We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. With the advances of deep learning, current link prediction methods commonly compute features from subgraphs centered at two neighboring nodes and use the features to predict the label of the link between these two nodes. In this formalism, a link prediction problem is converted to a graph classification task. In order to extract fixed-size features for classification, graph pooling layers are necessary in the deep learning model, thereby incurring information loss. To overcome this key limitation, we propose to seek a radically different and novel path by making use of the line graphs in graph theory. In particular, each node in a line graph corresponds to a unique edge in the original graph. Therefore, link prediction problems in the original graph can be equivalently solved as a node classification problem in its corresponding line graph, instead of a graph classification task. Experimental results on fourteen datasets from different applications demonstrate that our proposed method consistently outperforms the state-of-the-art methods, while it has fewer parameters and high training efficiency.
Data augmentation helps neural networks generalize better by enlarging the training set, but it remains an open question how to effectively augment graph data to enhance the performance of GNNs (Graph Neural Networks). While most existing graph regularizers focus on manipulating graph topological structures by adding/removing edges, we offer a method to augment node features for better performance. We propose FLAG (Free Large-scale Adversarial Augmentation on Graphs), which iteratively augments node features with gradient-based adversarial perturbations during training. By making the model invariant to small fluctuations in input data, our method helps models generalize to out-of-distribution samples and boosts model performance at test time. FLAG is a general-purpose approach for graph data, which universally works in node classification, link prediction, and graph classification tasks. FLAG is also highly flexible and scalable, and is deployable with arbitrary GNN backbones and large-scale datasets. We demonstrate the efficacy and stability of our method through extensive experiments and ablation studies. We also provide intuitive observations for a deeper understanding of our method.
Pooling operations have shown to be effective on computer vision and natural language processing tasks. One challenge of performing pooling operations on graph data is the lack of locality that is not well-defined on graphs. Previous studies used global ranking methods to sample some of the important nodes, but most of them are not able to incorporate graph topology. In this work, we propose the topology-aware pooling (TAP) layer that explicitly considers graph topology. Our TAP layer is a two-stage voting process that selects more important nodes in a graph. It first performs local voting to generate scores for each node by attending each node to its neighboring nodes. The scores are generated locally such that topology information is explicitly considered. In addition, graph topology is incorporated in global voting to compute the importance score of each node globally in the entire graph. Altogether, the final ranking score for each node is computed by combining its local and global voting scores. To encourage better graph connectivity in the sampled graph, we propose to add a graph connectivity term to the computation of ranking scores. Results on graph classification tasks demonstrate that our methods achieve consistently better performance than previous methods.
The graphlet kernel is a classical method in graph classification. It however suffers from a high computation cost due to the isomorphism test it includes. As a generic proxy, and in general at the cost of losing some information, this test can be efficiently replaced by a user-defined mapping that computes various graph characteristics. In this paper, we propose to leverage kernel random features within the graphlet framework, and establish a theoretical link with a mean kernel metric. If this method can still be prohibitively costly for usual random features, we then incorporate optical random features that can be computed in constant time. Experiments show that the resulting algorithm is orders of magnitude faster that the graphlet kernel for the same, or better, accuracy.
Graph Neural Network (GNN) aggregates the neighborhood of each node into the node embedding and shows its powerful capability for graph representation learning. However, most existing GNN variants aggregate the neighborhood information in a fixed non-injective fashion, which may map different graphs or nodes to the same embedding, reducing the model expressiveness. We present a theoretical framework to design a continuous injective set function for neighborhood aggregation in GNN. Using the framework, we propose expressive GNN that aggregates the neighborhood of each node with a continuous injective set function, so that a GNN layer maps similar nodes with similar neighborhoods to similar embeddings, different nodes to different embeddings and the equivalent nodes or isomorphic graphs to the same embeddings. Moreover, the proposed expressive GNN can naturally learn expressive representations for graphs with continuous node attributes. We validate the proposed expressive GNN (ExpGNN) for graph classification on multiple benchmark datasets including simple graphs and attributed graphs. The experimental results demonstrate that our model achieves state-of-the-art performances on most of the benchmarks.
Graphs have been widely adopted to denote structural connections between entities. The relations are in many cases heterogeneous, but entangled together and denoted merely as a single edge between a pair of nodes. For example, in a social network graph, users in different latent relationships like friends and colleagues, are usually connected via a bare edge that conceals such intrinsic connections. In this paper, we introduce a novel graph convolutional network (GCN), termed as factorizable graph convolutional network(FactorGCN), that explicitly disentangles such intertwined relations encoded in a graph. FactorGCN takes a simple graph as input, and disentangles it into several factorized graphs, each of which represents a latent and disentangled relation among nodes. The features of the nodes are then aggregated separately in each factorized latent space to produce disentangled features, which further leads to better performances for downstream tasks. We evaluate the proposed FactorGCN both qualitatively and quantitatively on the synthetic and real-world datasets, and demonstrate that it yields truly encouraging results in terms of both disentangling and feature aggregation. Code is publicly available at https://github.com/ihollywhy/FactorGCN.PyTorch.
