Cytoarchitecture describes the spatial organization of neuronal cells in the brain, including their arrangement into layers and columns with respect to cell density, orientation, or presence of certain cell types. It allows to segregate the brain into cortical areas and subcortical nuclei, links structure with connectivity and function, and provides a microstructural reference for human brain atlases. Mapping boundaries between areas requires to scan histological sections at microscopic resolution. While recent high-throughput scanners allow to scan a complete human brain in the order of a year, it is practically impossible to delineate regions at the same pace using the established gold standard method. Researchers have recently addressed cytoarchitectonic mapping of cortical regions with deep neural networks, relying on image patches from individual 2D sections for classification. However, the 3D context, which is needed to disambiguate complex or obliquely cut brain regions, is not taken into account. In this work, we combine 2D histology with 3D topology by reformulating the mapping task as a node classification problem on an approximate 3D midsurface mesh through the isocortex. We extract deep features from cortical patches in 2D histological sections which are descriptive of cytoarchitecture, and assign them to the corresponding nodes on the 3D mesh to construct a large attributed graph. By solving the brain mapping problem on this graph using graph neural networks, we obtain significantly improved classification results. The proposed framework lends itself nicely to integration of additional neuroanatomical priors for mapping.
Attention based neural networks are state of the art in a large range of applications. However, their performance tends to degrade when the number of layers increases. In this work, we show that enforcing Lipschitz continuity by normalizing the attention scores can significantly improve the performance of deep attention models. First, we show that, for deep graph attention networks (GAT), gradient explosion appears during training, leading to poor performance of gradient-based training algorithms. To address this issue, we derive a theoretical analysis of the Lipschitz continuity of attention modules and introduce LipschitzNorm, a simple and parameter-free normalization for self-attention mechanisms that enforces the model to be Lipschitz continuous. We then apply LipschitzNorm to GAT and Graph Transformers and show that their performance is substantially improved in the deep setting (10 to 30 layers). More specifically, we show that a deep GAT model with LipschitzNorm achieves state of the art results for node label prediction tasks that exhibit long-range dependencies, while showing consistent improvements over their unnormalized counterparts in benchmark node classification tasks.
Graph neural networks (GNNs) are important tools for transductive learning tasks, such as node classification in graphs, due to their expressive power in capturing complex interdependency between nodes. To enable graph neural network learning, existing works typically assume that labeled nodes, from two or multiple classes, are provided, so that a discriminative classifier can be learned from the labeled data. In reality, this assumption might be too restrictive for applications, as users may only provide labels of interest in a single class for a small number of nodes. In addition, most GNN models only aggregate information from short distances (e.g., 1-hop neighbors) in each round, and fail to capture long distance relationship in graphs. In this paper, we propose a novel graph neural network framework, long-short distance aggregation networks (LSDAN), to overcome these limitations. By generating multiple graphs at different distance levels, based on the adjacency matrix, we develop a long-short distance attention model to model these graphs. The direct neighbors are captured via a short-distance attention mechanism, and neighbors with long distance are captured by a long distance attention mechanism. Two novel risk estimators are further employed to aggregate long-short-distance networks, for PU learning and the loss is back-propagated for model learning. Experimental results on real-world datasets demonstrate the effectiveness of our algorithm.
This article unveils a new relation between the Nishimori temperature parametrizing a distribution P and the Bethe free energy on random Erdos-Renyi graphs with edge weights distributed according to P. Estimating the Nishimori temperature being a task of major importance in Bayesian inference problems, as a practical corollary of this new relation, a numerical method is proposed to accurately estimate the Nishimori temperature from the eigenvalues of the Bethe Hessian matrix of the weighted graph. The algorithm, in turn, is used to propose a new spectral method for node classification in weighted (possibly sparse) graphs. The superiority of the method over competing state-of-the-art approaches is demonstrated both through theoretical arguments and real-world data experiments.
