In graph instance representation learning, both the diverse graph instance sizes and the graph node orderless property have been the major obstacles that render existing representation learning models fail to work. In this paper, we will examine the effectiveness of GRAPH-BERT on graph instance representation learning, which was designed for node representation learning tasks originally. To adapt GRAPH-BERT to the new problem settings, we re-design it with a segmented architecture instead, which is also named as SEG-BERT (Segmented GRAPH-BERT) for reference simplicity in this paper. SEG-BERT involves no node-order-variant inputs or functional components anymore, and it can handle the graph node orderless property naturally. What's more, SEG-BERT has a segmented architecture and introduces three different strategies to unify the graph instance sizes, i.e., full-input, padding/pruning and segment shifting, respectively. SEG-BERT is pre-trainable in an unsupervised manner, which can be further transferred to new tasks directly or with necessary fine-tuning. We have tested the effectiveness of SEG-BERT with experiments on seven graph instance benchmark datasets, and SEG-BERT can out-perform the comparison methods on six out of them with significant performance advantages.
Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they are not equally suitable for visualisation purposes. In this work, we merge Mapper, an algorithm from the field of Topological Data Analysis (TDA), with the expressive power of Graph Neural Networks (GNNs) to produce hierarchical, topologically-grounded visualisations of graphs. These visualisations do not only help discern the structure of complex graphs but also provide a means of understanding the models applied to them for solving various tasks. We further demonstrate the suitability of Mapper as a topological framework for graph pooling by mathematically proving an equivalence with Min-Cut and Diff Pool. Building upon this framework, we introduce a novel pooling algorithm based on PageRank, which obtains competitive results with state of the art methods on graph classification benchmarks.
Graph Convolution Network (GCN) has become new state-of-the-art for collaborative filtering. Nevertheless, the reasons of its effectiveness for recommendation are not well understood. Existing work that adapts GCN to recommendation lacks thorough ablation analyses on GCN, which is originally designed for graph classification tasks and equipped with many neural network operations. However, we empirically find that the two most common designs in GCNs -- feature transformation and nonlinear activation -- contribute little to the performance of collaborative filtering. Even worse, including them adds to the difficulty of training and degrades recommendation performance. In this work, we aim to simplify the design of GCN to make it more concise and appropriate for recommendation. We propose a new model named LightGCN, including only the most essential component in GCN -- neighborhood aggregation -- for collaborative filtering. Specifically, LightGCN learns user and item embeddings by linearly propagating them on the user-item interaction graph, and uses the weighted sum of the embeddings learned at all layers as the final embedding. Such simple, linear, and neat model is much easier to implement and train, exhibiting substantial improvements (about 16.0\% relative improvement on average) over Neural Graph Collaborative Filtering (NGCF) -- a state-of-the-art GCN-based recommender model -- under exactly the same experimental setting. Further analyses are provided towards the rationality of the simple LightGCN from both analytical and empirical perspectives.
Various methods to deal with graph data have been proposed in recent years. However, most of these methods focus on graph feature aggregation rather than graph pooling. Besides, the existing top-k selection graph pooling methods have a few problems. First, to construct the pooled graph topology, current top-k selection methods evaluate the importance of the node from a single perspective only, which is simplistic and unobjective. Second, the feature information of unselected nodes is directly lost during the pooling process, which inevitably leads to a massive loss of graph feature information. To solve these problems mentioned above, we propose a novel graph self-adaptive pooling method with the following objectives: (1) to construct a reasonable pooled graph topology, structure and feature information of the graph are considered simultaneously, which provide additional veracity and objectivity in node selection; and (2) to make the pooled nodes contain sufficiently effective graph information, node feature information is aggregated before discarding the unimportant nodes; thus, the selected nodes contain information from neighbor nodes, which can enhance the use of features of the unselected nodes. Experimental results on four different datasets demonstrate that our method is effective in graph classification and outperforms state-of-the-art graph pooling methods.
Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between input graphs, defining an appropriate distance metric for graphs remains a controversial issue. Hence, we propose a supervised distance metric learning method for the graph classification problem. Our method, named interpretable graph metric learning (IGML), learns discriminative metrics in a subgraph-based feature space, which has a strong graph representation capability. By introducing a sparsity-inducing penalty on the weight of each subgraph, IGML can identify a small number of important subgraphs that can provide insight into the given classification task. Because our formulation has a large number of optimization variables, an efficient algorithm that uses pruning techniques based on safe screening and working set selection methods is also proposed. An important property of IGML is that solution optimality is guaranteed because the problem is formulated as a convex problem and our pruning strategies only discard unnecessary subgraphs. Furthermore, we show that IGML is also applicable to other structured data such as itemset and sequence data, and that it can incorporate vertex-label similarity by using a transportation-based subgraph feature. We empirically evaluate the computational efficiency and classification performance of IGML on several benchmark datasets and provide some illustrative examples of how IGML identifies important subgraphs from a given graph dataset.
