Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. As a specific case of higher order permutation equivariant networks, we present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable. We demonstrate the efficacy of this architecture on the tasks of link prediction in citation graphs and molecular graph generation.
The varying cortical geometry of the brain creates numerous challenges for its analysis. Recent developments have enabled learning surface data directly across multiple brain surfaces via graph convolutions on cortical data. However, current graph learning algorithms do fail when brain surface data are misaligned across subjects, thereby affecting their ability to deal with data from multiple domains. Adversarial training is widely used for domain adaptation to improve the segmentation performance across domains. In this paper, adversarial training is exploited to learn surface data across inconsistent graph alignments. This novel approach comprises a segmentator that uses a set of graph convolution layers to enable parcellation directly across brain surfaces in a source domain, and a discriminator that predicts a graph domain from segmentations. More precisely, the proposed adversarial network learns to generalize a parcellation across both, source and target domains. We demonstrate an 8% mean improvement in performance over a non-adversarial training strategy applied on multiple target domains extracted from MindBoggle, the largest publicly available manually-labeled brain surface dataset.
Recently, Graph Convolutional Networks (GCNs) have proven to be a powerful machine learning tool for Computer-Aided Diagnosis (CADx) and disease prediction. A key component in these models is to build a population graph, where the graph adjacency matrix represents pair-wise patient similarities. Until now, the similarity metrics have been defined manually, usually based on meta-features like demographics or clinical scores. The definition of the metric, however, needs careful tuning, as GCNs are very sensitive to the graph structure. In this paper, we demonstrate for the first time in the CADx domain that it is possible to learn a single, optimal graph towards the GCN's downstream task of disease classification. To this end, we propose a novel, end-to-end trainable graph learning architecture for dynamic and localized graph pruning. Unlike commonly employed spectral GCN approaches, our GCN is spatial and inductive, and can thus infer previously unseen patients as well. We demonstrate significant classification improvements with our learned graph on two CADx problems in medicine. We further explain and visualize this result using an artificial dataset, underlining the importance of graph learning for more accurate and robust inference with GCNs in medical applications.
This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is designed in the spatial or the spectral domain. The obtained general framework allows to lead a spectral analysis of the most popular ConvGNNs, explaining their performance and showing their limits. Moreover, the proposed framework is used to design new convolutions in spectral domain with a custom frequency profile while applying them in the spatial domain. We also propose a generalization of the depthwise separable convolution framework for graph convolutional networks, what allows to decrease the total number of trainable parameters by keeping the capacity of the model. To the best of our knowledge, such a framework has never been used in the GNNs literature. Our proposals are evaluated on both transductive and inductive graph learning problems. Obtained results show the relevance of the proposed method and provide one of the first experimental evidence of transferability of spectral filter coefficients from one graph to another. Our source codes are publicly available at: https://github.com/balcilar/Spectral-Designed-Graph-Convolutions
Graph Neural Networks (GNNs) have recently received significant research attention due to their superior performance on a variety of graph-related learning tasks. Most of the current works focus on either static or dynamic graph settings, addressing a single particular task, e.g., node/graph classification, link prediction. In this work, we investigate the question: can GNNs be applied to continuously learning a sequence of tasks? Towards that, we explore the Continual Graph Learning (CGL) paradigm and present the Experience Replay based framework ER-GNN for CGL to alleviate the catastrophic forgetting problem in existing GNNs. ER-GNN stores knowledge from previous tasks as experiences and replays them when learning new tasks to mitigate the catastrophic forgetting issue. We propose three experience node selection strategies: mean of feature, coverage maximization, and influence maximization, to guide the process of selecting experience nodes. Extensive experiments on three benchmark datasets demonstrate the effectiveness of our ER-GNN and shed light on the incremental graph (non-Euclidean) structure learning.
Graph Convolutional Network (GCN) has been widely used in graph learning tasks. However, GCN-based models (GCNs) is an inherently coupled training framework repetitively conducting the complex neighboring aggregation, which leads to the limitation of flexibility in processing large-scale graph. With the depth of layers increases, the computational and memory cost of GCNs grow explosively due to the recursive neighborhood expansion. To tackle these issues, we present Node2Grids, a flexible uncoupled training framework that leverages the independent mapped data for obtaining the embedding. Instead of directly processing the coupled nodes as GCNs, Node2Grids supports a more efficacious method in practice, mapping the coupled graph data into the independent grid-like data which can be fed into the efficient Convolutional Neural Network (CNN). This simple but valid strategy significantly saves memory and computational resource while achieving comparable results with the leading GCN-based models. Specifically, by ranking each node's influence through degree, Node2Grids selects the most influential first-order as well as second-order neighbors with central node fusion information to construct the grid-like data. For further improving the efficiency of downstream tasks, a simple CNN-based neural network is employed to capture the significant information from the mapped grid-like data. Moreover, the grid-level attention mechanism is implemented, which enables implicitly specifying the different weights for neighboring nodes with different influences. In addition to the typical transductive and inductive learning tasks, we also verify our framework on million-scale graphs to demonstrate the superiority of the proposed Node2Grids model against the state-of-the-art GCN-based approaches.
