Representation learning on user-item graph for recommendation has evolved from using single ID or interaction history to exploiting higher-order neighbors. This leads to the success of graph convolution networks (GCNs) for recommendation such as PinSage and LightGCN. Despite effectiveness, we argue that they suffer from two limitations: (1) high-degree nodes exert larger impact on the representation learning, deteriorating the recommendations of low-degree (long-tail) items; and (2) representations are vulnerable to noisy interactions, as the neighborhood aggregation scheme further enlarges the impact of observed edges. In this work, we explore self-supervised learning on user-item graph, so as to improve the accuracy and robustness of GCNs for recommendation. The idea is to supplement the classical supervised task of recommendation with an auxiliary self-supervised task, which reinforces node representation learning via self-discrimination. Specifically, we generate multiple views of a node, maximizing the agreement between different views of the same node compared to that of other nodes. We devise three operators to generate the views -- node dropout, edge dropout, and random walk -- that change the graph structure in different manners. We term this new learning paradigm as \textit{Self-supervised Graph Learning} (SGL), implementing it on the state-of-the-art model LightGCN. Through theoretical analyses, we find that SGL has the ability of automatically mining hard negatives. Empirical studies on three benchmark datasets demonstrate the effectiveness of SGL, which improves the recommendation accuracy, especially on long-tail items, and the robustness against interaction noises. Our implementations are available at \url{https://github.com/wujcan/SGL}.
Graph neural networks (GNNs) can process graphs of different sizes, but their ability to generalize across sizes, specifically from small to large graphs, is still not well understood. In this paper, we identify an important type of data where generalization from small to large graphs is challenging: graph distributions for which the local structure depends on the graph size. This effect occurs in multiple important graph learning domains, including social and biological networks. We first prove that when there is a difference between the local structures, GNNs are not guaranteed to generalize across sizes: there are "bad" global minima that do well on small graphs but fail on large graphs. We then study the size-generalization problem empirically and demonstrate that when there is a discrepancy in local structure, GNNs tend to converge to non-generalizing solutions. Finally, we suggest two approaches for improving size generalization, motivated by our findings. Notably, we propose a novel Self-Supervised Learning (SSL) task aimed at learning meaningful representations of local structures that appear in large graphs. Our SSL task improves classification accuracy on several popular datasets.
Given the input graph and its label/property, several key problems of graph learning, such as finding interpretable subgraphs, graph denoising and graph compression, can be attributed to the fundamental problem of recognizing a subgraph of the original one. This subgraph shall be as informative as possible, yet contains less redundant and noisy structure. This problem setting is closely related to the well-known information bottleneck (IB) principle, which, however, has less been studied for the irregular graph data and graph neural networks (GNNs). In this paper, we propose a framework of Graph Information Bottleneck (GIB) for the subgraph recognition problem in deep graph learning. Under this framework, one can recognize the maximally informative yet compressive subgraph, named IB-subgraph. However, the GIB objective is notoriously hard to optimize, mostly due to the intractability of the mutual information of irregular graph data and the unstable optimization process. In order to tackle these challenges, we propose: i) a GIB objective based-on a mutual information estimator for the irregular graph data; ii) a bi-level optimization scheme to maximize the GIB objective; iii) a connectivity loss to stabilize the optimization process. We evaluate the properties of the IB-subgraph in three application scenarios: improvement of graph classification, graph interpretation and graph denoising. Extensive experiments demonstrate that the information-theoretic IB-subgraph enjoys superior graph properties.
It has become a de-facto standard to represent words as elements of a vector space (word2vec, GloVe). While this approach is convenient, it is unnatural for language: words form a graph with a latent hierarchical structure, and this structure has to be revealed and encoded by word embeddings. We introduce GraphGlove: unsupervised graph word representations which are learned end-to-end. In our setting, each word is a node in a weighted graph and the distance between words is the shortest path distance between the corresponding nodes. We adopt a recent method learning a representation of data in the form of a differentiable weighted graph and use it to modify the GloVe training algorithm. We show that our graph-based representations substantially outperform vector-based methods on word similarity and analogy tasks. Our analysis reveals that the structure of the learned graphs is hierarchical and similar to that of WordNet, the geometry is highly non-trivial and contains subgraphs with different local topology.
