Multivariate Data Anomaly Detection Based on Graph Structure Learning

Graph neural networks (GNNs) have recently achieved remarkable success on a variety of graph-related tasks, while such success relies heavily on a given graph structure that may not always be available in real-world applications. To address this problem, graph structure learning (GSL) is emerging as a promising research topic where task-specific graph structure and GNN parameters are jointly learned in an end-to-end unified framework. Despite their great progress, existing approaches mostly focus on the design of similarity metrics or graph construction, but directly default to adopting downstream objectives as supervision, which lacks deep insight into the power of supervision signals. More importantly, these approaches struggle to explain how GSL helps GNNs, and when and why this help fails. In this article, we conduct a systematic experimental evaluation to reveal that GSL and GNNs enjoy consistent optimization goals in terms of improving the graph homophily. Furthermore, we demonstrate theoretically and experimentally that task-specific downstream supervision may be insufficient to support the learning of both graph structure and GNN parameters, especially when the labeled data are extremely limited. Therefore, as a complement to downstream supervision, we propose homophily-enhanced self-supervision for GSL (HES-GSL), a method that provides more supervision for learning an underlying graph structure. A comprehensive experimental study demonstrates that HES-GSL scales well to various datasets and outperforms other leading methods. Our code will be available in https://github.com/LirongWu/Homophily-Enhanced-Self-supervision.

Graph neural networks (GNNs) have achieved considerable success in dealing with graph-structured data by the message-passing mechanism. Actually, this mechanism relies on a fundamental assumption that the graph structure along which information propagates is perfect. However, the real-world graphs are inevitably incomplete or noisy, which violates the assumption, thus resulting in limited performance. Therefore, optimizing graph structure for GNNs is indispensable and important. Although current semi-supervised graph structure learning (GSL) methods have achieved a promising performance, the potential of labels and prior graph structure has not been fully exploited yet. Inspired by this, we examine GSL with dual reinforcement of label and prior structure in this article. Specifically, to enhance label utilization, we first propose to construct the prior label-constrained matrices to refine the graph structure by identifying label consistency. Second, to adequately leverage the prior structure to guide GSL, we develop spectral contrastive learning that extracts global properties embedded in the prior graph structure. Moreover, contrastive fusion with prior spatial structure is further adopted, which promotes the learned structure to integrate local spatial information from the prior graph. To extensively evaluate our proposal, we perform sufficient experiments on seven benchmark datasets, where experimental results confirm the effectiveness of our method and the rationality of the learned structure from various aspects.

Graph neural networks (GNNs) often struggle to learn discriminative node representations for heterophilic graphs, where connected nodes tend to have dissimilar labels and feature similarity provides weak structural cues. We propose frequency-guided graph structure learning (FgGSL), an end-to-end graph inference framework that jointly learns homophilic and heterophilic graph structures along with a spectral encoder. FgGSL employs a learnable, symmetric, feature-driven masking function to infer said complementary graphs, which are processed using pre-designed low- and high-pass graph filter banks. A label-based structural loss explicitly promotes the recovery of homophilic and heterophilic edges, enabling task-driven graph structure learning. We derive stability bounds for the structural loss and establish robustness guarantees for the filter banks under graph perturbations. Experiments on six heterophilic benchmarks demonstrate that FgGSL consistently outperforms state-of-the-art GNNs and graph rewiring methods, highlighting the benefits of combining frequency information with supervised topology inference.

Graph Neural Networks (GNNs) are de facto solutions to structural data learning. However, it is susceptible to low-quality and unreliable structure, which has been a norm rather than an exception in real-world graphs. Existing graph structure learning (GSL) frameworks still lack robustness and interpretability. This paper proposes a general GSL framework, SE-GSL, through structural entropy and the graph hierarchy abstracted in the encoding tree. Particularly, we exploit the one-dimensional structural entropy to maximize embedded information content when auxiliary neighbourhood attributes are fused to enhance the original graph. A new scheme of constructing optimal encoding trees is proposed to minimize the uncertainty and noises in the graph whilst assuring proper community partition in hierarchical abstraction. We present a novel sample-based mechanism for restoring the graph structure via node structural entropy distribution. It increases the connectivity among nodes with larger uncertainty in lower-level communities. SE-GSL is compatible with various GNN models and enhances the robustness towards noisy and heterophily structures. Extensive experiments show significant improvements in the effectiveness and robustness of structure learning and node representation learning.

BGCSL: An unsupervised framework reveals the underlying structure of large-scale whole-brain functional connectivity networks.