3D dynamic point clouds provide a natural discrete representation of real-world objects or scenes in motion, with a wide range of applications in immersive telepresence, autonomous driving, surveillance, \etc. Nevertheless, dynamic point clouds are often perturbed by noise due to hardware, software or other causes. While a plethora of methods have been proposed for static point cloud denoising, few efforts are made for the denoising of dynamic point clouds, which is quite challenging due to the irregular sampling patterns both spatially and temporally. In this paper, we represent dynamic point clouds naturally on spatial-temporal graphs, and exploit the temporal consistency with respect to the underlying surface (manifold). In particular, we define a manifold-to-manifold distance and its discrete counterpart on graphs to measure the variation-based intrinsic distance between surface patches in the temporal domain, provided that graph operators are discrete counterparts of functionals on Riemannian manifolds. Then, we construct the spatial-temporal graph connectivity between corresponding surface patches based on the temporal distance and between points in adjacent patches in the spatial domain. Leveraging the initial graph representation, we formulate dynamic point cloud denoising as the joint optimization of the desired point cloud and underlying graph representation, regularized by both spatial smoothness and temporal consistency. We reformulate the optimization and present an efficient algorithm. Experimental results show that the proposed method significantly outperforms independent denoising of each frame from state-of-the-art static point cloud denoising approaches, on both Gaussian noise and simulated LiDAR noise.
Graph classification aims to extract accurate information from graph-structured data for classification and is becoming more and more important in graph learning community. Although Graph Neural Networks (GNNs) have been successfully applied to graph classification tasks, most of them overlook the scarcity of labeled graph data in many applications. For example, in bioinformatics, obtaining protein graph labels usually needs laborious experiments. Recently, few-shot learning has been explored to alleviate this problem with only given a few labeled graph samples of test classes. The shared sub-structures between training classes and test classes are essential in few-shot graph classification. Exiting methods assume that the test classes belong to the same set of super-classes clustered from training classes. However, according to our observations, the label spaces of training classes and test classes usually do not overlap in real-world scenario. As a result, the existing methods don't well capture the local structures of unseen test classes. To overcome the limitation, in this paper, we propose a direct method to capture the sub-structures with well initialized meta-learner within a few adaptation steps. More specifically, (1) we propose a novel framework consisting of a graph meta-learner, which uses GNNs based modules for fast adaptation on graph data, and a step controller for the robustness and generalization of meta-learner; (2) we provide quantitative analysis for the framework and give a graph-dependent upper bound of the generalization error based on our framework; (3) the extensive experiments on real-world datasets demonstrate that our framework gets state-of-the-art results on several few-shot graph classification tasks compared to baselines.
In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. We prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We show how this allows us to achieve state-of-the-art performance on four different well-known datasets in graph classification and separate classes of graphs that other graph-learning methods cannot. Our approach is inspired by persistent homology, dependency parsing for NLP, and multivalued functions. The complexity of the underlying algorithm is O(#edges x #nodes) and code is publicly available (https://github.com/bruel-gabrielsson/universal-function-approximation-on-graphs).
Botnets are now a major source for many network attacks, such as DDoS attacks and spam. However, most traditional detection methods heavily rely on heuristically designed multi-stage detection criteria. In this paper, we consider the neural network design challenges of using modern deep learning techniques to learn policies for botnet detection automatically. To generate training data, we synthesize botnet connections with different underlying communication patterns overlaid on large-scale real networks as datasets. To capture the important hierarchical structure of centralized botnets and the fast-mixing structure for decentralized botnets, we tailor graph neural networks (GNN) to detect the properties of these structures. Experimental results show that GNNs are better able to capture botnet structure than previous non-learning methods when trained with appropriate data, and that deeper GNNs are crucial for learning difficult botnet topologies. We believe our data and studies can be useful for both the network security and graph learning communities.
