Recently, there has been great success in applying deep neural networks on graph structured data. Most work, however, focuses on either node- or graph-level supervised learning, such as node, link or graph classification or node-level unsupervised learning (e.g. node clustering). Despite its wide range of possible applications, graph-level unsupervised learning has not received much attention yet. This might be mainly attributed to the high representation complexity of graphs, which can be represented by n! equivalent adjacency matrices, where n is the number of nodes. In this work we address this issue by proposing a permutation-invariant variational autoencoder for graph structured data. Our proposed model indirectly learns to match the node ordering of input and output graph, without imposing a particular node ordering or performing expensive graph matching. We demonstrate the effectiveness of our proposed model on various graph reconstruction and generation tasks and evaluate the expressive power of extracted representations for downstream graph-level classification and regression.
Hyperbolic graph convolutional networks (GCNs) demonstrate powerful representation ability to model graphs with hierarchical structure. Existing hyperbolic GCNs resort to tangent spaces to realize graph convolution on hyperbolic manifolds, which is inferior because tangent space is only a local approximation of a manifold. In this paper, we propose a hyperbolic-to-hyperbolic graph convolutional network (H2H-GCN) that directly works on hyperbolic manifolds. Specifically, we developed a manifold-preserving graph convolution that consists of a hyperbolic feature transformation and a hyperbolic neighborhood aggregation. The hyperbolic feature transformation works as linear transformation on hyperbolic manifolds. It ensures the transformed node representations still lie on the hyperbolic manifold by imposing the orthogonal constraint on the transformation sub-matrix. The hyperbolic neighborhood aggregation updates each node representation via the Einstein midpoint. The H2H-GCN avoids the distortion caused by tangent space approximations and keeps the global hyperbolic structure. Extensive experiments show that the H2H-GCN achieves substantial improvements on the link prediction, node classification, and graph classification tasks.
Graph Convolutional Networks (GCNs) have been extensively used to classify vertices in graphs and have been shown to outperform other vertex classification methods. GCNs have been extended to graph classification tasks (GCT). In GCT, graphs with different numbers of edges and vertices belong to different classes, and one attempts to predict the graph class. GCN based GCT have mostly used pooling and attention-based models. The accuracy of existing GCT methods is still limited. We here propose a novel solution combining GCN, methods from knowledge graphs, and a new self-regularized activation function to significantly improve the accuracy of the GCN based GCT. We present quadratic GCN (QGCN) - A GCN formalism with a quadratic layer. Such a layer produces an output with fixed dimensions, independent of the graph vertex number. We applied this method to a wide range of graph classification problems, and show that when using a self regularized activation function, QGCN outperforms the state of the art methods for all graph classification tasks tested with or without external input on each graph. The code for QGCN is available at: https://github.com/Unknown-Data/QGCN .
The anonymity of blockchain has accelerated the growth of illegal activities and criminal behaviors on cryptocurrency platforms. Although decentralization is one of the typical characteristics of blockchain, we urgently call for effective regulation to detect these illegal behaviors to ensure the safety and stability of user transactions. Identity inference, which aims to make a preliminary inference about account identity, plays a significant role in blockchain security. As a common tool, graph mining technique can effectively represent the interactive information between accounts and be used for identity inference. However, existing methods cannot balance scalability and end-to-end architecture, resulting high computational consumption and weak feature representation. In this paper, we present a novel approach to analyze user's behavior from the perspective of the transaction subgraph, which naturally transforms the identity inference task into a graph classification pattern and effectively avoids computation in large-scale graph. Furthermore, we propose a generic end-to-end graph neural network model, named $\text{I}^2 \text{BGNN}$, which can accept subgraph as input and learn a function mapping the transaction subgraph pattern to account identity, achieving de-anonymization. Extensive experiments on EOSG and ETHG datasets demonstrate that the proposed method achieve the state-of-the-art performance in identity inference.
Graph neural networks (GNN) have been proven to be mature enough for handling graph-structured data on node-level graph representation learning tasks. However, the graph pooling technique for learning expressive graph-level representation is critical yet still challenging. Existing pooling methods either struggle to capture the local substructure or fail to effectively utilize high-order dependency, thus diminishing the expression capability. In this paper we propose HAP, a hierarchical graph-level representation learning framework, which is adaptively sensitive to graph structures, i.e., HAP clusters local substructures incorporating with high-order dependencies. HAP utilizes a novel cross-level attention mechanism MOA to naturally focus more on close neighborhood while effectively capture higher-order dependency that may contain crucial information. It also learns a global graph content GCont that extracts the graph pattern properties to make the pre- and post-coarsening graph content maintain stable, thus providing global guidance in graph coarsening. This novel innovation also facilitates generalization across graphs with the same form of features. Extensive experiments on fourteen datasets show that HAP significantly outperforms twelve popular graph pooling methods on graph classification task with an maximum accuracy improvement of 22.79%, and exceeds the performance of state-of-the-art graph matching and graph similarity learning algorithms by over 3.5% and 16.7%.