It has been demonstrated that adversarial graphs, i.e., graphs with imperceptible perturbations added, can cause deep graph models to fail on node/graph classification tasks. In this paper, we extend adversarial graphs to the problem of community detection which is much more difficult. We focus on black-box attack and aim to hide targeted individuals from the detection of deep graph community detection models, which has many applications in real-world scenarios, for example, protecting personal privacy in social networks and understanding camouflage patterns in transaction networks. We propose an iterative learning framework that takes turns to update two modules: one working as the constrained graph generator and the other as the surrogate community detection model. We also find that the adversarial graphs generated by our method can be transferred to other learning based community detection models.
Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we carry out a range of experiments on both graph data and shape data, aiming to decouple and inspect the effects of different factors involved. To this end, we also propose the so-called \emph{permutation test} for persistence diagrams to delineate critical values and pairings of critical values. For graph classification tasks, we note that while persistence pairing yields consistent improvement over various benchmark datasets, it appears that for various filtration functions tested, most discriminative power comes from critical values. For shape segmentation and classification, however, we note that persistence pairing shows significant power on most of the benchmark datasets, and improves over both summaries based on merely critical values, and those based on permutation tests. Our results help provide insights on when persistence diagram based summaries could be more suitable.
Recent research efforts have shown the possibility to discover anticancer drug-like molecules in food from their effect on protein-protein interaction networks, opening a potential pathway to disease-beating diet design. We formulate this task as a graph classification problem on which graph neural networks (GNNs) have achieved state-of-the-art results. However, GNNs are difficult to train on sparse low-dimensional features according to our empirical evidence. Here, we present graph augmented features, integrating graph structural information and raw node attributes with varying ratios, to ease the training of networks. We further introduce a novel neural network architecture on graphs, the Graph Attentional Autoencoder (GAA) to predict food compounds with anticancer properties based on perturbed protein networks. We demonstrate that the method outperforms the baseline approach and state-of-the-art graph classification models in this task.
Graph neural networks (GNN) rely on graph operations that include neural network training for various graph related tasks. Recently, several attempts have been made to apply the GNNs to functional magnetic resonance image (fMRI) data. Despite recent progresses, a common limitation is its difficulty to explain the classification results in a neuroscientifically explainable way. Here, we develop a framework for analyzing the fMRI data using the Graph Isomorphism Network (GIN), which was recently proposed as a powerful GNN for graph classification. One of the important contributions of this paper is the observation that the GIN is a dual representation of convolutional neural network (CNN) in the graph space where the shift operation is defined using the adjacency matrix. This understanding enables us to exploit CNN-based saliency map techniques for the GNN, which we tailor to the proposed GIN with one-hot encoding, to visualize the important regions of the brain. We validate our proposed framework using large-scale resting-state fMRI (rs-fMRI) data for classifying the sex of the subject based on the graph structure of the brain. The experiment was consistent with our expectation such that the obtained saliency map show high correspondence with previous neuroimaging evidences related to sex differences.
Hierarchical abstractions are a methodology for solving large-scale graph problems in various disciplines. Coarsening is one such approach: it generates a pyramid of graphs whereby the one in the next level is a structural summary of the prior one. With a long history in scientific computing, many coarsening strategies were developed based on mathematically driven heuristics. Recently, resurgent interests exist in deep learning to design hierarchical methods learnable through differentiable parameterization. These approaches are paired with downstream tasks for supervised learning. In practice, however, supervised signals (e.g., labels) are scarce and are often laborious to obtain. In this work, we propose an unsupervised approach, coined OTCoarsening, with the use of optimal transport. Both the coarsening matrix and the transport cost matrix are parameterized, so that an optimal coarsening strategy can be learned and tailored for a given set of graphs. We demonstrate that the proposed approach produces meaningful coarse graphs and yields competitive performance compared with supervised methods for graph classification and regression.
