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.
Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: encounter the expensive time overhead, fail in exploring the explicit clusters, and cannot generalize to unseen data points. In this work, we propose a scalable graph learning framework, seeking to address the above three challenges simultaneously. Specifically, it is based on the ideas of anchor points and bipartite graph. Rather than building a $n\times n$ graph, where $n$ is the number of samples, we construct a bipartite graph to depict the relationship between samples and anchor points. Meanwhile, a connectivity constraint is employed to ensure that the connected components indicate clusters directly. We further establish the connection between our method and the K-means clustering. Moreover, a model to process multi-view data is also proposed, which is linear scaled with respect to $n$. Extensive experiments demonstrate the efficiency and effectiveness of our approach with respect to many state-of-the-art clustering methods.
The recent success of graph neural networks has significantly boosted molecular property prediction, advancing activities such as drug discovery. The existing deep neural network methods usually require large training dataset for each property, impairing their performances in cases (especially for new molecular properties) with a limited amount of experimental data, which are common in real situations. To this end, we propose Meta-MGNN, a novel model for few-shot molecular property prediction. Meta-MGNN applies molecular graph neural network to learn molecular representation and builds a meta-learning framework for model optimization. To exploit unlabeled molecular information and address task heterogeneity of different molecular properties, Meta-MGNN further incorporates molecular structure, attribute based self-supervised modules and self-attentive task weights into the former framework, strengthening the whole learning model. Extensive experiments on two public multi-property datasets demonstrate that Meta-MGNN outperforms a variety of state-of-the-art methods.
Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.
The electrocardiogram (ECG) signal is the most widely used non-invasive tool for the investigation of cardiovascular diseases. Automatic delineation of ECG fiducial points, in particular the R-peak, serves as the basis for ECG processing and analysis. This study proposes a new method of ECG signal analysis by introducing a new class of graphical models based on optimal changepoint detection models, named the graph-constrained changepoint detection (GCCD) model. The GCCD model treats fiducial points delineation in the non-stationary ECG signal as a changepoint detection problem. The proposed model exploits the sparsity of changepoints to detect abrupt changes within the ECG signal; thereby, the R-peak detection task can be relaxed from any preprocessing step. In this novel approach, prior biological knowledge about the expected sequence of changes is incorporated into the model using the constraint graph, which can be defined manually or automatically. First, we define the constraint graph manually; then, we present a graph learning algorithm that can search for an optimal graph in a greedy scheme. Finally, we compare the manually defined graphs and learned graphs in terms of graph structure and detection accuracy. We evaluate the performance of the algorithm using the MIT-BIH Arrhythmia Database. The proposed model achieves an overall sensitivity of 99.64%, positive predictivity of 99.71%, and detection error rate of 0.19 for the manually defined constraint graph and overall sensitivity of 99.76%, positive predictivity of 99.68%, and detection error rate of 0.55 for the automatic learning constraint graph.
This study presents a new viewpoint on ECG signal analysis by applying a graph-based changepoint detection model to locate R-peak positions. This model is based on a new graph learning algorithm to learn the constraint graph given the labeled ECG data. The proposed learning algorithm starts with a simple initial graph and iteratively edits the graph so that the final graph has the maximum accuracy in R-peak detection. We evaluate the performance of the algorithm on the MIT-BIH Arrhythmia Database. The evaluation results demonstrate that the proposed method can obtain comparable results to other state-of-the-art approaches. The proposed method achieves the overall sensitivity of Sen = 99.64%, positive predictivity of PPR = 99.71%, and detection error rate of DER = 0.19.
Semi-supervised learning on graphs is a widely applicable problem in network science and machine learning. Two standard algorithms -- label propagation and graph neural networks -- both operate by repeatedly passing information along edges, the former by passing labels and the latter by passing node features, modulated by neural networks. These two types of algorithms have largely developed separately, and there is little understanding about the structure of network data that would make one of these approaches work particularly well compared to the other or when the approaches can be meaningfully combined. Here, we develop a Markov random field model for the data generation process of node attributes, based on correlations of attributes on and between vertices, that motivates and unifies these algorithmic approaches. We show that label propagation, a linearized graph convolutional network, and their combination can all be derived as conditional expectations under our model, when conditioning on different attributes. In addition, the data model highlights deficiencies in existing graph neural networks (while producing new algorithmic solutions), serves as a rigorous statistical framework for understanding graph learning issues such as over-smoothing, creates a testbed for evaluating inductive learning performance, and provides a way to sample graphs attributes that resemble empirical data. We also find that a new algorithm derived from our data generation model, which we call a Linear Graph Convolution, performs extremely well in practice on empirical data, and provide theoretical justification for why this is the case.
