Efficient outage location is critical to enhancing the resilience of power distribution systems. However, accurate outage location requires combining massive evidence received from diverse data sources, including smart meter (SM) last gasp signals, customer trouble calls, social media messages, weather data, vegetation information, and physical parameters of the network. This is a computationally complex task due to the high dimensionality of data in distribution grids. In this paper, we propose a multi-source data fusion approach to locate outage events in partially observable distribution systems using Bayesian networks (BNs). A novel aspect of the proposed approach is that it takes multi-source evidence and the complex structure of distribution systems into account using a probabilistic graphical method. Our method can radically reduce the computational complexity of outage location inference in high-dimensional spaces. The graphical structure of the proposed BN is established based on the network's topology and the causal relationship between random variables, such as the states of branches/customers and evidence. Utilizing this graphical model, accurate outage locations are obtained by leveraging a Gibbs sampling (GS) method, to infer the probabilities of de-energization for all branches. Compared with commonly-used exact inference methods that have exponential complexity in the size of the BN, GS quantifies the target conditional probability distributions in a timely manner. A case study of several real-world distribution systems is presented to validate the proposed method.
Organ segmentation in CT volumes is an important pre-processing step in many computer assisted intervention and diagnosis methods. In recent years, convolutional neural networks have dominated the state of the art in this task. However, since this problem presents a challenging environment due to high variability in the organ's shape and similarity between tissues, the generation of false negative and false positive regions in the output segmentation is a common issue. Recent works have shown that the uncertainty analysis of the model can provide us with useful information about potential errors in the segmentation. In this context, we proposed a segmentation refinement method based on uncertainty analysis and graph convolutional networks. We employ the uncertainty levels of the convolutional network in a particular input volume to formulate a semi-supervised graph learning problem that is solved by training a graph convolutional network. To test our method we refine the initial output of a 2D U-Net. We validate our framework with the NIH pancreas dataset and the spleen dataset of the medical segmentation decathlon. We show that our method outperforms the state-of-the-art CRF refinement method by improving the dice score by 1% for the pancreas and 2% for spleen, with respect to the original U-Net's prediction. Finally, we perform a sensitivity analysis on the parameters of our proposal and discuss the applicability to other CNN architectures, the results, and current limitations of the model for future work in this research direction. For reproducibility purposes, we make our code publicly available at https://github.com/rodsom22/gcn_refinement.
Unsupervised/self-supervised pre-training methods for graph representation learning have recently attracted increasing research interests, and they are shown to be able to generalize to various downstream applications. Yet, the adversarial robustness of such pre-trained graph learning models remains largely unexplored. More importantly, most existing defense techniques designed for end-to-end graph representation learning methods require pre-specified label definitions, and thus cannot be directly applied to the pre-training methods. In this paper, we propose an unsupervised defense technique to robustify pre-trained deep graph models, so that the perturbations on the input graph can be successfully identified and blocked before the model is applied to different downstream tasks. Specifically, we introduce a mutual information-based measure, \textit{graph representation vulnerability (GRV)}, to quantify the robustness of graph encoders on the representation space. We then formulate an optimization problem to learn the graph representation by carefully balancing the trade-off between the expressive power and the robustness (\emph{i.e.}, GRV) of the graph encoder. The discrete nature of graph topology and the joint space of graph data make the optimization problem intractable to solve. To handle the above difficulty and to reduce computational expense, we further relax the problem and thus provide an approximate solution. Additionally, we explore a provable connection between the robustness of the unsupervised graph encoder and that of models on downstream tasks. Extensive experiments demonstrate that even without access to labels and tasks, our model is still able to enhance robustness against adversarial attacks on three downstream tasks (node classification, link prediction, and community detection) by an average of +16.5% compared with existing methods.
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work lies in the search for a connectome model which properly captures brain functionality upon observing activities in different regions of the brain and possibly of individual neurons. We formulate the problem as a quadratic objective functional of observed node signals over short time intervals, subjected to the proper regularization reflecting the graph smoothness and other dynamics involving the underlying graph's Laplacian, as well as the time evolution smoothness of the underlying graph. The resulting joint optimization is solved by a continuous relaxation and an introduced novel gradient-projection scheme. We apply our algorithm to a real-world dataset comprising recorded activities of individual brain cells. The resulting model is shown to not only be viable but also efficiently computable.