Experimental reproducibility and replicability are critical topics in machine learning. Authors have often raised concerns about their lack in scientific publications to improve the quality of the field. Recently, the graph representation learning field has attracted the attention of a wide research community, which resulted in a large stream of works. As such, several Graph Neural Network models have been developed to effectively tackle graph classification. However, experimental procedures often lack rigorousness and are hardly reproducible. Motivated by this, we provide an overview of common practices that should be avoided to fairly compare with the state of the art. To counter this troubling trend, we ran more than 47000 experiments in a controlled and uniform framework to re-evaluate five popular models across nine common benchmarks. Moreover, by comparing GNNs with structure-agnostic baselines we provide convincing evidence that, on some datasets, structural information has not been exploited yet. We believe that this work can contribute to the development of the graph learning field, by providing a much needed grounding for rigorous evaluations of graph classification models.
Graph neural networks (GNN) has been demonstrated to be effective in classifying graph structures. To further improve the graph representation learning ability, hierarchical GNN has been explored. It leverages the differentiable pooling to cluster nodes into fixed groups, and generates a coarse-grained structure accompanied with the shrinking of the original graph. However, such clustering would discard some graph information and achieve the suboptimal results. It is because the node inherently has different characteristics or roles, and two non-isomorphic graphs may have the same coarse-grained structure that cannot be distinguished after pooling. To compensate the loss caused by coarse-grained clustering and further advance GNN, we propose a multi-channel graph convolutional networks (MuchGCN). It is motivated by the convolutional neural networks, at which a series of channels are encoded to preserve the comprehensive characteristics of the input image. Thus, we define the specific graph convolutions to learn a series of graph channels at each layer, and pool graphs iteratively to encode the hierarchical structures. Experiments have been carefully carried out to demonstrate the superiority of MuchGCN over the state-of-the-art graph classification algorithms.
In clinical practice, human radiologists actually review medical images with high resolution monitors and zoom into region of interests (ROIs) for a close-up examination. Inspired by this observation, we propose a hierarchical graph neural network to detect abnormal lesions from medical images by automatically zooming into ROIs. We focus on mammogram analysis for breast cancer diagnosis for this study. Our proposed network consist of two graph attention networks performing two tasks: (1) node classification to predict whether to zoom into next level; (2) graph classification to classify whether a mammogram is normal/benign or malignant. The model is trained and evaluated on INbreast dataset and we obtain comparable AUC with state-of-the-art methods.
Deep learning models are full of hyperparameters, which are set manually before the learning process can start. To find the best configuration for these hyperparameters in such a high dimensional space, with time-consuming and expensive model training / validation, is not a trivial challenge. Bayesian optimization is a powerful tool for the joint optimization of hyperparameters, efficiently trading off exploration and exploitation of the hyperparameter space. In this paper, we discuss Bayesian hyperparameter optimization, including hyperparameter optimization, Bayesian optimization, and Gaussian processes. We also review BoTorch, GPyTorch and Ax, the new open-source frameworks that we use for Bayesian optimization, Gaussian process inference and adaptive experimentation, respectively. For experimentation, we apply Bayesian hyperparameter optimization, for optimizing group weights, to weighted group pooling, which couples unsupervised tiered graph autoencoders learning and supervised graph prediction learning for molecular graphs. We find that Ax, BoTorch and GPyTorch together provide a simple-to-use but powerful framework for Bayesian hyperparameter optimization, using Ax's high-level API that constructs and runs a full optimization loop and returns the best hyperparameter configuration.
In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks(MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node attributes, and show that this representation is a universal approximator of continuous functions on graphs with node attributes. Our method relies on separability , a key topological characteristic that allows to extend well-chosen neural networks into universal representations. Finally, we show experimentally that CLIP is capable of capturing structural characteristics that traditional MPNNs fail to distinguish,while being state-of-the-art on benchmark graph classification datasets.
Graph Neural Networks (GNNs) have proved to be an effective representation learning framework for graph-structured data, and have achieved state-of-the-art performance on many practical predictive tasks, such as node classification, link prediction and graph classification. Among the variants of GNNs, Graph Attention Networks (GATs) learn to assign dense attention coefficients over all neighbors of a node for feature aggregation, and improve the performance of many graph learning tasks. However, real-world graphs are often very large and noisy, and GATs are prone to overfitting if not regularized properly. Even worse, the local aggregation mechanism of GATs may fail on disassortative graphs, where nodes within local neighborhood provide more noise than useful information for feature aggregation. In this paper, we propose Sparse Graph Attention Networks (SGATs) that learn sparse attention coefficients under an $L_0$-norm regularization, and the learned sparse attentions are then used for all GNN layers, resulting in an edge-sparsified graph. By doing so, we can identify noisy/task-irrelevant edges, and thus perform feature aggregation on most informative neighbors. Extensive experiments on synthetic and real-world graph learning benchmarks demonstrate the superior performance of SGATs. In particular, SGATs can remove about 50\%-80\% edges from large assortative graphs, while retaining similar classification accuracies. On disassortative graphs, SGATs prune majority of noisy edges and outperform GATs in classification accuracies by significant margins. Furthermore, the removed edges can be interpreted intuitively and quantitatively. To the best of our knowledge, this is the first graph learning algorithm that shows significant redundancies in graphs and edge-sparsified graphs can achieve similar or sometimes higher predictive performances than original graphs.