With the advancement of sensing technology, multivariate time series classification (MTSC) has recently received considerable attention. Existing deep learning-based MTSC techniques, which mostly rely on convolutional or recurrent neural networks, are primarily concerned with the temporal dependency of single time series. As a result, they struggle to express pairwise dependencies among multivariate variables directly. Furthermore, current spatial-temporal modeling (e.g., graph classification) methodologies based on Graph Neural Networks (GNNs) are inherently flat and cannot aggregate hub data in a hierarchical manner. To address these limitations, we propose a novel graph pooling-based framework MTPool to obtain the expressive global representation of MTS. We first convert MTS slices to graphs by utilizing interactions of variables via graph structure learning module and attain the spatial-temporal graph node features via temporal convolutional module. To get global graph-level representation, we design an "encoder-decoder" based variational graph pooling module for creating adaptive centroids for cluster assignments. Then we combine GNNs and our proposed variational graph pooling layers for joint graph representation learning and graph coarsening, after which the graph is progressively coarsened to one node. At last, a differentiable classifier takes this coarsened representation to get the final predicted class. Experiments on ten benchmark datasets exhibit MTPool outperforms state-of-the-art strategies in the MTSC task.
Given the input graph and its label/property, several key problems of graph learning, such as finding interpretable subgraphs, graph denoising and graph compression, can be attributed to the fundamental problem of recognizing a subgraph of the original one. This subgraph shall be as informative as possible, yet contains less redundant and noisy structure. This problem setting is closely related to the well-known information bottleneck (IB) principle, which, however, has less been studied for the irregular graph data and graph neural networks (GNNs). In this paper, we propose a framework of Graph Information Bottleneck (GIB) for the subgraph recognition problem in deep graph learning. Under this framework, one can recognize the maximally informative yet compressive subgraph, named IB-subgraph. However, the GIB objective is notoriously hard to optimize, mostly due to the intractability of the mutual information of irregular graph data and the unstable optimization process. In order to tackle these challenges, we propose: i) a GIB objective based-on a mutual information estimator for the irregular graph data; ii) a bi-level optimization scheme to maximize the GIB objective; iii) a connectivity loss to stabilize the optimization process. We evaluate the properties of the IB-subgraph in three application scenarios: improvement of graph classification, graph interpretation and graph denoising. Extensive experiments demonstrate that the information-theoretic IB-subgraph enjoys superior graph properties.
Graph convolutional networks (GCNs) have been widely used for representation learning on graph data, which can capture structural patterns on a graph via specifically designed convolution and readout operations. In many graph classification applications, GCN-based approaches have outperformed traditional methods. However, most of the existing GCNs are inefficient to preserve local information of graphs -- a limitation that is especially problematic for graph classification. In this work, we propose a locality-preserving dense GCN with graph context-aware node representations. Specifically, our proposed model incorporates a local node feature reconstruction module to preserve initial node features into node representations, which is realized via a simple but effective encoder-decoder mechanism. To capture local structural patterns in neighbourhoods representing different ranges of locality, dense connectivity is introduced to connect each convolutional layer and its corresponding readout with all previous convolutional layers. To enhance node representativeness, the output of each convolutional layer is concatenated with the output of the previous layer's readout to form a global context-aware node representation. In addition, a self-attention module is introduced to aggregate layer-wise representations to form the final representation. Experiments on benchmark datasets demonstrate the superiority of the proposed model over state-of-the-art methods in terms of classification accuracy.
We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations. The incorporation of our LEGS-module in GNNs enables the learning of longer-range graph relations compared to many popular GNNs, which often rely on encoding graph structure via smoothness or similarity between neighbors. Further, its wavelet priors result in simplified architectures with significantly fewer learned parameters compared to competing GNNs. We demonstrate the predictive performance of LEGS-based networks on graph classification benchmarks, as well as the descriptive quality of their learned features in biochemical graph data exploration tasks.
The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent anisotropic kernels for GNNs, allowing for graph convolutions that are defined according to topologicaly-derived directional flows. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then, we propose the use of the Laplacian eigenvectors as such vector field. We show that the method generalizes CNNs on an $n$-dimensional grid and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. We evaluate our method on different standard benchmarks and see a relative error reduction of 8% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset, and a relative increase in precision of 1.6% on the MolPCBA dataset. An important outcome of this work is that it enables graph networks to embed directions in an unsupervised way, thus allowing a better representation of the anisotropic features in different physical or biological problems.