One practice of employing deep neural networks is to apply the same architecture to all the input instances. However, a fixed architecture may not be representative enough for data with high diversity. To promote the model capacity, existing approaches usually employ larger convolutional kernels or deeper network structure, which may increase the computational cost. In this paper, we address this issue by raising the Dynamic Graph Network (DG-Net). The network learns the instance-aware connectivity, which creates different forward paths for different instances. Specifically, the network is initialized as a complete directed acyclic graph, where the nodes represent convolutional blocks and the edges represent the connection paths. We generate edge weights by a learnable module \textit{router} and select the edges whose weights are larger than a threshold, to adjust the connectivity of the neural network structure. Instead of using the same path of the network, DG-Net aggregates features dynamically in each node, which allows the network to have more representation ability. To facilitate the training, we represent the network connectivity of each sample in an adjacency matrix. The matrix is updated to aggregate features in the forward pass, cached in the memory, and used for gradient computing in the backward pass. We verify the effectiveness of our method with several static architectures, including MobileNetV2, ResNet, ResNeXt, and RegNet. Extensive experiments are performed on ImageNet classification and COCO object detection, which shows the effectiveness and generalization ability of our approach.
Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of using Laplacian in deriving regularization operators on graphs and its consequent use with spectral GCNN filter designs. In this work, we explore the regularization properties of graph Laplacian and proposed a generalized framework for regularized filter designs in spectral GCNNs. We found that the filters used in many state-of-the-art GCNNs can be derived as a special case of the framework we developed. We designed new filters that are associated with well-defined regularization behavior and tested their performance on semi-supervised node classification tasks. Their performance was found to be superior to that of the other state-of-the-art techniques.
This article presents matrix backpropagation algorithms for the QR decomposition of matrices $A_{m, n}$, that are either square (m = n), wide (m < n), or deep (m > n), with rank $k = min(m, n)$. Furthermore, we derive novel matrix backpropagation results for the pivoted (full-rank) QR decomposition and for the LQ decomposition of deep input matrices. Differentiable QR decomposition offers a numerically stable, computationally efficient method to solve least squares problems frequently encountered in machine learning and computer vision. Other use cases such as graph learning and network compression are listed in the article. Software implementation across popular deep learning frameworks (PyTorch, TensorFlow, MXNet) incorporate the methods for general use within the deep learning community. Furthermore, this article aids the practitioner in understanding the matrix backpropagation methodology as part of larger computational graphs.
Knowledge graphs capture entities and relations from long documents and can facilitate reasoning in many downstream applications. Extracting compact knowledge graphs containing only salient entities and relations is important but challenging for understanding and summarizing long documents. We introduce a new text-to-graph task of predicting summarized knowledge graphs from long documents. We develop a dataset of 200k document/graph pairs using automatic and human annotations. We also develop strong baselines for this task based on graph learning and text summarization, and provide quantitative and qualitative studies of their effect.
Nowadays, deep learning methods, especially the Graph Convolutional Network (GCN), have shown impressive performance in hyperspectral image (HSI) classification. However, the current GCN-based methods treat graph construction and image classification as two separate tasks, which often results in suboptimal performance. Another defect of these methods is that they mainly focus on modeling the local pairwise importance between graph nodes while lack the capability to capture the global contextual information of HSI. In this paper, we propose a Multi-level GCN with Automatic Graph Learning method (MGCN-AGL) for HSI classification, which can automatically learn the graph information at both local and global levels. By employing attention mechanism to characterize the importance among spatially neighboring regions, the most relevant information can be adaptively incorporated to make decisions, which helps encode the spatial context to form the graph information at local level. Moreover, we utilize multiple pathways for local-level graph convolution, in order to leverage the merits from the diverse spatial context of HSI and to enhance the expressive power of the generated representations. To reconstruct the global contextual relations, our MGCN-AGL encodes the long range dependencies among image regions based on the expressive representations that have been produced at local level. Then inference can be performed along the reconstructed graph edges connecting faraway regions. Finally, the multi-level information is adaptively fused to generate the network output. In this means, the graph learning and image classification can be integrated into a unified framework and benefit each other. Extensive experiments have been conducted on three real-world hyperspectral datasets, which are shown to outperform the state-of-the-art methods.