Graph neural networks (GNNs) have achieved state-of-the-art performance for node classification on graphs. The vast majority of existing works assume that genuine node labels are always provided for training. However, there has been very little research effort on how to improve the robustness of GNNs in the presence of label noise. Learning with label noise has been primarily studied in the context of image classification, but these techniques cannot be directly applied to graph-structured data, due to two major challenges -- label sparsity and label dependency -- faced by learning on graphs. In this paper, we propose a new framework, UnionNET, for learning with noisy labels on graphs under a semi-supervised setting. Our approach provides a unified solution for robustly training GNNs and performing label correction simultaneously. The key idea is to perform label aggregation to estimate node-level class probability distributions, which are used to guide sample reweighting and label correction. Compared with existing works, UnionNET has two appealing advantages. First, it requires no extra clean supervision, or explicit estimation of the noise transition matrix. Second, a unified learning framework is proposed to robustly train GNNs in an end-to-end manner. Experimental results show that our proposed approach: (1) is effective in improving model robustness against different types and levels of label noise; (2) yields significant improvements over state-of-the-art baselines.
Semi-supervised learning on graphs is an important problem in the machine learning area. In recent years, state-of-the-art classification methods based on graph neural networks (GNNs) have shown their superiority over traditional ones such as label propagation. However, the sophisticated architectures of these neural models will lead to a complex prediction mechanism, which could not make full use of valuable prior knowledge lying in the data, e.g., structurally correlated nodes tend to have the same class. In this paper, we propose a framework based on knowledge distillation to address the above issues. Our framework extracts the knowledge of an arbitrary learned GNN model (teacher model), and injects it into a well-designed student model. The student model is built with two simple prediction mechanisms, i.e., label propagation and feature transformation, which naturally preserves structure-based and feature-based prior knowledge, respectively. In specific, we design the student model as a trainable combination of parameterized label propagation and feature transformation modules. As a result, the learned student can benefit from both prior knowledge and the knowledge in GNN teachers for more effective predictions. Moreover, the learned student model has a more interpretable prediction process than GNNs. We conduct experiments on five public benchmark datasets and employ seven GNN models including GCN, GAT, APPNP, SAGE, SGC, GCNII and GLP as the teacher models. Experimental results show that the learned student model can consistently outperform its corresponding teacher model by 1.4% - 4.7% on average. Code and data are available at https://github.com/BUPT-GAMMA/CPF
Graph Convolutional Networks (GCNs) have achieved impressive empirical advancement across a wide variety of semi-supervised node classification tasks. Despite their great success, training GCNs on large graphs suffers from computational and memory issues. A potential path to circumvent these obstacles is sampling-based methods, where at each layer a subset of nodes is sampled. Although recent studies have empirically demonstrated the effectiveness of sampling-based methods, these works lack theoretical convergence guarantees under realistic settings and cannot fully leverage the information of evolving parameters during optimization. In this paper, we describe and analyze a general doubly variance reduction schema that can accelerate any sampling method under the memory budget. The motivating impetus for the proposed schema is a careful analysis of the variance of sampling methods where it is shown that the induced variance can be decomposed into node embedding approximation variance (zeroth-order variance) during forward propagation and layerwise-gradient variance (first-order variance) during backward propagation. We theoretically analyze the convergence of the proposed schema and show that it enjoys an $\mathcal{O}(1/T)$ convergence rate. We complement our theoretical results by integrating the proposed schema in different sampling methods and applying them to different large real-world graphs.
Segmenting histology images into diagnostically relevant regions is imperative to support timely and reliable decisions by pathologists. To this end, computer-aided techniques have been proposed to delineate relevant regions in scanned histology slides. However, the techniques necessitate task-specific large datasets of annotated pixels, which is tedious, time-consuming, expensive, and infeasible to acquire for many histology tasks. Thus, weakly-supervised semantic segmentation techniques are proposed to utilize weak supervision that is cheaper and quicker to acquire. In this paper, we propose SegGini, a weakly supervised segmentation method using graphs, that can utilize weak multiplex annotations, i.e. inexact and incomplete annotations, to segment arbitrary and large images, scaling from tissue microarray (TMA) to whole slide image (WSI). Formally, SegGini constructs a tissue-graph representation for an input histology image, where the graph nodes depict tissue regions. Then, it performs weakly-supervised segmentation via node classification by using inexact image-level labels, incomplete scribbles, or both. We evaluated SegGini on two public prostate cancer datasets containing TMAs and WSIs. Our method achieved state-of-the-art segmentation performance on both datasets for various annotation settings while being comparable to a pathologist baseline.