Graph autoencoders (GAEs) are powerful tools in representation learning for graph embedding. However, the performance of GAEs is very dependent on the quality of the graph structure, i.e., of the adjacency matrix. In other words, GAEs would perform poorly when the adjacency matrix is incomplete or be disturbed. In this paper, two novel unsupervised graph embedding methods, unsupervised graph embedding via adaptive graph learning (BAGE) and unsupervised graph embedding via variational adaptive graph learning (VBAGE) are proposed. The proposed methods expand the application range of GAEs on graph embedding, i.e, on the general datasets without graph structure. Meanwhile, the adaptive learning mechanism can initialize the adjacency matrix without be affected by the parameter. Besides that, the latent representations are embedded in the laplacian graph structure to preserve the topology structure of the graph in the vector space. Moreover, the adjacency matrix can be self-learned for better embedding performance when the original graph structure is incomplete. With adaptive learning, the proposed method is much more robust to the graph structure. Experimental studies on several datasets validate our design and demonstrate that our methods outperform baselines by a wide margin in node clustering, node classification, and graph visualization tasks.
Graph neural networks (GNNs) are effective machine learning models for various graph learning problems. Despite their empirical successes, the theoretical limitations of GNNs have been revealed recently. Consequently, many GNN models have been proposed to overcome these limitations. In this survey, we provide a comprehensive overview of the expressive power of GNNs and provably powerful variants of GNNs.
The insurance industry has been creating innovative products around the emerging online shopping activities. Such e-commerce insurance is designed to protect buyers from potential risks such as impulse purchases and counterfeits. Fraudulent claims towards online insurance typically involve multiple parties such as buyers, sellers, and express companies, and they could lead to heavy financial losses. In order to uncover the relations behind organized fraudsters and detect fraudulent claims, we developed a large-scale insurance fraud detection system, i.e., InfDetect, which provides interfaces for commonly used graphs, standard data processing procedures, and a uniform graph learning platform. InfDetect is able to process big graphs containing up to 100 millions of nodes and billions of edges. In this paper, we investigate different graphs to facilitate fraudster mining, such as a device-sharing graph, a transaction graph, a friendship graph, and a buyer-seller graph. These graphs are fed to a uniform graph learning platform containing supervised and unsupervised graph learning algorithms. Cases on widely applied e-commerce insurance are described to demonstrate the usage and capability of our system. InfDetect has successfully detected thousands of fraudulent claims and saved over tens of thousands of dollars daily.
Fraudulent claim detection is one of the greatest challenges the insurance industry faces. Alibaba's return-freight insurance, providing return-shipping postage compensations over product return on the e-commerce platform, receives thousands of potentially fraudulent claims every day. Such deliberate abuse of the insurance policy could lead to heavy financial losses. In order to detect and prevent fraudulent insurance claims, we developed a novel data-driven procedure to identify groups of organized fraudsters, one of the major contributions to financial losses, by learning network information. In this paper, we introduce a device-sharing network among claimants, followed by developing an automated solution for fraud detection based on graph learning algorithms, to separate fraudsters from regular customers and uncover groups of organized fraudsters. This solution applied at Alibaba achieves more than 80% precision while covering 44% more suspicious accounts compared with a previously deployed rule-based classifier after human expert investigations. Our approach can easily and effectively generalizes to other types of insurance.
Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of the data and facilitates various information processing tasks. However, in cases where the underlying graph is unavailable, it needs to be learned from the data itself for data representation, data processing and inference purposes. Existing literature on learning graphs from data has mostly considered arbitrary graphs, whereas the graphs generating real-world data tend to have additional structure that can be incorporated in the graph learning procedure. Structure-aware graph learning methods require learning fewer parameters and have the potential to reduce computational, memory and sample complexities. In light of this, the focus of this paper is to devise a method to learn structured graphs from data that are given in the form of product graphs. Product graphs arise naturally in many real-world datasets and provide an efficient and compact representation of large-scale graphs through several smaller factor graphs. To this end, first the graph learning problem is posed as a linear program, which (on average) outperforms the state-of-the-art graph learning algorithms. This formulation is of independent interest itself as it shows that graph learning is possible through a simple linear program. Afterwards, an alternating minimization-based algorithm aimed at learning various types of product graphs is proposed, and local convergence guarantees to the true solution are established for this algorithm. Finally the performance gains, reduced sample complexity, and inference capabilities of the proposed algorithm over existing methods are also validated through numerical simulations on synthetic and real datasets.
