We propose a new Graph Neural Network that combines recent advancements in the field. We give theoretical contributions by proving that the model is strictly more general than the Graph Isomorphism Network and the Gated Graph Neural Network, as it can approximate the same functions and deal with arbitrary edge values. Then, we show how a single node information can flow through the graph unchanged.
Existing graph neural networks may suffer from the "suspended animation problem" when the model architecture goes deep. Meanwhile, for some graph learning scenarios, e.g., nodes with text/image attributes or graphs with long-distance node correlations, deep graph neural networks will be necessary for effective graph representation learning. In this paper, we propose a new graph neural network, namely DIFNET (Graph Diffusive Neural Network), for graph representation learning and node classification. DIFNET utilizes both neural gates and graph residual learning for node hidden state modeling, and includes an attention mechanism for node neighborhood information diffusion. Extensive experiments will be done in this paper to compare DIFNET against several state-of-the-art graph neural network models. The experimental results can illustrate both the learning performance advantages and effectiveness of DIFNET, especially in addressing the "suspended animation problem".
Conventional sequential learning methods such as Recurrent Neural Networks (RNNs) focus on interactions between consecutive inputs, i.e. first-order Markovian dependency. However, most of sequential data, as seen with videos, have complex dependency structures that imply variable-length semantic flows and their compositions, and those are hard to be captured by conventional methods. Here, we propose Cut-Based Graph Learning Networks (CB-GLNs) for learning video data by discovering these complex structures of the video. The CB-GLNs represent video data as a graph, with nodes and edges corresponding to frames of the video and their dependencies respectively. The CB-GLNs find compositional dependencies of the data in multilevel graph forms via a parameterized kernel with graph-cut and a message passing framework. We evaluate the proposed method on the two different tasks for video understanding: Video theme classification (Youtube-8M dataset) and Video Question and Answering (TVQA dataset). The experimental results show that our model efficiently learns the semantic compositional structure of video data. Furthermore, our model achieves the highest performance in comparison to other baseline methods.
We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of available measurements. To achieve this, we introduce two regularization terms in convex optimization problems that constrain sparseness of temporal variations of the time-varying networks. Moreover, a computationally-scalable algorithm is introduced to efficiently solve the optimization problem. The experimental results with synthetic and real datasets (point cloud and temperature data) demonstrate our proposed method outperforms the existing state-of-the-art methods.
In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and requires more global inference to oversee the whole graph. To make it scalable for large-scale graphs and patterns, we propose a learning framework which augments different representation learning architectures and iteratively attends pattern and target data graphs to memorize subgraph isomorphisms for the global counting. We develop both small graphs (<= 1,024 subgraph isomorphisms in each) and large graphs (<= 4,096 subgraph isomorphisms in each) sets to evaluate different models. A mutagenic compound dataset, MUTAG, is also used to evaluate neural models and demonstrate the success of transfer learning. While the learning based approach is inexact, we are able to generalize to count large patterns and data graphs in linear time compared to the exponential time of the original NP-complete problem. Experimental results show that learning based subgraph isomorphism counting can speed up the traditional algorithm, VF2, 10-1,000 times with acceptable errors. Domain adaptation based on fine-tuning also shows the usefulness of our approach in real-world applications.
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.
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among neighboring nodes. There is a large body of literature examining the effect of the graph structure on the performance of decentralized processing strategies. In this article, we examine the inverse problem and consider the reverse question: How much information does observing the behavior at the nodes of a graph convey about the underlying topology? For large-scale networks, the difficulty in addressing such inverse problems is compounded by the fact that usually only a limited fraction of the nodes can be probed, giving rise to a second important question: Despite the presence of unobserved nodes, can partial observations still be sufficient to discover the graph linking the probed nodes? The article surveys recent advances on this challenging learning problem and related questions.
In this paper, we propose an end-to-end graph learning framework, namely Deep Iterative and Adaptive Learning for Graph Neural Networks (DIAL-GNN), for jointly learning the graph structure and graph embeddings simultaneously. We first cast the graph structure learning problem as a similarity metric learning problem and leverage an adapted graph regularization for controlling smoothness, connectivity and sparsity of the generated graph. We further propose a novel iterative method for searching for a hidden graph structure that augments the initial graph structure. Our iterative method dynamically stops when the learned graph structure approaches close enough to the optimal graph. Our extensive experiments demonstrate that the proposed DIAL-GNN model can consistently outperform or match state-of-the-art baselines in terms of both downstream task performance and computational time. The proposed approach can cope with both transductive learning and inductive learning.