Lots of neural network architectures have been proposed to deal with learning tasks on graph-structured data. However, most of these models concentrate on only node features during the learning process. The edge features, which usually play a similarly important role as the nodes, are often ignored or simplified by these models. In this paper, we present edge-featured graph attention networks, namely EGATs, to extend the use of graph neural networks to those tasks learning on graphs with both node and edge features. These models can be regarded as extensions of graph attention networks (GATs). By reforming the model structure and the learning process, the new models can accept node and edge features as inputs, incorporate the edge information into feature representations, and iterate both node and edge features in a parallel but mutual way. The results demonstrate that our work is highly competitive against other node classification approaches, and can be well applied in edge-featured graph learning tasks.
A scalable semi-supervised node classification method on graph-structured data, called GraphHop, is proposed in this work. The graph contains attributes of all nodes but labels of a few nodes. The classical label propagation (LP) method and the emerging graph convolutional network (GCN) are two popular semi-supervised solutions to this problem. The LP method is not effective in modeling node attributes and labels jointly or facing a slow convergence rate on large-scale graphs. GraphHop is proposed to its shortcoming. With proper initial label vector embeddings, each iteration of GraphHop contains two steps: 1) label aggregation and 2) label update. In Step 1, each node aggregates its neighbors' label vectors obtained in the previous iteration. In Step 2, a new label vector is predicted for each node based on the label of the node itself and the aggregated label information obtained in Step 1. This iterative procedure exploits the neighborhood information and enables GraphHop to perform well in an extremely small label rate setting and scale well for very large graphs. Experimental results show that GraphHop outperforms state-of-the-art graph learning methods on a wide range of tasks (e.g., multi-label and multi-class classification on citation networks, social graphs, and commodity consumption graphs) in graphs of various sizes. Our codes are publicly available on GitHub (https://github.com/TianXieUSC/GraphHop).
The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph. Recently there has also seen tremendous progress in quantum computing techniques. In this work, we explore applications of multi-particle quantum walks on diffusing information across graphs. Our model is based on learning the operators that govern the dynamics of quantum random walkers on graphs. We demonstrate the effectiveness of our method on classification and regression tasks.
Heterogeneous graphs generally refers to graphs with different types of nodes and edges. A common approach for extracting useful information from heterogeneous graphs is to use meta-graphs, which can be seen as a special kind of directed acyclic graph (DAG) with same node and edge types as the heterogeneous graph. However, how to design proper meta-graphs is challenging. Recently, there have been many works on learning suitable meta-graphs from a heterogeneous graph. Existing methods generally introduce continuous weights for edges that are independent of each other, which ignores the topological stucture of meta-graphs and can be ineffective. To address this issue, we propose a new viewpoint from tensor on learning meta-graphs. Such a viewpoint not only helps interpret the limitation of existing works by CANDECOMP/PARAFAC (CP) decomposition, but also inspires us to propose a topology-aware tensor decomposition, called TENSUS, that reflects the structure of DAGs. The proposed topology-aware tensor decomposition is easy to use and simple to implement, and it can be taken as a plug-in part to upgrade many existing works, including node classification and recommendation on heterogeneous graphs. Experimental results on different tasks demonstrate that the proposed method can significantly improve the state-of-the-arts for all these tasks.
Attempt to fully discover the temporal diversity and chronological characteristics for self-supervised video representation learning, this work takes advantage of the temporal dependencies within videos and further proposes a novel self-supervised method named Temporal Contrastive Graph Learning (TCGL). In contrast to the existing methods that ignore modeling elaborate temporal dependencies, our TCGL roots in a hybrid graph contrastive learning strategy to jointly regard the inter-snippet and intra-snippet temporal dependencies as self-supervision signals for temporal representation learning. To model multi-scale temporal dependencies, our TCGL integrates the prior knowledge about the frame and snippet orders into graph structures, i.e., the intra-/inter- snippet temporal contrastive graphs. By randomly removing edges and masking nodes of the intra-snippet graphs or inter-snippet graphs, our TCGL can generate different correlated graph views. Then, specific contrastive learning modules are designed to maximize the agreement between nodes in different views. To adaptively learn the global context representation and recalibrate the channel-wise features, we introduce an adaptive video snippet order prediction module, which leverages the relational knowledge among video snippets to predict the actual snippet orders. Experimental results demonstrate the superiority of our TCGL over the state-of-the-art methods on large-scale action recognition and video retrieval benchmarks.