The machinery of topological data analysis becomes increasingly popular in a broad range of machine learning tasks, ranging from anomaly detection and manifold learning to graph classification. Persistent homology is one of the key approaches here, allowing us to systematically assess the evolution of various hidden patterns in the data as we vary a scale parameter. The extracted patterns, or homological features, along with information on how long such features persist throughout the considered filtration of a scale parameter, convey a critical insight into salient data characteristics and data organization. In this work, we introduce two new and easily interpretable topological summaries for single and multi-parameter persistence, namely, saw functions and multi-persistence grid functions, respectively. Compared to the existing topological summaries which tend to assess the numbers of topological features and/or their lifespans at a given filtration step, our proposed saw and multi-persistence grid functions allow us to explicitly account for essential complementary information such as the numbers of births and deaths at each filtration step. These new topological summaries can be regarded as the complexity measures of the evolving subspaces determined by the filtration and are of particular utility for applications of persistent homology on graphs. We derive theoretical guarantees on the stability of the new saw and multi-persistence grid functions and illustrate their applicability for graph classification tasks.
Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical properties and ability to take into account inductive bias. For this, we propose a high-performance implementation of a simple sampling algorithm which computes additive approximations of homomorphism densities. In the context of graph machine learning, we demonstrate in experiments that simple linear models trained on sample homomorphism densities can achieve performance comparable to graph neural networks on standard graph classification datasets. Finally, we show in experiments on synthetic data that this algorithm scales to very large graphs when implemented with Bloom filters.
Data augmentation refers to a wide range of techniques for improving model generalization by augmenting training examples. Oftentimes such methods require domain knowledge about the dataset at hand, spawning a plethora of recent literature surrounding automated techniques for data augmentation. In this work we apply one such method, bilevel optimization, to tackle the problem of graph classification on the ogbg-molhiv dataset. Our best performing augmentation achieved a test ROCAUC score of 77.77 % with a GIN+virtual classifier, which makes it the most effective augmenter for this classifier on the leaderboard. This framework combines a GIN layer augmentation generator with a bias transformation and outperforms the same classifier augmented using the state-of-the-art FLAG augmentation.
Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to enable effective representation learning that inherently incorporates a weight-sharing mechanism, we develop graph neural networks that leverage the properties of hypercomplex feature transformation. In particular, in our proposed class of models, the multiplication rule specifying the algebra itself is inferred from the data during training. Given a fixed model architecture, we present empirical evidence that our proposed model incorporates a regularization effect, alleviating the risk of overfitting. We also show that for fixed model capacity, our proposed method outperforms its corresponding real-formulated GNN, providing additional confirmation for the enhanced expressivity of HC embeddings. Finally, we test our proposed hypercomplex GNN on several open graph benchmark datasets and show that our models reach state-of-the-art performance while consuming a much lower memory footprint with 70& fewer parameters. Our implementations are available at https://github.com/bayer-science-for-a-better-life/phc-gnn.
Accurate video understanding involves reasoning about the relationships between actors, objects and their environment, often over long temporal intervals. In this paper, we propose a message passing graph neural network that explicitly models these spatio-temporal relations and can use explicit representations of objects, when supervision is available, and implicit representations otherwise. Our formulation generalises previous structured models for video understanding, and allows us to study how different design choices in graph structure and representation affect the model's performance. We demonstrate our method on two different tasks requiring relational reasoning in videos -- spatio-temporal action detection on AVA and UCF101-24, and video scene graph classification on the recent Action Genome dataset -- and achieve state-of-the-art results on all three datasets. Furthermore, we show quantitatively and qualitatively how our method is able to more effectively model relationships between relevant entities in the scene.
Graph classification is a challenging research problem in many applications across a broad range of domains. In these applications, it is very common that class distribution is imbalanced. Recently, Graph Neural Network (GNN) models have achieved superior performance on various real-world datasets. Despite their success, most of current GNN models largely overlook the important setting of imbalanced class distribution, which typically results in prediction bias towards majority classes. To alleviate the prediction bias, we propose to leverage semantic structure of dataset based on the distribution of node embedding. Specifically, we present GraphDIVE, a general framework leveraging mixture of diverse experts (i.e., graph classifiers) for imbalanced graph classification. With a divide-and-conquer principle, GraphDIVE employs a gating network to partition an imbalanced graph dataset into several subsets. Then each expert network is trained based on its corresponding subset. Experiments on real-world imbalanced graph datasets demonstrate the effectiveness of GraphDIVE.