Although algebraic graph theory based models have been widely applied in physical modeling and molecular studies, they are typically incompetent in the analysis and prediction of biomolecular properties when compared with other quantitative approaches. There is a need to explore the capability and limitation of algebraic graph theory for molecular and biomolecular modeling, analysis, and prediction. In this work, we propose novel algebraic graph learning (AGL) models that encode high-dimensional physical and biological information into intrinsically low-dimensional representations. The proposed AGL model introduces multiscale weighted colored subgraphs to describe crucial molecular and biomolecular interactions via graph invariants associated with the graph Laplacian, its pseudo-inverse, and adjacent matrix. Additionally, the AGL models are incorporated with an advanced machine learning algorithm to connect the low-dimensional graph representation of biomolecular structures with their macroscopic properties. Three popular protein-ligand binding affinity benchmarks, namely CASF-2007, CASF-2013, and CASF-2016, are employed to validate the accuracy, robustness, and reliability of the present AGL model. Numerical results indicate that the proposed AGL method outperforms the other state-of-the-art methods in the binding affinity predictions of the protein-ligand complexes.
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics impact the properties of the graph signals of interest. Such an assumption is often untenable beyond applications dealing with e.g., directly observable social and infrastructure networks; and typically adopted graph construction schemes are largely informal, distinctly lacking an element of validation. This tutorial offers an overview of graph learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology. Fairly mature statistical approaches are surveyed first, where correlation analysis takes center stage along with its connections to covariance selection and high-dimensional regression for learning Gaussian graphical models. Recent GSP-based network inference frameworks are also described, which postulate that the network exists as a latent underlying structure, and that observations are generated as a result of a network process defined in such a graph. A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks, nonlinear models of pairwise interaction, as well as extensions to directed graphs and their relation to causal inference. All in all, this paper introduces readers to challenges and opportunities for signal processing research in emerging topic areas at the crossroads of modeling, prediction, and control of complex behavior arising in networked systems that evolve over time.
Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the heterogeneous structures and semantics for downstream tasks (e.g., node/graph classification, node clustering, link prediction), has drawn considerable attentions in recent years. In this survey, we perform a comprehensive review of the recent development on HG embedding methods and techniques. We first introduce the basic concepts of HG and discuss the unique challenges brought by the heterogeneity for HG embedding in comparison with homogeneous graph representation learning; and then we systemically survey and categorize the state-of-the-art HG embedding methods based on the information they used in the learning process to address the challenges posed by the HG heterogeneity. In particular, for each representative HG embedding method, we provide detailed introduction and further analyze its pros and cons; meanwhile, we also explore the transformativeness and applicability of different types of HG embedding methods in the real-world industrial environments for the first time. In addition, we further present several widely deployed systems that have demonstrated the success of HG embedding techniques in resolving real-world application problems with broader impacts. To facilitate future research and applications in this area, we also summarize the open-source code, existing graph learning platforms and benchmark datasets. Finally, we explore the additional issues and challenges of HG embedding and forecast the future research directions in this field.
Planning - the ability to analyze the structure of a problem in the large and decompose it into interrelated subproblems - is a hallmark of human intelligence. While deep reinforcement learning (RL) has shown great promise for solving relatively straightforward control tasks, it remains an open problem how to best incorporate planning into existing deep RL paradigms to handle increasingly complex environments. One prominent framework, Model-Based RL, learns a world model and plans using step-by-step virtual rollouts. This type of world model quickly diverges from reality when the planning horizon increases, thus struggling at long-horizon planning. How can we learn world models that endow agents with the ability to do temporally extended reasoning? In this work, we propose to learn graph-structured world models composed of sparse, multi-step transitions. We devise a novel algorithm to learn latent landmarks that are scattered (in terms of reachability) across the goal space as the nodes on the graph. In this same graph, the edges are the reachability estimates distilled from Q-functions. On a variety of high-dimensional continuous control tasks ranging from robotic manipulation to navigation, we demonstrate that our method, named L3P, significantly outperforms prior work, and is oftentimes the only method capable of leveraging both the robustness of model-free RL and generalization of graph-search algorithms. We believe our work is an important step towards scalable planning in reinforcement learning.