In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of practitioners' toolboxes. In this paper, we investigate the fundamental problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market times series data. In particular, we present natural justifications, supported by empirical evidence, for the usage of the Laplacian matrix as a model for the precision matrix of financial assets, while also establishing a direct link that reveals how Laplacian constraints are coupled to meaningful physical interpretations related to the market index factor and to conditional correlations between stocks. Those interpretations lead to a set of guidelines that practitioners should be aware of when estimating graphs in financial markets. In addition, we design numerical algorithms based on the alternating direction method of multipliers to learn undirected, weighted graphs that take into account stylized facts that are intrinsic to financial data such as heavy tails and modularity. We illustrate how to leverage the learned graphs into practical scenarios such as stock time series clustering and foreign exchange network estimation. The proposed graph learning algorithms outperform the state-of-the-art methods in an extensive set of practical experiments. Furthermore, we obtain theoretical and empirical convergence results for the proposed algorithms. Along with the developed methodologies for graph learning in financial markets, we release an R package, called fingraph, accommodating the code and data to obtain all the experimental results.
Accurate and timely air quality and weather predictions are of great importance to urban governance and human livelihood. Though many efforts have been made for air quality or weather prediction, most of them simply employ one another as feature input, which ignores the inner-connection between two predictive tasks. On the one hand, the accurate prediction of one task can help improve another task's performance. On the other hand, geospatially distributed air quality and weather monitoring stations provide additional hints for city-wide spatiotemporal dependency modeling. Inspired by the above two insights, in this paper, we propose the Multi-adversarial spatiotemporal recurrent Graph Neural Networks (MasterGNN) for joint air quality and weather predictions. Specifically, we first propose a heterogeneous recurrent graph neural network to model the spatiotemporal autocorrelation among air quality and weather monitoring stations. Then, we develop a multi-adversarial graph learning framework to against observation noise propagation introduced by spatiotemporal modeling. Moreover, we present an adaptive training strategy by formulating multi-adversarial learning as a multi-task learning problem. Finally, extensive experiments on two real-world datasets show that MasterGNN achieves the best performance compared with seven baselines on both air quality and weather prediction tasks.
Heterogeneous graphs are pervasive in practical scenarios, where each graph consists of multiple types of nodes and edges. Representation learning on heterogeneous graphs aims to obtain low-dimensional node representations that could preserve both node attributes and relation information. However, most of the existing graph convolution approaches were designed for homogeneous graphs, and therefore cannot handle heterogeneous graphs. Some recent methods designed for heterogeneous graphs are also faced with several issues, including the insufficient utilization of heterogeneous properties, structural information loss, and lack of interpretability. In this paper, we propose HGConv, a novel Heterogeneous Graph Convolution approach, to learn comprehensive node representations on heterogeneous graphs with a hybrid micro/macro level convolutional operation. Different from existing methods, HGConv could perform convolutions on the intrinsic structure of heterogeneous graphs directly at both micro and macro levels: A micro-level convolution to learn the importance of nodes within the same relation, and a macro-level convolution to distinguish the subtle difference across different relations. The hybrid strategy enables HGConv to fully leverage heterogeneous information with proper interpretability. Moreover, a weighted residual connection is designed to aggregate both inherent attributes and neighbor information of the focal node adaptively. Extensive experiments on various tasks demonstrate not only the superiority of HGConv over existing methods, but also the intuitive interpretability of our approach for graph analysis.