We propose a novel graph cross network (GXN) to achieve comprehensive feature learning from multiple scales of a graph. Based on trainable hierarchical representations of a graph, GXN enables the interchange of intermediate features across scales to promote information flow. Two key ingredients of GXN include a novel vertex infomax pooling (VIPool), which creates multiscale graphs in a trainable manner, and a novel feature-crossing layer, enabling feature interchange across scales. The proposed VIPool selects the most informative subset of vertices based on the neural estimation of mutual information between vertex features and neighborhood features. The intuition behind is that a vertex is informative when it can maximally reflect its neighboring information. The proposed feature-crossing layer fuses intermediate features between two scales for mutual enhancement by improving information flow and enriching multiscale features at hidden layers. The cross shape of the feature-crossing layer distinguishes GXN from many other multiscale architectures. Experimental results show that the proposed GXN improves the classification accuracy by 2.12% and 1.15% on average for graph classification and vertex classification, respectively. Based on the same network, the proposed VIPool consistently outperforms other graph-pooling methods.
Graph Neural Networks (GNNs), a generalization of neural networks to graph-structured data, are often implemented using message passes between entities of a graph. While GNNs are effective for node classification, link prediction and graph classification, they are vulnerable to adversarial attacks, i.e., a small perturbation to the structure can lead to a non-trivial performance degradation. In this work, we propose Uncertainty Matching GNN (UM-GNN), that is aimed at improving the robustness of GNN models, particularly against poisoning attacks to the graph structure, by leveraging epistemic uncertainties from the message passing framework. More specifically, we propose to build a surrogate predictor that does not directly access the graph structure, but systematically extracts reliable knowledge from a standard GNN through a novel uncertainty-matching strategy. Interestingly, this uncoupling makes UM-GNN immune to evasion attacks by design, and achieves significantly improved robustness against poisoning attacks. Using empirical studies with standard benchmarks and a suite of global and target attacks, we demonstrate the effectiveness of UM-GNN, when compared to existing baselines including the state-of-the-art robust GCN.
Graph Neural Networks (GNNs) have attracted considerable attention and have emerged as a new promising paradigm to process graph-structured data. GNNs are usually stacked to multiple layers and the node representations in each layer are computed through propagating and aggregating the neighboring node features with respect to the graph. By stacking to multiple layers, GNNs are able to capture the long-range dependencies among the data on the graph and thus bring performance improvements. To train a GNN with multiple layers effectively, some normalization techniques (e.g., node-wise normalization, batch-wise normalization) are necessary. However, the normalization techniques for GNNs are highly task-relevant and different application tasks prefer to different normalization techniques, which is hard to know in advance. To tackle this deficiency, in this paper, we propose to learn graph normalization by optimizing a weighted combination of normalization techniques at four different levels, including node-wise normalization, adjacency-wise normalization, graph-wise normalization, and batch-wise normalization, in which the adjacency-wise normalization and the graph-wise normalization are newly proposed in this paper to take into account the local structure and the global structure on the graph, respectively. By learning the optimal weights, we are able to automatically select a single best or a best combination of multiple normalizations for a specific task. We conduct extensive experiments on benchmark datasets for different tasks, including node classification, link prediction, graph classification and graph regression, and confirm that the learned graph normalization leads to competitive results and that the learned weights suggest the appropriate normalization techniques for the specific task. Source code is released here https://github.com/cyh1112/GraphNormalization.
We present a new method to regularize graph neural networks (GNNs) for better generalization in graph classification. Observing that the omission of sub-structures does not necessarily change the class label of the whole graph, we develop the \textbf{GraphCrop} (Subgraph Cropping) data augmentation method to simulate the real-world noise of sub-structure omission. In principle, GraphCrop utilizes a node-centric strategy to crop a contiguous subgraph from the original graph while maintaining its connectivity. By preserving the valid structure contexts for graph classification, we encourage GNNs to understand the content of graph structures in a global sense, rather than rely on a few key nodes or edges, which may not always be present. GraphCrop is parameter learning free and easy to implement within existing GNN-based graph classifiers. Qualitatively, GraphCrop expands the existing training set by generating novel and informative augmented graphs, which retain the original graph labels in most cases. Quantitatively, GraphCrop yields significant and consistent gains on multiple standard datasets, and thus enhances the popular GNNs to outperform the baseline methods.