In recent years, graph neural networks (GNNs) have been widely adopted in the representation learning of graph-structured data and provided state-of-the-art performance in various applications such as link prediction, node classification, and recommendation. Motivated by recent advances of self-supervision for representation learning in natural language processing and computer vision, self-supervised learning has been recently studied to leverage unlabeled graph-structured data. However, employing self-supervision tasks as auxiliary tasks to assist a primary task has been less explored in the literature on graphs. In this paper, we propose a novel self-supervised auxiliary learning framework to effectively learn graph neural networks. Moreover, this work is the first study showing that a meta-path prediction is beneficial as a self-supervised auxiliary task for heterogeneous graphs. Our method is learning to learn a primary task with various auxiliary tasks to improve generalization performance. The proposed method identifies an effective combination of auxiliary tasks and automatically balances them to improve the primary task. Our methods can be applied to any graph neural network in a plug-in manner without manual labeling or additional data. Also, it can be extended to any other auxiliary tasks. Our experiments demonstrate that the proposed method consistently improves the performance of node classification and link prediction.
Disease prediction is a well-known classification problem in medical applications. GCNs provide a powerful tool for analyzing the patients' features relative to each other. This can be achieved by modeling the problem as a graph node classification task, where each node is a patient. Due to the nature of such medical datasets, class imbalance is a prevalent issue in the field of disease prediction, where the distribution of classes is skewed. When the class imbalance is present in the data, the existing graph-based classifiers tend to be biased towards the major class(es) and neglect the samples in the minor class(es). On the other hand, the correct diagnosis of the rare positive cases among all the patients is vital in a healthcare system. In conventional methods, such imbalance is tackled by assigning appropriate weights to classes in the loss function which is still dependent on the relative values of weights, sensitive to outliers, and in some cases biased towards the minor class(es). In this paper, we propose a Re-weighted Adversarial Graph Convolutional Network (RA-GCN) to prevent the graph-based classifier from emphasizing the samples of any particular class. This is accomplished by associating a graph-based neural network to each class, which is responsible for weighting the class samples and changing the importance of each sample for the classifier. Therefore, the classifier adjusts itself and determines the boundary between classes with more attention to the important samples. The parameters of the classifier and weighting networks are trained by an adversarial approach. We show experiments on synthetic and three publicly available medical datasets. RA-GCN demonstrates the superiority compared to recent methods in identifying the patient's status on all three datasets. The detailed analysis is provided as quantitative and qualitative experiments on synthetic datasets.
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.
Existing graph neural networks (GNNs) largely rely on node embeddings, which represent a node as a vector by its identity, type, or content. However, graphs with unattributed nodes widely exist in real-world applications (e.g., anonymized social networks). Previous GNNs either assign random labels to nodes (which introduces artefacts to the GNN) or assign one embedding to all nodes (which fails to explicitly distinguish one node from another). Further, when these GNNs are applied to unattributed node classification problems, they have an undesired equivariance property, which are fundamentally unable to address the data with multiple possible outputs. In this paper, we analyze the limitation of existing approaches to node classification problems. Inspired by our analysis, we propose a generalized equivariance property and a Preferential Labeling technique that satisfies the desired property asymptotically. Experimental results show that we achieve high performance in several unattributed node classification tasks.
The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets naturally modeled as directed graphs, including citation, website, and traffic networks, the vast majority of this research focuses on undirected graphs. In this paper, we propose MagNet, a spectral GNN for directed graphs based on a complex Hermitian matrix known as the magnetic Laplacian. This matrix encodes undirected geometric structure in the magnitude of its entries and directional information in their phase. A "charge" parameter attunes spectral information to variation among directed cycles. We apply our network to a variety of directed graph node classification and link prediction tasks showing that MagNet performs well on all tasks and that its performance exceeds all other methods on a majority of such tasks. The underlying principles of MagNet are such that it can be adapted to other spectral GNN architectures.