The ability to segment teeth precisely from digitized 3D dental models is an essential task in computer-aided orthodontic surgical planning. To date, deep learning based methods have been popularly used to handle this task. State-of-the-art methods directly concatenate the raw attributes of 3D inputs, namely coordinates and normal vectors of mesh cells, to train a single-stream network for fully-automated tooth segmentation. This, however, has the drawback of ignoring the different geometric meanings provided by those raw attributes. This issue might possibly confuse the network in learning discriminative geometric features and result in many isolated false predictions on the dental model. Against this issue, we propose a two-stream graph convolutional network (TSGCNet) to learn multi-view geometric information from different geometric attributes. Our TSGCNet adopts two graph-learning streams, designed in an input-aware fashion, to extract more discriminative high-level geometric representations from coordinates and normal vectors, respectively. These feature representations learned from the designed two different streams are further fused to integrate the multi-view complementary information for the cell-wise dense prediction task. We evaluate our proposed TSGCNet on a real-patient dataset of dental models acquired by 3D intraoral scanners, and experimental results demonstrate that our method significantly outperforms state-of-the-art methods for 3D shape segmentation.
Bayesian Optimization (BO) has shown significant success in tackling expensive low-dimensional black-box optimization problems. Many optimization problems of interest are high-dimensional, and scaling BO to such settings remains an important challenge. In this paper, we consider generalized additive models in which low-dimensional functions with overlapping subsets of variables are composed to model a high-dimensional target function. Our goal is to lower the computational resources required and facilitate faster model learning by reducing the model complexity while retaining the sample-efficiency of existing methods. Specifically, we constrain the underlying dependency graphs to tree structures in order to facilitate both the structure learning and optimization of the acquisition function. For the former, we propose a hybrid graph learning algorithm based on Gibbs sampling and mutation. In addition, we propose a novel zooming-based algorithm that permits generalized additive models to be employed more efficiently in the case of continuous domains. We demonstrate and discuss the efficacy of our approach via a range of experiments on synthetic functions and real-world datasets.
In this paper, we focus on learning product graphs from multi-domain data. We assume that the product graph is formed by the Cartesian product of two smaller graphs, which we refer to as graph factors. We pose the product graph learning problem as the problem of estimating the graph factor Laplacian matrices. To capture local interactions in data, we seek sparse graph factors and assume a smoothness model for data. We propose an efficient iterative solver for learning sparse product graphs from data. We then extend this solver to infer multi-component graph factors with applications to product graph clustering by imposing rank constraints on the graph Laplacian matrices. Although working with smaller graph factors is computationally more attractive, not all graphs may readily admit an exact Cartesian product factorization. To this end, we propose efficient algorithms to approximate a graph by a nearest Cartesian product of two smaller graphs. The efficacy of the developed framework is demonstrated using several numerical experiments on synthetic data and real data.
Graph Contrastive Learning (GCL) has proven highly effective in promoting the performance of Semi-Supervised Node Classification (SSNC). However, existing GCL methods are generally transferred from other fields like CV or NLP, whose underlying working mechanism remains under-explored. In this work, we first deeply probe the working mechanism of GCL in SSNC, and find that the promotion brought by GCL is severely unevenly distributed: the improvement mainly comes from subgraphs with less annotated information, which is fundamentally different from contrastive learning in other fields. However, existing GCL methods generally ignore this uneven distribution of annotated information and apply GCL evenly to the whole graph. To remedy this issue and further improve GCL in SSNC, we propose the Topology InFormation gain-Aware Graph Contrastive Learning (TIFA-GCL) framework that considers the annotated information distribution across graph in GCL. Extensive experiments on six benchmark graph datasets, including the enormous OGB-Products graph, show that TIFA-GCL can bring a larger improvement than existing GCL methods in both transductive and inductive settings. Further experiments demonstrate the generalizability and interpretability of TIFA-GCL.
For graph learning tasks, many existing methods utilize a message-passing mechanism where vertex features are updated iteratively by aggregation of neighbor information. This strategy provides an efficient means for graph features extraction, but obtained features after many iterations might contain too much information from other vertices, and tend to be similar to each other. This makes their representations less expressive. Learning graphs using paths, on the other hand, can be less adversely affected by this problem because it does not involve all vertex neighbors. However, most of them can only compare paths with the same length, which might engender information loss. To resolve this difficulty, we propose a new Graph Kernel based on a Longest Common Subsequence (LCS) similarity. Moreover, we found that the widely-used R-convolution framework is unsuitable for path-based Graph Kernel because a huge number of comparisons between dissimilar paths might deteriorate graph distances calculation. Therefore, we propose a novel metric space by exploiting the proposed LCS-based similarity, and compute a new Wasserstein-based graph distance in this metric space, which emphasizes more the comparison between similar paths. Furthermore, to reduce the computational cost, we propose an adjacent point merging operation to sparsify point clouds in the metric space.