Collaborative object localization aims to collaboratively estimate locations of objects observed from multiple views or perspectives, which is a critical ability for multi-agent systems such as connected vehicles. To enable collaborative localization, several model-based state estimation and learning-based localization methods have been developed. Given their encouraging performance, model-based state estimation often lacks the ability to model the complex relationships among multiple objects, while learning-based methods are typically not able to fuse the observations from an arbitrary number of views and cannot well model uncertainty. In this paper, we introduce a novel spatiotemporal graph filter approach that integrates graph learning and model-based estimation to perform multi-view sensor fusion for collaborative object localization. Our approach models complex object relationships using a new spatiotemporal graph representation and fuses multi-view observations in a Bayesian fashion to improve location estimation under uncertainty. We evaluate our approach in the applications of connected autonomous driving and multiple pedestrian localization. Experimental results show that our approach outperforms previous techniques and achieves the state-of-the-art performance on collaboration localization.
Ride-hailing platforms generally provide various service options to customers, such as solo ride services, shared ride services, etc. It is generally expected that demands for different service modes are correlated, and the prediction of demand for one service mode can benefit from historical observations of demands for other service modes. Moreover, an accurate joint prediction of demands for multiple service modes can help the platforms better allocate and dispatch vehicle resources. Although there is a large stream of literature on ride-hailing demand predictions for one specific service mode, little efforts have been paid towards joint predictions of ride-hailing demands for multiple service modes. To address this issue, we propose a deep multi-task multi-graph learning approach, which combines two components: (1) multiple multi-graph convolutional (MGC) networks for predicting demands for different service modes, and (2) multi-task learning modules that enable knowledge sharing across multiple MGC networks. More specifically, two multi-task learning structures are established. The first one is the regularized cross-task learning, which builds cross-task connections among the inputs and outputs of multiple MGC networks. The second one is the multi-linear relationship learning, which imposes a prior tensor normal distribution on the weights of various MGC networks. Although there are no concrete bridges between different MGC networks, the weights of these networks are constrained by each other and subject to a common prior distribution. Evaluated with the for-hire-vehicle datasets in Manhattan, we show that our propose approach outperforms the benchmark algorithms in prediction accuracy for different ride-hailing modes.
Data-driven graph learning models a network by determining the strength of connections between its nodes. The data refers to a graph signal which associates a value with each graph node. Existing graph learning methods either use simplified models for the graph signal, or they are prohibitively expensive in terms of computational and memory requirements. This is particularly true when the number of nodes is high or there are temporal changes in the network. In order to consider richer models with a reasonable computational tractability, we introduce a graph learning method based on representation learning on graphs. Representation learning generates an embedding for each graph node, taking the information from neighbouring nodes into account. Our graph learning method further modifies the embeddings to compute the graph similarity matrix. In this work, graph learning is used to examine brain networks for brain state identification. We infer time-varying brain graphs from an extensive dataset of intracranial electroencephalographic (iEEG) signals from ten patients. We then apply the graphs as input to a classifier to distinguish seizure vs. non-seizure brain states. Using the binary classification metric of area under the receiver operating characteristic curve (AUC), this approach yields an average of 9.13 percent improvement when compared to two widely used brain network modeling methods.