Graph convolutional neural network provides good solutions for node classification and other tasks with non-Euclidean data. There are several graph convolutional models that attempt to develop deep networks but do not cause serious over-smoothing at the same time. Considering that the wavelet transform generally has a stronger ability to extract useful information than the Fourier transform, we propose a new deep graph wavelet convolutional network (DeepGWC) for semi-supervised node classification tasks. Based on the optimized static filtering matrix parameters of vanilla graph wavelet neural networks and the combination of Fourier bases and wavelet ones, DeepGWC is constructed together with the reuse of residual connection and identity mappings in network architectures. Extensive experiments on three benchmark datasets including Cora, Citeseer, and Pubmed are conducted. The experimental results demonstrate that our DeepGWC outperforms existing graph deep models with the help of additional wavelet bases and achieves new state-of-the-art performances eventually.
We consider two popular Graph Representation Learning (GRL) methods: message passing for node classification and network embedding for link prediction. For each, we pick a popular model that we: (i) linearize and (ii) and switch its training objective to Frobenius norm error minimization. These simplifications can cast the training into finding the optimal parameters in closed-form. We program in TensorFlow a functional form of Truncated Singular Value Decomposition (SVD), such that, we could decompose a dense matrix $\mathbf{M}$, without explicitly computing $\mathbf{M}$. We achieve competitive performance on popular GRL tasks while providing orders of magnitude speedup. We open-source our code at http://github.com/samihaija/tf-fsvd
While there exists a wide variety of graph neural networks (GNN) for node classification, only a minority of them adopt mechanisms that effectively target noise propagation during the message-passing procedure. Additionally, a very important challenge that significantly affects graph neural networks is the issue of scalability which limits their application to larger graphs. In this paper we propose our method named NODE-SELECT: an efficient graph neural network that uses subsetting layers which only allow the best sharing-fitting nodes to propagate their information. By having a selection mechanism within each layer which we stack in parallel, our proposed method NODE-SELECT is able to both reduce the amount noise propagated and adapt the restrictive sharing concept observed in real world graphs. Our NODE-SELECT significantly outperformed existing GNN frameworks in noise experiments and matched state-of-the art results in experiments without noise over different benchmark datasets.
Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.
Networks have been widely used to represent the relations between objects such as academic networks and social networks, and learning embedding for networks has thus garnered plenty of research attention. Self-supervised network representation learning aims at extracting node embedding without external supervision. Recently, maximizing the mutual information between the local node embedding and the global summary (e.g. Deep Graph Infomax, or DGI for short) has shown promising results on many downstream tasks such as node classification. However, there are two major limitations of DGI. Firstly, DGI merely considers the extrinsic supervision signal (i.e., the mutual information between node embedding and global summary) while ignores the intrinsic signal (i.e., the mutual dependence between node embedding and node attributes). Secondly, nodes in a real-world network are usually connected by multiple edges with different relations, while DGI does not fully explore the various relations among nodes. To address the above-mentioned problems, we propose a novel framework, called High-order Deep Multiplex Infomax (HDMI), for learning node embedding on multiplex networks in a self-supervised way. To be more specific, we first design a joint supervision signal containing both extrinsic and intrinsic mutual information by high-order mutual information, and we propose a High-order Deep Infomax (HDI) to optimize the proposed supervision signal. Then we propose an attention based fusion module to combine node embedding from different layers of the multiplex network. Finally, we evaluate the proposed HDMI on various downstream tasks such as unsupervised clustering and supervised classification. The experimental results show that HDMI achieves state-of-the-art performance on these tasks.
Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection, or link prediction. The main challenge is that one needs to make sure that embeddings describe the properties of the graphs well. As a result, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments we formulate two general conclusions. First, if one needs to pick one embedding algorithm before running the experiments, then node2vec is the best choice as it performed best in our tests. Having said that, there is no single winner in all tests and, additionally, most embedding algorithms have hyperparameters that should be tuned and are randomized. Therefore, our main recommendation for practitioners is, if possible, to generate several embeddings for a problem at hand and then use a general framework that provides a tool for an unsupervised graph embedding comparison. This framework (introduced recently in the literature and easily available on GitHub repository) assigns the divergence score to embeddings to help distinguish good ones from bad ones.