signal filters or vice versa. Further, we derive the solution of the graph comparison model as a classic generalized eigenvalue decomposition problem, which has an exactly closed-form solution. Finally, GWCA together with movie/text graphs generation are unified into the framework of movie retrieval to evaluate our proposed method. Extensive experiments on MovieGrpahs dataset demonstrate the effectiveness of our GWCA as well as the entire framework.

Graph Wasserstein Correlation Analysis for Movie Retrieval.

pdf/graph-wasserstein-correlation-analysis-for-movie-retrieval-2kx4atjuyc.pdf

Graph Wasserstein Correlation Analysis for Movie Retrieval

The existing graph convolution methods usually suffer high computation burden, large memory requirement and intractable batch-process. In this paper, we propose a high-efficient hyper-walk gridded convolution (hyper-WGC) method to encode non-regular graph data, which overcomes all these aforementioned problems. To high-efficient capture graph topology structures, we propose random hyper-walk by taking advantages of random-walks as well as node/edge encapsulation. The random hyper-walk could greatly mitigate the problem of exponentially explosive sampling times occurred in the original random walk, while well preserving graph structures to some extent. To efficiently encode local hyper-walks around one reference node, we project hyper-walks into an order space to form image-like grid data, which more favors those conventional convolution networks. We experimentally validate the efficiency and effectiveness of our proposed hyper-WGC, which has high-efficient computation speed, and comparable or even better performance when compared with those baseline GCNs.

Fast Hyper-walk Gridded Convolution on Graph

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