Graphs with complete node attributes have been widely explored recently. While in practice, there is a graph where attributes of only partial nodes could be available and those of the others might be entirely missing. This attribute-missing graph is related to numerous real-world applications and there are limited studies investigating the corresponding learning problems. Existing graph learning methods including the popular GNN cannot provide satisfied learning performance since they are not specified for attribute-missing graphs. Thereby, designing a new GNN for these graphs is a burning issue to the graph learning community. In this paper, we make a shared-latent space assumption on graphs and develop a novel distribution matching based GNN called structure-attribute transformer (SAT) for attribute-missing graphs. SAT leverages structures and attributes in a decoupled scheme and achieves the joint distribution modeling of structures and attributes by distribution matching techniques. It could not only perform the link prediction task but also the newly introduced node attribute completion task. Furthermore, practical measures are introduced to quantify the performance of node attribute completion. Extensive experiments on seven real-world datasets indicate SAT shows better performance than other methods on both link prediction and node attribute completion tasks. Codes and data are available online: https://github.com/xuChenSJTU/SAT-master-online
Automatic surgical gesture recognition is fundamentally important to enable intelligent cognitive assistance in robotic surgery. With recent advancement in robot-assisted minimally invasive surgery, rich information including surgical videos and robotic kinematics can be recorded, which provide complementary knowledge for understanding surgical gestures. However, existing methods either solely adopt uni-modal data or directly concatenate multi-modal representations, which can not sufficiently exploit the informative correlations inherent in visual and kinematics data to boost gesture recognition accuracies. In this regard, we propose a novel online approach of multi-modal relational graph network (i.e., MRG-Net) to dynamically integrate visual and kinematics information through interactive message propagation in the latent feature space. In specific, we first extract embeddings from video and kinematics sequences with temporal convolutional networks and LSTM units. Next, we identify multi-relations in these multi-modal embeddings and leverage them through a hierarchical relational graph learning module. The effectiveness of our method is demonstrated with state-of-the-art results on the public JIGSAWS dataset, outperforming current uni-modal and multi-modal methods on both suturing and knot typing tasks. Furthermore, we validated our method on in-house visual-kinematics datasets collected with da Vinci Research Kit (dVRK) platforms in two centers, with consistent promising performance achieved.
In many applications, a dataset can be considered as a set of observed signals that live on an unknown underlying graph structure. Some of these signals may be seen as white noise that has been filtered on the graph topology by a graph filter. Hence, the knowledge of the filter and the graph provides valuable information about the underlying data generation process and the complex interactions that arise in the dataset. We hence introduce a novel graph signal processing framework for jointly learning the graph and its generating filter from signal observations. We cast a new optimisation problem that minimises the Wasserstein distance between the distribution of the signal observations and the filtered signal distribution model. Our proposed method outperforms state-of-the-art graph learning frameworks on synthetic data. We then apply our method to a temperature anomaly dataset, and further show how this framework can be used to infer missing values if only very little information is available.
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while preserving the specific structure that allows us to eventually identify communities or clusters that are crucial in the analysis of graph data. To do so, we learn a clustered representative graph by solving an optimization problem that involves a data fidelity term to the observed layers, and a regularization pushing for a sparse and community-aware graph. We use the contrastive loss as a data fidelity term, in order to properly aggregate the observed layers into a representative graph. The regularization is based on a measure of graph sparsification called "effective resistance", coupled with a penalization of the first few eigenvalues of the representative graph Laplacian matrix to favor the formation of communities. The proposed optimization problem is nonconvex but fully differentiable, and thus can be solved via the projected gradient method. Experiments show that our method leads to a significant improvement w.r.t. state-of-the-art multilayer graph learning algorithms for solving clustering problems.
Recently, there has been increasing interest in the challenge of how to discriminatively vectorize graphs. To address this, we propose a method called Iterative Graph Self-Distillation (IGSD) which learns graph-level representation in an unsupervised manner through instance discrimination using a self-supervised contrastive learning approach. IGSD involves a teacher-student distillation process that uses graph diffusion augmentations and constructs the teacher model using an exponential moving average of the student model. The intuition behind IGSD is to predict the teacher network representation of the graph pairs under different augmented views. As a natural extension, we also apply IGSD to semi-supervised scenarios by jointly regularizing the network with both supervised and self-supervised contrastive loss. Finally, we show that finetuning the IGSD-trained models with self-training can further improve the graph representation power. Empirically, we achieve significant and consistent performance gain on various graph datasets in both unsupervised and semi-supervised settings, which well validates the superiority of IGSD.