Action Detection is a complex task that aims to detect and classify human actions in video clips. Typically, it has been addressed by processing fine-grained features extracted from a video classification backbone. Recently, thanks to the robustness of object and people detectors, a deeper focus has been added on relationship modelling. Following this line, we propose a graph-based framework to learn high-level interactions between people and objects, in both space and time. In our formulation, spatio-temporal relationships are learned through self-attention on a multi-layer graph structure which can connect entities from consecutive clips, thus considering long-range spatial and temporal dependencies. The proposed module is backbone independent by design and does not require end-to-end training. Extensive experiments are conducted on the AVA dataset, where our model demonstrates state-of-the-art results and consistent improvements over baselines built with different backbones. Code is publicly available at https://github.com/aimagelab/STAGE_action_detection.
Multi-view clustering is an important approach to analyze multi-view data in an unsupervised way. Among various methods, the multi-view subspace clustering approach has gained increasing attention due to its encouraging performance. Basically, it integrates multi-view information into graphs, which are then fed into spectral clustering algorithm for final result. However, its performance may degrade due to noises existing in each individual view or inconsistency between heterogeneous features. Orthogonal to current work, we propose to fuse multi-view information in a partition space, which enhances the robustness of Multi-view clustering. Specifically, we generate multiple partitions and integrate them to find the shared partition. The proposed model unifies graph learning, generation of basic partitions, and view weight learning. These three components co-evolve towards better quality outputs. We have conducted comprehensive experiments on benchmark datasets and our empirical results verify the effectiveness and robustness of our approach.
Tremendous recent literature show that associations between different brain regions, i.e., brain connectivity, provide early symptoms of neurological disorders. Despite significant efforts made for graph neural network (GNN) techniques, their focus on graph nodes makes the state-of-the-art GNN methods not suitable for classifying brain connectivity as graphs where the objective is to characterize disease-relevant network dysfunction patterns on graph links. To address this issue, we propose Multi-resolution Edge Network (MENET) to detect disease-specific connectomic benchmarks with high discrimination power across diagnostic categories. The core of MENET is a novel graph edge-wise transform that we propose, which allows us to capture multi-resolution ``connectomic'' features. Using a rich set of the connectomic features, we devise a graph learning framework to jointly select discriminative edges and assign diagnostic labels for graphs. Experiments on two real datasets show that MENET accurately predicts diagnostic labels and identify brain connectivities highly associated with neurological disorders such as Alzheimer's Disease and Attention-Deficit/Hyperactivity Disorder.
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.
Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first time, we present a highly-scalable spectral approach (GRASPEL) for learning large graphs from data. By limiting the precision matrix to be a graph Laplacian, our approach aims to estimate ultra-sparse (tree-like) weighted undirected graphs and shows a clear connection with the prior graphical Lasso method. By interleaving the latest high-performance nearly-linear time spectral methods for graph sparsification, coarsening and embedding, ultra-sparse yet spectrally-robust graphs can be learned by identifying and including the most spectrally-critical edges into the graph. Compared with prior state-of-the-art graph learning approaches, GRASPEL is more scalable and allows substantially improving computing efficiency and solution quality of a variety of data mining and machine learning applications, such as spectral clustering (SC), and t-Distributed Stochastic Neighbor Embedding (t-SNE). {For example, when comparing with graphs constructed using existing methods, GRASPEL achieved the best spectral clustering efficiency and accuracy.
The analysis of the brain surface modeled as a graph mesh is a challenging task. Conventional deep learning approaches often rely on data lying in the Euclidean space. As an extension to irregular graphs, convolution operations are defined in the Fourier or spectral domain. This spectral domain is obtained by decomposing the graph Laplacian, which captures relevant shape information. However, the spectral decomposition across different brain graphs causes inconsistencies between the eigenvectors of individual spectral domains, causing the graph learning algorithm to fail. Current spectral graph convolution methods handle this variance by separately aligning the eigenvectors to a reference brain in a slow iterative step. This paper presents a novel approach for learning the transformation matrix required for aligning brain meshes using a direct data-driven approach. Our alignment and graph processing method provides a fast analysis of brain surfaces. The novel Spectral Graph Transformer (SGT) network proposed in this paper uses very few randomly sub-sampled nodes in the spectral domain to learn the alignment matrix for multiple brain surfaces. We validate the use of this SGT network along with a graph convolution network to perform cortical parcellation. Our method on 101 manually-labeled brain surfaces shows improved parcellation performance over a no-alignment strategy, gaining a significant speed (1400 fold) over traditional iterative alignment approaches.