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture long-range dependencies in underlying graphs. To overcome this difficulty, we propose a graph learning framework, called Implicit Graph Neural Networks (IGNN), where predictions are based on the solution of a fixed-point equilibrium equation involving implicitly defined "state" vectors. We use the Perron-Frobenius theory to derive sufficient conditions that ensure well-posedness of the framework. Leveraging implicit differentiation, we derive a tractable projected gradient descent method to train the framework. Experiments on a comprehensive range of tasks show that IGNNs consistently capture long-range dependencies and outperform the state-of-the-art GNN models.
Recent studies on Graph Convolutional Networks (GCNs) reveal that the initial node representations (i.e., the node representations before the first-time graph convolution) largely affect the final model performance. However, when learning the initial representation for a node, most existing work linearly combines the embeddings of node features, without considering the interactions among the features (or feature embeddings). We argue that when the node features are categorical, e.g., in many real-world applications like user profiling and recommender system, feature interactions usually carry important signals for predictive analytics. Ignoring them will result in suboptimal initial node representation and thus weaken the effectiveness of the follow-up graph convolution. In this paper, we propose a new GCN model named CatGCN, which is tailored for graph learning when the node features are categorical. Specifically, we integrate two ways of explicit interaction modeling into the learning of initial node representation, i.e., local interaction modeling on each pair of node features and global interaction modeling on an artificial feature graph. We then refine the enhanced initial node representations with the neighborhood aggregation-based graph convolution. We train CatGCN in an end-to-end fashion and demonstrate it on semi-supervised node classification. Extensive experiments on three tasks of user profiling (the prediction of user age, city, and purchase level) from Tencent and Alibaba datasets validate the effectiveness of CatGCN, especially the positive effect of performing feature interaction modeling before graph convolution.
Nonnegative matrix factorization is usually powerful for learning the "shallow" parts-based representation, but it clearly fails to discover deep hierarchical information within both the basis and representation spaces. In this paper, we technically propose a new enriched prior based Dual-constrained Deep Semi-Supervised Coupled Factorization Network, called DS2CF-Net, for learning the hierarchical coupled representations. To ex-tract hidden deep features, DS2CF-Net is modeled as a deep-structure and geometrical structure-constrained neural network. Specifically, DS2CF-Net designs a deep coupled factorization architecture using multi-layers of linear transformations, which coupled updates the bases and new representations in each layer. To improve the discriminating ability of learned deep representations and deep coefficients, our network clearly considers enriching the supervised prior by the joint deep coefficients-regularized label prediction, and incorporates enriched prior information as additional label and structure constraints. The label constraint can enable the samples of the same label to have the same coordinate in the new feature space, while the structure constraint forces the coefficient matrices in each layer to be block-diagonal so that the enhanced prior using the self-expressive label propagation are more accurate. Our network also integrates the adaptive dual-graph learning to retain the local manifold structures of both the data manifold and feature manifold by minimizing the reconstruction errors in each layer. Extensive experiments on several real databases demonstrate that our DS2CF-Net can obtain state-of-the-art performance for representation learning and clustering.