Graph, as an important data representation, is ubiquitous in many real world applications ranging from social network analysis to biology. How to correctly and effectively learn and extract information from graph is essential for a large number of machine learning tasks. Graph embedding is a way to transform and encode the data structure in high dimensional and non-Euclidean feature space to a low dimensional and structural space, which is easily exploited by other machine learning algorithms. We have witnessed a huge surge of such embedding methods, from statistical approaches to recent deep learning methods such as the graph convolutional networks (GCN). Deep learning approaches usually outperform the traditional methods in most graph learning benchmarks by building an end-to-end learning framework to optimize the loss function directly. However, most of the existing GCN methods can only perform convolution operations with node features, while ignoring the handy information in edge features, such as relations in knowledge graphs. To address this problem, we present CensNet, Convolution with Edge-Node Switching graph neural network, for learning tasks in graph-structured data with both node and edge features. CensNet is a general graph embedding framework, which embeds both nodes and edges to a latent feature space. By using line graph of the original undirected graph, the role of nodes and edges are switched, and two novel graph convolution operations are proposed for feature propagation. Experimental results on real-world academic citation networks and quantum chemistry graphs show that our approach achieves or matches the state-of-the-art performance in four graph learning tasks, including semi-supervised node classification, multi-task graph classification, graph regression, and link prediction.
Learning a suitable graph is an important precursor to many graph signal processing (GSP) pipelines, such as graph spectral signal compression and denoising. Previous graph learning algorithms either i) make some assumptions on connectivity (e.g., graph sparsity), or ii) make simple graph edge assumptions such as positive edges only. In this paper, given an empirical covariance matrix $\bar{C}$ computed from data as input, we consider a structural assumption on the graph Laplacian matrix $L$: the first $K$ eigenvectors of $L$ are pre-selected, e.g., based on domain-specific criteria, such as computation requirement, and the remaining eigenvectors are then learned from data. One example use case is image coding, where the first eigenvector is pre-chosen to be constant, regardless of available observed data. We first prove that the subspace of symmetric positive semi-definite (PSD) matrices $H_{u}^+$ with the first $K$ eigenvectors being $\{u_k\}$ in a defined Hilbert space is a convex cone. We then construct an operator to project a given positive definite (PD) matrix $L$ to $H_{u}^+$, inspired by the Gram-Schmidt procedure. Finally, we design an efficient hybrid graphical lasso/projection algorithm to compute the most suitable graph Laplacian matrix $L^* \in H_{u}^+$ given $\bar{C}$. Experimental results show that given the first $K$ eigenvectors as a prior, our algorithm outperforms competing graph learning schemes using a variety of graph comparison metrics.
Neural networks have achieved remarkable successes in machine learning tasks. This has recently been extended to graph learning using neural networks. However, there is limited theoretical work in understanding how and when they perform well, especially relative to established statistical learning techniques such as spectral embedding. In this short paper, we present a simple generative model where unsupervised graph convolutional network fails, while the adjacency spectral embedding succeeds. Specifically, unsupervised graph convolutional network is unable to look beyond the first eigenvector in certain approximately regular graphs, thus missing inference signals in non-leading eigenvectors. The phenomenon is demonstrated by visual illustrations and comprehensive simulations.
In this paper, we focus on graph learning from multi-view data of shared entities for spectral clustering. We can explain interactions between the entities in multi-view data using a multi-layer graph with a common vertex set, which represents the shared entities. The edges of different layers capture the relationships of the entities. Assuming a smoothness data model, we jointly estimate the graph Laplacian matrices of the individual graph layers and low-dimensional embedding of the common vertex set. We constrain the rank of the graph Laplacian matrices to obtain multi-component graph layers for clustering. The low-dimensional node embeddings, common to all the views, assimilate the complementary information present in the views. We propose an efficient solver based on alternating minimization to solve the proposed multi-layer multi-component graph learning problem. Numerical experiments on synthetic and real datasets demonstrate that the proposed algorithm outperforms state-of-the-art multi-view clustering techniques.