In this work, we study the phenomenon of catastrophic forgetting in the graph representation learning scenario. The primary objective of the analysis is to understand whether classical continual learning techniques for flat and sequential data have a tangible impact on performances when applied to graph data. To do so, we experiment with a structure-agnostic model and a deep graph network in a robust and controlled environment on three different datasets. The benchmark is complemented by an investigation on the effect of structure-preserving regularization techniques on catastrophic forgetting. We find that replay is the most effective strategy in so far, which also benefits the most from the use of regularization. Our findings suggest interesting future research at the intersection of the continual and graph representation learning fields. Finally, we provide researchers with a flexible software framework to reproduce our results and carry out further experiments.
Graph representation learning for static graphs is a well studied topic. Recently, a few studies have focused on learning temporal information in addition to the topology of a graph. Most of these studies have relied on learning to represent nodes and substructures in dynamic graphs. However, the representation learning problem for entire graphs in a dynamic context is yet to be addressed. In this paper, we propose an unsupervised representation learning architecture for dynamic graphs, designed to learn both the topological and temporal features of the graphs that evolve over time. The approach consists of a sequence-to-sequence encoder-decoder model embedded with gated graph neural networks (GGNNs) and long short-term memory networks (LSTMs). The GGNN is able to learn the topology of the graph at each time step, while LSTMs are leveraged to propagate the temporal information among the time steps. Moreover, an encoder learns the temporal dynamics of an evolving graph and a decoder reconstructs the dynamics over the same period of time using the encoded representation provided by the encoder. We demonstrate that our approach is capable of learning the representation of a dynamic graph through time by applying the embeddings to dynamic graph classification using a real world dataset of animal behaviour. Graph representation learning for static graphs is a well studied topic. Recently, a few studies have focused on learning temporal information in addition to the topology of a graph. Most of these studies have relied on learning to represent nodes and substructures in dynamic graphs. However, the representation learning problem for entire graphs in a dynamic context is yet to be addressed. In this paper, we propose an unsupervised representation learning architecture for dynamic graphs, designed to learn both the topological and temporal features of the graphs that evolve over time. The approach consists of a sequence-to-sequence encoder-decoder model embedded with gated graph neural networks (GGNNs) and long short-term memory networks (LSTMs). The GGNN is able to learn the topology of the graph at each time step, while LSTMs are leveraged to propagate the temporal information among the time steps. Moreover, an encoder learns the temporal dynamics of an evolving graph and a decoder reconstructs the dynamics over the same period of time using the encoded representation provided by the encoder. We demonstrate that our approach is capable of learning the representation of a dynamic graph through time by applying the embeddings to dynamic graph classification using a real world dataset of animal behaviour.
Though the multiscale graph learning techniques have enabled advanced feature extraction frameworks, the classic ensemble strategy may show inferior performance while encountering the high homogeneity of the learnt representation, which is caused by the nature of existing graph pooling methods. To cope with this issue, we propose a diversified multiscale graph learning model equipped with two core ingredients: a graph self-correction (GSC) mechanism to generate informative embedded graphs, and a diversity boosting regularizer (DBR) to achieve a comprehensive characterization of the input graph. The proposed GSC mechanism compensates the pooled graph with the lost information during the graph pooling process by feeding back the estimated residual graph, which serves as a plug-in component for popular graph pooling methods. Meanwhile, pooling methods enhanced with the GSC procedure encourage the discrepancy of node embeddings, and thus it contributes to the success of ensemble learning strategy. The proposed DBR instead enhances the ensemble diversity at the graph-level embeddings by leveraging the interaction among individual classifiers. Extensive experiments on popular graph classification benchmarks show that the proposed GSC mechanism leads to significant improvements over state-of-the-art graph pooling methods. Moreover, the ensemble multiscale graph learning models achieve superior enhancement by combining both GSC and DBR.
Graph Neural Networks (GNNs) are the first choice for learning algorithms on graph data. GNNs promise to integrate (i) node features as well as (ii) edge information in an end-to-end learning algorithm. How does this promise work out practically? In this paper, we study to what extend GNNs are necessary to solve prominent graph classification problems. We find that for graph classification, a GNN is not more than the sum of its parts. We also find that, unlike features, predictions with an edge-only model do not always transfer to GNNs.