Graph classification is a widely studied problem and has broad applications. In many real-world problems, the number of labeled graphs available for training classification models is limited, which renders these models prone to overfitting. To address this problem, we propose two approaches based on contrastive self-supervised learning (CSSL) to alleviate overfitting. In the first approach, we use CSSL to pretrain graph encoders on widely-available unlabeled graphs without relying on human-provided labels, then finetune the pretrained encoders on labeled graphs. In the second approach, we develop a regularizer based on CSSL, and solve the supervised classification task and the unsupervised CSSL task simultaneously. To perform CSSL on graphs, given a collection of original graphs, we perform data augmentation to create augmented graphs out of the original graphs. An augmented graph is created by consecutively applying a sequence of graph alteration operations. A contrastive loss is defined to learn graph encoders by judging whether two augmented graphs are from the same original graph. Experiments on various graph classification datasets demonstrate the effectiveness of our proposed methods.
Graph classification has practical applications in diverse fields. Recent studies show that graph-based machine learning models are especially vulnerable to adversarial perturbations due to the non i.i.d nature of graph data. By adding or deleting a small number of edges in the graph, adversaries could greatly change the graph label predicted by a graph classification model. In this work, we propose to build a smoothed graph classification model with certified robustness guarantee. We have proven that the resulting graph classification model would output the same prediction for a graph under $l_0$ bounded adversarial perturbation. We also evaluate the effectiveness of our approach under graph convolutional network (GCN) based multi-class graph classification model.
Normalization is known to help the optimization of deep neural networks. Curiously, different architectures require specialized normalization methods. In this paper, we study what normalization is effective for Graph Neural Networks (GNNs). First, we adapt and evaluate the existing methods from other domains to GNNs. Faster convergence is achieved with InstanceNorm compared to BatchNorm and LayerNorm. We provide an explanation by showing that InstanceNorm serves as a preconditioner for GNNs, but such preconditioning effect is weaker with BatchNorm due to the heavy batch noise in graph datasets. Second, we show that the shift operation in InstanceNorm results in an expressiveness degradation of GNNs for highly regular graphs. We address this issue by proposing GraphNorm with a learnable shift. Empirically, GNNs with GraphNorm converge faster compared to GNNs using other normalization. GraphNorm also improves the generalization of GNNs, achieving better performance on graph classification benchmarks.
Graph neural networks (GNN) are powerful models for many graph-structured tasks. Existing models often assume that the complete structure of the graph is available during training. In practice, however, graph-structured data is usually formed in a streaming fashion so that learning a graph continuously is often necessary. In this paper, we bridge GNN and lifelong learning by converting a continual graph learning problem to a regular graph learning problem so GNN can inherit the lifelong learning techniques developed for convolutional neural networks (CNN). We propose a new topology, the feature graph, which takes features as new nodes and turns nodes into independent graphs. This successfully converts the original problem of node classification to graph classification. In the experiments, we demonstrate the efficiency and effectiveness of feature graph networks (FGN) by continuously learning a sequence of classical graph datasets. We also show that FGN achieves superior performance in two applications, i.e., lifelong human action recognition with wearable devices and feature matching. To the best of our knowledge, FGN is the first method to bridge graph learning and lifelong learning via a novel graph topology. Source code is available at https://github.com/wang-chen/LGL
Graph convolutional neural networks (GCNNs) have received much attention recently, owing to their capability in handling graph-structured data. Among the existing GCNNs, many methods can be viewed as instances of a neural message passing motif; features of nodes are passed around their neighbors, aggregated and transformed to produce better nodes' representations. Nevertheless, these methods seldom use node transition probabilities, a measure that has been found useful in exploring graphs. Furthermore, when the transition probabilities are used, their transition direction is often improperly considered in the feature aggregation step, resulting in an inefficient weighting scheme. In addition, although a great number of GCNN models with increasing level of complexity have been introduced, the GCNNs often suffer from over-fitting when being trained on small graphs. Another issue of the GCNNs is over-smoothing, which tends to make nodes' representations indistinguishable. This work presents a new method to improve the message passing process based on node transition probabilities by properly considering the transition direction, leading to a better weighting scheme in nodes' features aggregation compared to the existing counterpart. Moreover, we propose a novel regularization method termed DropNode to address the over-fitting and over-smoothing issues simultaneously. DropNode randomly discards part of a graph, thus it creates multiple deformed versions of the graph, leading to data augmentation regularization effect. Additionally, DropNode lessens the connectivity of the graph, mitigating the effect of over-smoothing in deep GCNNs. Extensive experiments on eight benchmark datasets for node and graph classification tasks demonstrate the effectiveness of the proposed methods in comparison with the state of the art.