Predicting a user's preference in a short anonymous interaction session instead of long-term history is a challenging problem in the real-life session-based recommendation, e.g., e-commerce and media stream. Recent research of the session-based recommender system mainly focuses on sequential patterns by utilizing the attention mechanism, which is straightforward for the session's natural sequence sorted by time. However, the user's preference is much more complicated than a solely consecutive time pattern in the transition of item choices. In this paper, therefore, we study the item transition pattern by constructing a session graph and propose a novel model which collaboratively considers the sequence order and the latent order in the session graph for a session-based recommender system. We formulate the next item recommendation within the session as a graph classification problem. Specifically, we propose a weighted attention graph layer and a Readout function to learn embeddings of items and sessions for the next item recommendation. Extensive experiments have been conducted on two benchmark E-commerce datasets, Yoochoose and Diginetica, and the experimental results show that our model outperforms other state-of-the-art methods.
We address the problem of disentangled representation learning with independent latent factors in graph convolutional networks (GCNs). The current methods usually learn node representation by describing its neighborhood as a perceptual whole in a holistic manner while ignoring the entanglement of the latent factors. However, a real-world graph is formed by the complex interaction of many latent factors (e.g., the same hobby, education or work in social network). While little effort has been made toward exploring the disentangled representation in GCNs. In this paper, we propose a novel Independence Promoted Graph Disentangled Networks (IPGDN) to learn disentangled node representation while enhancing the independence among node representations. In particular, we firstly present disentangled representation learning by neighborhood routing mechanism, and then employ the Hilbert-Schmidt Independence Criterion (HSIC) to enforce independence between the latent representations, which is effectively integrated into a graph convolutional framework as a regularizer at the output layer. Experimental studies on real-world graphs validate our model and demonstrate that our algorithms outperform the state-of-the-arts by a wide margin in different network applications, including semi-supervised graph classification, graph clustering and graph visualization.
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the alignment of geometric node embeddings of graphs, yield state-of-the-art performance. However, these graph kernels are not necessarily positive-definite. More importantly, computing the graph kernel matrix will have at least quadratic {time} complexity in terms of the number and the size of the graphs. In this paper, we propose a new family of global alignment graph kernels, which take into account the global properties of graphs by using geometric node embeddings and an associated node transportation based on earth mover's distance. Compared to existing global kernels, the proposed kernel is positive-definite. Our graph kernel is obtained by defining a distribution over \emph{random graphs}, which can naturally yield random feature approximations. The random feature approximations lead to our graph embeddings, which is named as "random graph embeddings" (RGE). In particular, RGE is shown to achieve \emph{(quasi-)linear scalability} with respect to the number and the size of the graphs. The experimental results on nine benchmark datasets demonstrate that RGE outperforms or matches twelve state-of-the-art graph classification algorithms.
Graph Neural Networks (GNN) have been shown to work effectively for modeling graph structured data to solve tasks such as node classification, link prediction and graph classification. There has been some recent progress in defining the notion of pooling in graphs whereby the model tries to generate a graph level representation by downsampling and summarizing the information present in the nodes. Existing pooling methods either fail to effectively capture the graph substructure or do not easily scale to large graphs. In this work, we propose ASAP (Adaptive Structure Aware Pooling), a sparse and differentiable pooling method that addresses the limitations of previous graph pooling architectures. ASAP utilizes a novel self-attention network along with a modified GNN formulation to capture the importance of each node in a given graph. It also learns a sparse soft cluster assignment for nodes at each layer to effectively pool the subgraphs to form the pooled graph. Through extensive experiments on multiple datasets and theoretical analysis, we motivate our choice of the components used in ASAP. Our experimental results show that combining existing GNN architectures with ASAP leads to state-of-the-art results on multiple graph classification benchmarks. ASAP has an average improvement of 4%, compared to current sparse hierarchical state-of-the-art method.