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning paradigm is based on the combination of random walks for sampling context nodes and the traditional \textit{Skip-Gram} model to capture center-context node relationships. In this paper, we emphasize on exponential family distributions to capture rich interaction patterns between nodes in random walk sequences. We introduce the generic \textit{exponential family graph embedding} model, that generalizes random walk-based network representation learning techniques to exponential family conditional distributions. We study three particular instances of this model, analyzing their properties and showing their relationship to existing unsupervised learning models. Our experimental evaluation on real-world datasets demonstrates that the proposed techniques outperform well-known baseline methods in two downstream machine learning tasks.
Knowledge graph learning plays a critical role in integrating domain specific knowledge bases when deploying machine learning and data mining models in practice. Existing methods on knowledge graph learning primarily focus on modeling the relations among entities as translations among the relations and entities, and many of these methods are not able to handle zero-shot problems, when new entities emerge. In this paper, we present a new convolutional neural network (CNN)-based dual-chain model. Different from translation based methods, in our model, interactions among relations and entities are directly captured via CNN over their embeddings. Moreover, a secondary chain of learning is conducted simultaneously to incorporate additional information and to enable better performance. We also present an extension of this model, which incorporates descriptions of entities and learns a second set of entity embeddings from the descriptions. As a result, the extended model is able to effectively handle zero-shot problems. We conducted comprehensive experiments, comparing our methods with 15 methods on 8 benchmark datasets. Extensive experimental results demonstrate that our proposed methods achieve or outperform the state-of-the-art results on knowledge graph learning, and outperform other methods on zero-shot problems. In addition, our methods applied to real-world biomedical data are able to produce results that conform to expert domain knowledge.
Recently, graph convolutional networks (GCNs) have shown great potential for the task of graph matching. It can integrate graph node feature embedding, node-wise affinity learning and matching optimization together in a unified end-to-end model. One important aspect of graph matching is the construction of two matching graphs. However, the matching graphs we feed to existing graph convolutional matching networks are generally fixed and independent of graph matching, which thus are not guaranteed to be optimal for the graph matching task. Also, existing GCN matching method employs several general smoothing-based graph convolutional layers to generate graph node embeddings, in which extensive smoothing convolution operation may dilute the desired discriminatory information of graph nodes. To overcome these issues, we propose a novel Graph Learning-Matching Network (GLMNet) for graph matching problem. GLMNet has three main aspects. (1) It integrates graph learning into graph matching which thus adaptively learn a pair of optimal graphs that best serve graph matching task. (2) It further employs a Laplacian sharpening convolutional module to generate more discriminative node embeddings for graph matching. (3) A new constraint regularized loss is designed for GLMNet training which can encode the desired one-to-one matching constraints in matching optimization. Experiments on two benchmarks demonstrate the effectiveness of GLMNet and advantages of its main modules.
Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets. Furthermore, GDC is not limited to GNNs but can trivially be combined with any graph-based model or algorithm (e.g. spectral clustering) without requiring any changes to the latter or affecting its computational complexity. Our implementation is available online.
Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive performance, the techniques have a limited capability to incorporate the uncertainty in the underlined graph structure. In order to address this issue, a Bayesian GCNN (BGCN) framework was recently proposed. In this framework, the observed graph is considered to be a random realization from a parametric random graph model and the joint Bayesian inference of the graph and GCNN weights is performed. In this paper, we propose a non-parametric generative model for graphs and incorporate it within the BGCN framework. In addition to the observed graph, our approach effectively uses the node features and training labels in the posterior inference of graphs and attains superior or comparable performance in benchmark node classification tasks.
Visual commonsense reasoning task aims at leading the research field into solving cognition-level reasoning with the ability of predicting correct answers and meanwhile providing convincing reasoning paths, resulting in three sub-tasks i.e., Q->A, QA->R and Q->AR. It poses great challenges over the proper semantic alignment between vision and linguistic domains and knowledge reasoning to generate persuasive reasoning paths. Existing works either resort to a powerful end-to-end network that cannot produce interpretable reasoning paths or solely explore intra-relationship of visual objects (homogeneous graph) while ignoring the cross-domain semantic alignment among visual concepts and linguistic words. In this paper, we propose a new Heterogeneous Graph Learning (HGL) framework for seamlessly integrating the intra-graph and inter-graph reasoning in order to bridge vision and language domain. Our HGL consists of a primal vision-to-answer heterogeneous graph (VAHG) module and a dual question-to-answer heterogeneous graph (QAHG) module to interactively refine reasoning paths for semantic agreement. Moreover, our HGL integrates a contextual voting module to exploit a long-range visual context for better global reasoning. Experiments on the large-scale Visual Commonsense Reasoning benchmark demonstrate the superior performance of our proposed modules on three tasks (improving 5% accuracy on Q->A, 3.5% on QA->R, 5.8% on Q->AR)