In general, graph representation learning methods assume that the train and test data come from the same distribution. In this work we consider an underexplored area of an otherwise rapidly developing field of graph representation learning: The task of out-of-distribution (OOD) graph classification, where train and test data have different distributions, with test data unavailable during training. Our work shows it is possible to use a causal model to learn approximately invariant representations that better extrapolate between train and test data. Finally, we conclude with synthetic and real-world dataset experiments showcasing the benefits of representations that are invariant to train/test distribution shifts.
Graph classification is a highly impactful task that plays a crucial role in a myriad of real-world applications such as molecular property prediction and protein function prediction.Aiming to handle the new classes with limited labeled graphs, few-shot graph classification has become a bridge of existing graph classification solutions and practical usage.This work explores the potential of metric-based meta-learning for solving few-shot graph classification.We highlight the importance of considering structural characteristics in the solution and propose a novel framework which explicitly considers global structure and local structure of the input graph. An implementation upon GIN, named SMF-GIN, is tested on two datasets, Chembl and TRIANGLES, where extensive experiments validate the effectiveness of the proposed method. The Chembl is constructed to fill in the gap of lacking large-scale benchmark for few-shot graph classification evaluation, which is released together with the implementation of SMF-GIN at: https://github.com/jiangshunyu/SMF-GIN.
Graph neural networks (GNNs) have been widely used to learn vector representation of graph-structured data and achieved better task performance than conventional methods. The foundation of GNNs is the message passing procedure, which propagates the information in a node to its neighbors. Since this procedure proceeds one step per layer, the range of the information propagation among nodes is small in the lower layers, and it expands toward the higher layers. Therefore, a GNN model has to be deep enough to capture global structural information in a graph. On the other hand, it is known that deep GNN models suffer from performance degradation because they lose nodes' local information, which would be essential for good model performance, through many message passing steps. In this study, we propose multi-level attention pooling (MLAP) for graph-level classification tasks, which can adapt to both local and global structural information in a graph. It has an attention pooling layer for each message passing step and computes the final graph representation by unifying the layer-wise graph representations. The MLAP architecture allows models to utilize the structural information of graphs with multiple levels of localities because it preserves layer-wise information before losing them due to oversmoothing. Results of our experiments show that the MLAP architecture improves the graph classification performance compared to the baseline architectures. In addition, analyses on the layer-wise graph representations suggest that aggregating information from multiple levels of localities indeed has the potential to improve the discriminability of learned graph representations.
Graph neural networks (GNNs) have attracted tremendous attention from the graph learning community in recent years. It has been widely adopted in various real-world applications from diverse domains, such as social networks and biological graphs. The research and applications of graph deep learning present new challenges, including the sparse nature of graph data, complicated training of GNNs, and non-standard evaluation of graph tasks. To tackle the issues, we present CogDL, a comprehensive library for graph deep learning that allows researchers and practitioners to conduct experiments, compare methods, and build applications with ease and efficiency. In CogDL, we propose a unified design for the training and evaluation of GNN models for various graph tasks, making it unique among existing graph learning libraries. By utilizing this unified trainer, CogDL can optimize the GNN training loop with several training techniques, such as mixed precision training. Moreover, we develop efficient sparse operators for CogDL, enabling it to become the most competitive graph library for efficiency. Another important CogDL feature is its focus on ease of use with the aim of facilitating open and reproducible research of graph learning. We leverage CogDL to report and maintain benchmark results on fundamental graph tasks, which can be reproduced and directly used by the community.
Deep learning is effective in graph analysis. It is widely applied in many related areas, such as link prediction, node classification, community detection, and graph classification etc. Graph embedding, which learns low-dimensional representations for vertices or edges in the graph, usually employs deep models to derive the embedding vector. However, these models are vulnerable. We envision that graph embedding methods based on deep models can be easily attacked using adversarial examples. Thus, in this paper, we propose Graphfool, a novel targeted label adversarial attack on graph embedding. It can generate adversarial graph to attack graph embedding methods via classifying boundary and gradient information in graph convolutional network (GCN). Specifically, we perform the following steps: 1),We first estimate the classification boundaries of different classes. 2), We calculate the minimal perturbation matrix to misclassify the attacked vertex according to the target classification boundary. 3), We modify the adjacency matrix according to the maximal absolute value of the disturbance matrix. This process is implemented iteratively. To the best of our knowledge, this is the first targeted label attack technique. The experiments on real-world graph networks demonstrate that Graphfool can derive better performance than state-of-art techniques. Compared with the second best algorithm, Graphfool can achieve an average improvement of 11.44% in attack success rate.