This paper presents a novel attention-based neural network for structured reconstruction, which takes a 2D raster image as an input and reconstructs a planar graph depicting an underlying geometric structure. The approach detects corners and classifies edge candidates between corners in an end-to-end manner. Our contribution is a holistic edge classification architecture, which 1) initializes the feature of an edge candidate by a trigonometric positional encoding of its end-points; 2) fuses image feature to each edge candidate by deformable attention; 3) employs two weight-sharing Transformer decoders to learn holistic structural patterns over the graph edge candidates; and 4) is trained with a masked learning strategy. The corner detector is a variant of the edge classification architecture, adapted to operate on pixels as corner candidates. We conduct experiments on two structured reconstruction tasks: outdoor building architecture and indoor floorplan planar graph reconstruction. Extensive qualitative and quantitative evaluations demonstrate the superiority of our approach over the state of the art. Code and pre-trained models are available at https://heat-structured-reconstruction.github.io.
Graph is an important data representation ubiquitously existing in the real world. However, analyzing the graph data is computationally difficult due to its non-Euclidean nature. Graph embedding is a powerful tool to solve the graph analytics problem by transforming the graph data into low-dimensional vectors. These vectors could also be shared with third parties to gain additional insights of what is behind the data. While sharing graph embedding is intriguing, the associated privacy risks are unexplored. In this paper, we systematically investigate the information leakage of the graph embedding by mounting three inference attacks. First, we can successfully infer basic graph properties, such as the number of nodes, the number of edges, and graph density, of the target graph with up to 0.89 accuracy. Second, given a subgraph of interest and the graph embedding, we can determine with high confidence that whether the subgraph is contained in the target graph. For instance, we achieve 0.98 attack AUC on the DD dataset. Third, we propose a novel graph reconstruction attack that can reconstruct a graph that has similar graph structural statistics to the target graph. We further propose an effective defense mechanism based on graph embedding perturbation to mitigate the inference attacks without noticeable performance degradation for graph classification tasks. Our code is available at https://github.com/Zhangzhk0819/GNN-Embedding-Leaks.
We propose a decentralised "local2global" approach to graph representation learning, that one can a-priori use to scale any embedding technique. Our local2global approach proceeds by first dividing the input graph into overlapping subgraphs (or "patches") and training local representations for each patch independently. In a second step, we combine the local representations into a globally consistent representation by estimating the set of rigid motions that best align the local representations using information from the patch overlaps, via group synchronization. A key distinguishing feature of local2global relative to existing work is that patches are trained independently without the need for the often costly parameter synchronisation during distributed training. This allows local2global to scale to large-scale industrial applications, where the input graph may not even fit into memory and may be stored in a distributed manner. Preliminary results on medium-scale data sets (up to $\sim$7K nodes and $\sim$200K edges) are promising, with a graph reconstruction performance for local2global that is comparable to that of globally trained embeddings. A thorough evaluation of local2global on large scale data and applications to downstream tasks, such as node classification and link prediction, constitutes ongoing work.
Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges. After obtaining edge representations from the hypergraphs, we then cluster or drop edges to obtain holistic graph-level edge representations. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance, on which our method largely outperforms existing graph representation learning methods. Moreover, our edge representation learning and pooling method also largely outperforms state-of-the-art graph pooling methods on graph classification, not only because of its accurate edge representation learning, but also due to its lossless compression of the nodes and removal of irrelevant edges for effective message-passing.
A table arranging data in rows and columns is a very effective data structure, which has been widely used in business and scientific research. Considering large-scale tabular data in online and offline documents, automatic table recognition has attracted increasing attention from the document analysis community. Though human can easily understand the structure of tables, it remains a challenge for machines to understand that, especially due to a variety of different table layouts and styles. Existing methods usually model a table as either the markup sequence or the adjacency matrix between different table cells, failing to address the importance of the logical location of table cells, e.g., a cell is located in the first row and the second column of the table. In this paper, we reformulate the problem of table structure recognition as the table graph reconstruction, and propose an end-to-end trainable table graph reconstruction network (TGRNet) for table structure recognition. Specifically, the proposed method has two main branches, a cell detection branch and a cell logical location branch, to jointly predict the spatial location and the logical location of different cells. Experimental results on three popular table recognition datasets and a new dataset with table graph annotations (TableGraph-350K) demonstrate the effectiveness of the proposed TGRNet for table structure recognition. Code and annotations will be made publicly available.
Existing pre-trained models for knowledge-graph-to-text (KG-to-text) generation simply fine-tune text-to-text pre-trained models such as BART or T5 on KG-to-text datasets, which largely ignore the graph structure during encoding and lack elaborate pre-training tasks to explicitly model graph-text alignments. To tackle these problems, we propose a graph-text joint representation learning model called JointGT. During encoding, we devise a structure-aware semantic aggregation module which is plugged into each Transformer layer to preserve the graph structure. Furthermore, we propose three new pre-training tasks to explicitly enhance the graph-text alignment including respective text / graph reconstruction, and graph-text alignment in the embedding space via Optimal Transport. Experiments show that JointGT obtains new state-of-the-art performance on various KG-to-text datasets.