Recently, a series of decomposition-based scene text detection methods has achieved impressive progress by decomposing challenging text regions into pieces and linking them in a bottom-up manner. However, most of them merely focus on linking independent text pieces while the context information is underestimated. In the puzzle game, the solver often put pieces together in a logical way according to the contextual information of each piece, in order to arrive at the correct solution. Inspired by it, we propose a novel decomposition-based method, termed Puzzle Networks (PuzzleNet), to address the challenging scene text detection task in this work. PuzzleNet consists of the Segment Proposal Network (SPN) that predicts the candidate text segments fitting arbitrary shape of text region, and the two-branch Multiple-Similarity Graph Convolutional Network (MSGCN) that models both appearance and geometry correlations between each segment to its contextual ones. By building segments as context graphs, MSGCN effectively employs segment context to predict combinations of segments. Final detections of polygon shape are produced by merging segments according to the predicted combinations. Evaluations on three benchmark datasets, ICDAR15, MSRA-TD500 and SCUT-CTW1500, have demonstrated that our method can achieve better or comparable performance than current state-of-the-arts, which is beneficial from the exploitation of segment context graph.
Deep neural networks, while generalize well, are known to be sensitive to small adversarial perturbations. This phenomenon poses severe security threat and calls for in-depth investigation of the robustness of deep learning models. With the emergence of neural networks for graph structured data, similar investigations are urged to understand their robustness. It has been found that adversarially perturbing the graph structure and/or node features may result in a significant degradation of the model performance. In this work, we show from a different angle that such fragility similarly occurs if the graph contains a few bad-actor nodes, which compromise a trained graph neural network through flipping the connections to any targeted victim. Worse, the bad actors found for one graph model severely compromise other models as well. We call the bad actors ``anchor nodes'' and propose an algorithm, named GUA, to identify them. Thorough empirical investigations suggest an interesting finding that the anchor nodes often belong to the same class; and they also corroborate the intuitive trade-off between the number of anchor nodes and the attack success rate. For the dataset Cora which contains 2708 nodes, as few as six anchor nodes will result in an attack success rate higher than 80\% for GCN and other three models.
Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some non-isomorphic graphs and they cannot learn efficient graph algorithms. In this paper, we demonstrate that GNNs become powerful just by adding a random feature to each node. We prove that the random features enable GNNs to learn almost optimal polynomial-time approximation algorithms for the minimum dominating set problem and maximum matching problem in terms of approximation ratios. The main advantage of our method is that it can be combined with off-the-shelf GNN models with slight modifications. Through experiments, we show that the addition of random features enables GNNs to solve various problems that normal GNNs, including the graph convolutional networks (GCNs) and graph isomorphism networks (GINs), cannot solve.
Graph distance metric learning serves as the foundation for many graph learning problems, e.g., graph clustering, graph classification and graph matching. Existing research works on graph distance metric (or graph kernels) learning fail to maintain the basic properties of such metrics, e.g., non-negative, identity of indiscernibles, symmetry and triangle inequality, respectively. In this paper, we will introduce a new graph neural network based distance metric learning approaches, namely GB-DISTANCE (GRAPH-BERT based Neural Distance). Solely based on the attention mechanism, GB-DISTANCE can learn graph instance representations effectively based on a pre-trained GRAPH-BERT model. Different from the existing supervised/unsupervised metrics, GB-DISTANCE can be learned effectively in a semi-supervised manner. In addition, GB-DISTANCE can also maintain the distance metric basic properties mentioned above. Extensive experiments have been done on several benchmark graph datasets, and the results demonstrate that GB-DISTANCE can out-perform the existing baseline methods, especially the recent graph neural network model based graph metrics, with a significant gap in computing the graph distance.
Graph convolutional networks (GCNs) have well-documented performance in various graph learning tasks, but their analysis is still at its infancy. Graph scattering transforms (GSTs) offer training-free deep GCN models that extract features from graph data, and are amenable to generalization and stability analyses. The price paid by GSTs is exponential complexity in space and time that increases with the number of layers. This discourages deployment of GSTs when a deep architecture is needed. The present work addresses the complexity limitation of GSTs by introducing an efficient so-termed pruned (p)GST approach. The resultant pruning algorithm is guided by a graph-spectrum-inspired criterion, and retains informative scattering features on-the-fly while bypassing the exponential complexity associated with GSTs. Stability of the novel pGSTs is also established when the input graph data or the network structure are perturbed. Furthermore, the sensitivity of pGST to random and localized signal perturbations is investigated analytically and experimentally. Numerical tests showcase that pGST performs comparably to the baseline GST at considerable computational savings. Furthermore, pGST achieves comparable performance to state-of-the-art GCNs in graph and 3D point cloud classification tasks. Upon analyzing the pGST pruning patterns, it is shown that graph data in different domains call for different network architectures, and that the pruning algorithm may be employed to guide the design choices for contemporary GCNs.