Graph neural networks (GNN) are powerful models for many graph-structured tasks. Existing models often assume that the complete structure of the graph is available during training. In practice, however, graph-structured data is usually formed in a streaming fashion so that learning a graph continuously is often necessary. In this paper, we bridge GNN and lifelong learning by converting a continual graph learning problem to a regular graph learning problem so GNN can inherit the lifelong learning techniques developed for convolutional neural networks (CNN). We propose a new topology, the feature graph, which takes features as new nodes and turns nodes into independent graphs. This successfully converts the original problem of node classification to graph classification. In the experiments, we demonstrate the efficiency and effectiveness of feature graph networks (FGN) by continuously learning a sequence of classical graph datasets. We also show that FGN achieves superior performance in two applications, i.e., lifelong human action recognition with wearable devices and feature matching. To the best of our knowledge, FGN is the first method to bridge graph learning and lifelong learning via a novel graph topology. Source code is available at https://github.com/wang-chen/LGL
Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance. This paper proposes a graph learning framework to preserve both the local and global structure of data. Specifically, our method uses the self-expressiveness of samples to capture the global structure and adaptive neighbor approach to respect the local structure. Furthermore, most existing graph-based methods conduct clustering and semi-supervised classification on the graph learned from the original data matrix, which doesn't have explicit cluster structure, thus they might not achieve the optimal performance. By considering rank constraint, the achieved graph will have exactly $c$ connected components if there are $c$ clusters or classes. As a byproduct of this, graph learning and label inference are jointly and iteratively implemented in a principled way. Theoretically, we show that our model is equivalent to a combination of kernel k-means and k-means methods under certain condition. Extensive experiments on clustering and semi-supervised classification demonstrate that the proposed method outperforms other state-of-the-art methods.
Graphs have been widely used to represent complex data in many applications. Efficient and effective analysis of graphs is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) problems, which are NP-hard. Recent studies have focused a lot on the potential of using machine learning (ML) to solve graph-based CO problems. Most recent methods follow the two-stage framework. The first stage is graph representation learning, which embeds the graphs into low-dimension vectors. The second stage uses ML to solve the CO problems using the embeddings of the graphs learned in the first stage. The works for the first stage can be classified into two categories, graph embedding (GE) methods and end-to-end (E2E) learning methods. For GE methods, learning graph embedding has its own objective, which may not rely on the CO problems to be solved. The CO problems are solved by independent downstream tasks. For E2E learning methods, the learning of graph embeddings does not have its own objective and is an intermediate step of the learning procedure of solving the CO problems. The works for the second stage can also be classified into two categories, non-autoregressive methods and autoregressive methods. Non-autoregressive methods predict a solution for a CO problem in one shot. A non-autoregressive method predicts a matrix that denotes the probability of each node/edge being a part of a solution of the CO problem. The solution can be computed from the matrix. Autoregressive methods iteratively extend a partial solution step by step. At each step, an autoregressive method predicts a node/edge conditioned to current partial solution, which is used to its extension. In this survey, we provide a thorough overview of recent studies of the graph learning-based CO methods. The survey ends with several remarks on future research directions.
Aiming at better representing multivariate relationships, this paper investigates a motif dimensional framework for higher-order graph learning. The graph learning effectiveness can be improved through OFFER. The proposed framework mainly aims at accelerating and improving higher-order graph learning results. We apply the acceleration procedure from the dimensional of network motifs. Specifically, the refined degree for nodes and edges are conducted in two stages: (1) employ motif degree of nodes to refine the adjacency matrix of the network; and (2) employ motif degree of edges to refine the transition probability matrix in the learning process. In order to assess the efficiency of the proposed framework, four popular network representation algorithms are modified and examined. By evaluating the performance of OFFER, both link prediction results and clustering results demonstrate that the graph representation learning algorithms enhanced with OFFER consistently outperform the original algorithms with higher efficiency.