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning, a class encompassing many of the previously used embedding targets. This enables us to introduce a new method, the use of Finsler metrics integrated in a Riemannian optimization scheme, that better adapts to dissimilar structures in the graph. We develop a tool to analyze the embeddings and infer structural properties of the data sets. For implementation, we choose Siegel spaces, a versatile family of symmetric spaces. Our approach outperforms competitive baselines for graph reconstruction tasks on various synthetic and real-world datasets. We further demonstrate its applicability on two downstream tasks, recommender systems and node classification.
Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds provide specific inductive biases for embedding hierarchical or spherical data. However, they cannot align well with data of mixed graph topologies. We consider a larger class of pseudo-Riemannian manifolds that generalize hyperboloid and sphere. We develop new geodesic tools that allow for extending neural network operations into geodesically disconnected pseudo-Riemannian manifolds. As a consequence, we derive a pseudo-Riemannian GCN that models data in pseudo-Riemannian manifolds of constant nonzero curvature in the context of graph neural networks. Our method provides a geometric inductive bias that is sufficiently flexible to model mixed heterogeneous topologies like hierarchical graphs with cycles. We demonstrate the representational capabilities of this method by applying it to the tasks of graph reconstruction, node classification and link prediction on a series of standard graphs with mixed topologies. Empirical results demonstrate that our method outperforms Riemannian counterparts when embedding graphs of complex topologies.
Graph embedding is essential for graph mining tasks. With the prevalence of graph data in real-world applications, many methods have been proposed in recent years to learn high-quality graph embedding vectors various types of graphs. However, most existing methods usually randomly select the negative samples from the original graph to enhance the training data without considering the noise. In addition, most of these methods only focus on the explicit graph structures and cannot fully capture complex semantics of edges such as various relationships or asymmetry. In order to address these issues, we propose a robust and generalized framework for adversarial graph embedding based on generative adversarial networks. Inspired by generative adversarial network, we propose a robust and generalized framework for adversarial graph embedding, named AGE. AGE generates the fake neighbor nodes as the enhanced negative samples from the implicit distribution, and enables the discriminator and generator to jointly learn each node's robust and generalized representation. Based on this framework, we propose three models to handle three types of graph data and derive the corresponding optimization algorithms, i.e., UG-AGE and DG-AGE for undirected and directed homogeneous graphs, respectively, and HIN-AGE for heterogeneous information networks. Extensive experiments show that our methods consistently and significantly outperform existing state-of-the-art methods across multiple graph mining tasks, including link prediction, node classification, and graph reconstruction.
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.
Graph neural networks have been widely used on modeling graph data, achieving impressive results on node classification and link prediction tasks. Yet, obtaining an accurate representation for a graph further requires a pooling function that maps a set of node representations into a compact form. A simple sum or average over all node representations considers all node features equally without consideration of their task relevance, and any structural dependencies among them. Recently proposed hierarchical graph pooling methods, on the other hand, may yield the same representation for two different graphs that are distinguished by the Weisfeiler-Lehman test, as they suboptimally preserve information from the node features. To tackle these limitations of existing graph pooling methods, we first formulate the graph pooling problem as a multiset encoding problem with auxiliary information about the graph structure, and propose a Graph Multiset Transformer (GMT) which is a multi-head attention based global pooling layer that captures the interaction between nodes according to their structural dependencies. We show that GMT satisfies both injectiveness and permutation invariance, such that it is at most as powerful as the Weisfeiler-Lehman graph isomorphism test. Moreover, our methods can be easily extended to the previous node clustering approaches for hierarchical graph pooling. Our experimental results show that GMT significantly outperforms state-of-the-art graph pooling methods on graph classification benchmarks with high memory and time efficiency, and obtains even larger performance gain on graph reconstruction and generation tasks.
Network homophily, the tendency of similar nodes to be connected, and transitivity, the tendency of two nodes being connected if they share a common neighbor, are conflated properties in network analysis, since one mechanism can drive the other. Here we present a generative model and corresponding inference procedure that are capable of distinguishing between both mechanisms. Our approach is based on a variation of the stochastic block model (SBM) with the addition of triadic closure edges, and its inference can identify the most plausible mechanism responsible for the existence of every edge in the network, in addition to the underlying community structure itself. We show how the method can evade the detection of spurious communities caused solely by the formation of triangles in the network, and how it can improve the performance of edge prediction when compared to the pure version of the SBM without triadic closure.
Graph neural networks (GNNs) are emerging machine learning models on graphs. Permutation-equivariance and proximity-awareness are two important properties highly desirable for GNNs. Both properties are needed to tackle some challenging graph problems, such as finding communities and leaders. In this paper, we first analytically show that the existing GNNs, mostly based on the message-passing mechanism, cannot simultaneously preserve the two properties. Then, we propose Stochastic Message Passing (SMP) model, a general and simple GNN to maintain both proximity-awareness and permutation-equivariance. In order to preserve node proximities, we augment the existing GNNs with stochastic node representations. We theoretically prove that the mechanism can enable GNNs to preserve node proximities, and at the same time, maintain permutation-equivariance with certain parametrization. We report extensive experimental results on ten datasets and demonstrate the effectiveness and efficiency of SMP for various typical graph mining tasks, including graph reconstruction, node classification, and link prediction.
Learning low-dimensional topological representation of a network in dynamic environments is attracting much attention due to the time-evolving nature of many real-world networks. The main and common objective of Dynamic Network Embedding (DNE) is to efficiently update node embeddings while preserving network topology at each time step. The idea of most existing DNE methods is to capture the topological changes at or around the most affected nodes (instead of all nodes) and accordingly update node embeddings. Unfortunately, this kind of approximation, although can improve efficiency, cannot effectively preserve the global topology of a dynamic network at each time step, due to not considering the inactive sub-networks that receive accumulated topological changes propagated via the high-order proximity. To tackle this challenge, we propose a novel node selecting strategy to diversely select the representative nodes over a network, which is coordinated with a new incremental learning paradigm of Skip-Gram based embedding approach. The extensive experiments show GloDyNE, with a small fraction of nodes being selected, can already achieve the superior or comparable performance w.r.t. the state-of-the-art DNE methods in three typical downstream tasks. Particularly, GloDyNE significantly outperforms other methods in the graph reconstruction task, which demonstrates its ability of global topology preservation. The source code is available at https://github.com/houchengbin/GloDyNE
Learning topological representation of a network in dynamic environments has recently attracted considerable attention due to the time-evolving nature of many real-world networks i.e. nodes/links might be added/removed as time goes on. Dynamic network embedding aims to learn low dimensional embeddings for unseen and seen nodes by using any currently available snapshots of a dynamic network. For seen nodes, the existing methods either treat them equally important or focus on the $k$ most affected nodes at each time step. However, the former solution is time-consuming, and the later solution that relies on incoming changes may lose the global topology---an important feature for downstream tasks. To address these challenges, we propose a dynamic network embedding method called DynWalks, which includes two key components: 1) An online network embedding framework that can dynamically and efficiently learn embeddings based on the selected nodes; 2) A novel online node selecting scheme that offers the flexible choices to balance global topology and recent changes, as well as to fulfill the real-time constraint if needed. The empirical studies on six real-world dynamic networks under three different slicing ways show that DynWalks significantly outperforms the state-of-the-art methods in graph reconstruction tasks, and obtains comparable results in link prediction tasks. Furthermore, the wall-clock time and complexity analysis demonstrate its excellent time and space efficiency. The source code of DynWalks is available at https://github.com/houchengbin/DynWalks
Effective modeling of electronic health records (EHR) is rapidly becoming an important topic in both academia and industry. A recent study showed that using the graphical structure underlying EHR data (e.g. relationship between diagnoses and treatments) improves the performance of prediction tasks such as heart failure prediction. However, EHR data do not always contain complete structure information. Moreover, when it comes to claims data, structure information is completely unavailable to begin with. Under such circumstances, can we still do better than just treating EHR data as a flat-structured bag-of-features? In this paper, we study the possibility of jointly learning the hidden structure of EHR while performing supervised prediction tasks on EHR data. Specifically, we discuss that Transformer is a suitable basis model to learn the hidden EHR structure, and propose Graph Convolutional Transformer, which uses data statistics to guide the structure learning process. The proposed model consistently outperformed previous approaches empirically, on both synthetic data and publicly available EHR data, for various prediction tasks such as graph reconstruction and readmission prediction, indicating that it can serve as an effective general-purpose representation learning algorithm for EHR data.
Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps, which constructs a graph embedding based on the spectral properties of the Laplacian matrix of G. The intuition behind it, and many other embedding techniques, is that the embedding of a graph must respect node similarity: similar nodes must have embeddings that are close to one another. Here, we dispose of this distance-minimization assumption. Instead, we use the Laplacian matrix to find an embedding with geometric properties instead of spectral ones, by leveraging the so-called simplex geometry of G. We introduce a new approach, Geometric Laplacian Eigenmap Embedding (or GLEE for short), and demonstrate that it outperforms various other techniques (including Laplacian Eigenmaps) in the tasks of graph reconstruction and link prediction.
DynamicGEM is an open-source Python library for learning node representations of dynamic graphs. It consists of state-of-the-art algorithms for defining embeddings of nodes whose connections evolve over time. The library also contains the evaluation framework for four downstream tasks on the network: graph reconstruction, static and temporal link prediction, node classification, and temporal visualization. We have implemented various metrics to evaluate the state-of-the-art methods, and examples of evolving networks from various domains. We have easy-to-use functions to call and evaluate the methods and have extensive usage documentation. Furthermore, DynamicGEM provides a template to add new algorithms with ease to facilitate further research on the topic.