Many users implicitly assume that software can only be exploited after it is installed. However, recent supply-chain attacks demonstrate that application integrity must be ensured during installation itself. We introduce SIGL, a new tool for detecting malicious behavior during software installation. SIGL collects traces of system call activity, building a data provenance graph that it analyzes using a novel autoencoder architecture with a graph long short-term memory network (graph LSTM) for the encoder and a standard multilayer perceptron for the decoder. SIGL flags suspicious installations as well as the specific installation-time processes that are likely to be malicious. Using a test corpus of 625 malicious installers containing real-world malware, we demonstrate that SIGL has a detection accuracy of 96%, outperforming similar systems from industry and academia by up to 87% in precision and recall and 45% in accuracy. We also demonstrate that SIGL can pinpoint the processes most likely to have triggered malicious behavior, works on different audit platforms and operating systems, and is robust to training data contamination and adversarial attack. It can be used with application-specific models, even in the presence of new software versions, as well as application-agnostic meta-models that encompass a wide range of applications and installers.
Graph learning has emerged as a promising technique for multi-view clustering with its ability to learn a unified and robust graph from multiple views. However, existing graph learning methods mostly focus on the multi-view consistency issue, yet often neglect the inconsistency across multiple views, which makes them vulnerable to possibly low-quality or noisy datasets. To overcome this limitation, we propose a new multi-view graph learning framework, which for the first time simultaneously and explicitly models multi-view consistency and multi-view inconsistency in a unified objective function, through which the consistent and inconsistent parts of each single-view graph as well as the unified graph that fuses the consistent parts can be iteratively learned. Though optimizing the objective function is NP-hard, we design a highly efficient optimization algorithm which is able to obtain an approximate solution with linear time complexity in the number of edges in the unified graph. Furthermore, our multi-view graph learning approach can be applied to both similarity graphs and dissimilarity graphs, which lead to two graph fusion-based variants in our framework. Experiments on twelve multi-view datasets have demonstrated the robustness and efficiency of the proposed approach.
The problem of graph learning concerns the construction of an explicit topological structure revealing the relationship between nodes representing data entities, which plays an increasingly important role in the success of many graph-based representations and algorithms in the field of machine learning and graph signal processing. In this paper, we propose a novel graph learning framework that incorporates the node-side and observation-side information, and in particular the covariates that help to explain the dependency structures in graph signals. To this end, we consider graph signals as functions in the reproducing kernel Hilbert space associated with a Kronecker product kernel, and integrate functional learning with smoothness-promoting graph learning to learn a graph representing the relationship between nodes. The functional learning increases the robustness of graph learning against missing and incomplete information in the graph signals. In addition, we develop a novel graph-based regularisation method which, when combined with the Kronecker product kernel, enables our model to capture both the dependency explained by the graph and the dependency due to graph signals observed under different but related circumstances, e.g. different points in time. The latter means the graph signals are free from the i.i.d. assumptions required by the classical graph learning models. Experiments on both synthetic and real-world data show that our methods outperform the state-of-the-art models in learning a meaningful graph topology from graph signals, in particular under heavy noise, missing values, and multiple dependency.
Domain adaptation aims to generalize a model from a source domain to tackle tasks in a related but different target domain. Traditional domain adaptation algorithms assume that enough labeled data, which are treated as the prior knowledge are available in the source domain. However, these algorithms will be infeasible when only a few labeled data exist in the source domain, and thus the performance decreases significantly. To address this challenge, we propose a Domain-invariant Graph Learning (DGL) approach for domain adaptation with only a few labeled source samples. Firstly, DGL introduces the Nystrom method to construct a plastic graph that shares similar geometric property as the target domain. And then, DGL flexibly employs the Nystrom approximation error to measure the divergence between plastic graph and source graph to formalize the distribution mismatch from the geometric perspective. Through minimizing the approximation error, DGL learns a domain-invariant geometric graph to bridge source and target domains. Finally, we integrate the learned domain-invariant graph with the semi-supervised learning and further propose an adaptive semi-supervised model to handle the cross-domain problems. The results of extensive experiments on popular datasets verify the superiority of DGL, especially when only a few labeled source samples are available.