At present, the graph neural network has achieved good results in the semisupervised classification of graph structure data. However, the classification effect is greatly limited in those data without graph structure, incomplete graph structure, or noise. It has no high prediction accuracy and cannot solve the problem of the missing graph structure. Therefore, in this paper, we propose a high-order graph learning attention neural network (HGLAT) for semisupervised classification. First, a graph learning module based on the improved variational graph autoencoder is proposed, which can learn and optimize graph structures for data sets without topological graph structure and data sets with missing topological structure and perform regular constraints on the generated graph structure to make the optimized graph structure more reasonable. Then, in view of the shortcomings of graph attention neural network (GAT) that cannot make full use of the graph high-order topology structure for node classification and graph structure learning, we propose a graph classification module that extends the attention mechanism to high-order neighbors, in which attention decays according to the increase of neighbor order. HGLAT performs joint optimization on the two modules of graph learning and graph classification and performs semisupervised node classification while optimizing the graph structure, which improves the classification performance. On 5 real data sets, by comparing 8 classification methods, the experiment shows that HGLAT has achieved good classification results on both a data set with graph structure and a data set without graph structure.

PurposeWith the introduction of graph structure learning into service classification, more accurate graph structures can significantly improve the precision of service classification. However, existing graph structure learning methods tend to rely on a single information source when attempting to eliminate noise in the original graph structure and lack consideration for the graph generation mechanism. To address this problem, this paper aims to propose a graph structure estimation neural network-based service classification (GSESC) model.Design/methodology/approachFirst, this method uses the local smoothing properties of graph convolutional networks (GCN) and combines them with the stochastic block model to serve as the graph generation mechanism. Next, it constructs a series of observation sets reflecting the intrinsic structure of the service from different perspectives to minimize biases introduced by a single information source. Subsequently, it integrates the observation model with the structural model to calculate the posterior distribution of the graph structure. Finally, it jointly optimizes GCN and the graph estimation process to obtain the optimal graph.FindingsThe authors conducted a series of experiments on the API data set and compared it with six baseline methods. The experimental results demonstrate the effectiveness of the GSESC model in service classification.Originality/valueThis paper argues that the data set used for service classification exhibits a strong community structure. In response to this, the paper innovatively applies a graph-based learning model that considers the underlying generation mechanism of the graph to the field of service classification and achieves good results.

Graph Neural Networks (GNNs) have achieved remarkable success in graph-related tasks by combining node features and graph topology elegantly. Most GNNs assume that the networks are homophilous, which is not always true in the real world, i.e., structure noise or disassortative graphs. Only a few works focus on generalizing graph neural networks to heterophilous or low homophilous networks, where connected nodes may have different labels. In this paper, we design a simple and effective Graph Structure Learning strategy based on Feature and Label consistency (GSLFL) to increase the homophilous level of networks for generalizing any existing GNNs to heterophilous networks. Specifically, we first introduce a method to learn graph structure based on node features and then modify the graph structure based on label consistency. Further, we combine the GSLFL with three existing GNNs to learn node representations and graph structure together. And we design a self-training method to iteratively train models and modify graph structure with pseudo-labels. Finally, our empirical results on 6 public networks with homophily or heterophily, and structure attacks show that our methods outperform the state-of-the-art methods in most cases.

Processes such as disease propagation and information diffusion often spread over some latent network structure that must be learned from observation. Given a set of unlabeled training examples representing occurrences of an event type of interest (such as a disease outbreak), the authors aim to learn a graph structure that can be used to accurately detect future events of that type. They propose a novel framework for learning graph structure from unlabeled data by comparing the most anomalous subsets detected with and without the graph constraints. Their framework uses the mean normalized log-likelihood ratio score to measure the quality of a graph structure, and it efficiently searches for the highest-scoring graph structure. Using simulated disease outbreaks injected into real-world Emergency Department data from Allegheny County, the authors show that their method learns a structure similar to the true underlying graph, but enables faster and more accurate detection.

Hierarchical clustering is a fundamental machine-learning technique for grouping data points into dendrograms. However, existing hierarchical clustering methods encounter two primary challenges: 1) Most methods specify dendrograms without a global objective. 2) Graph-based methods often neglect the significance of graph structure, optimizing objectives on complete or static predefined graphs. In this work, we propose Hyperbolic Continuous Structural Entropy neural networks, namely HypCSE, for structure-enhanced continuous hierarchical clustering. Our key idea is to map data points in the hyperbolic space and minimize the relaxed continuous structural entropy (SE) on structure-enhanced graphs. Specifically, we encode graph vertices in hyperbolic space using hyperbolic graph neural networks and minimize approximate SE defined on graph embeddings. To make the SE objective differentiable for optimization, we reformulate it into a function using the lowest common ancestor (LCA) on trees and then relax it into continuous SE (CSE) by the analogy of hyperbolic graph embeddings and partitioning trees. To ensure a graph structure that effectively captures the hierarchy of data points for CSE calculation, we employ a graph structure learning (GSL) strategy that updates the graph structure during training. Extensive experiments on seven datasets demonstrate the superior performance of HypCSE.

Due to the rapid adoption of 5G networks and the increasing number of devices and base stations (gNBs) connected to it, manually identifying malfunctioning machines or devices that cause a part of the networks to fail becomes more challenging. Furthermore, data collected from the networks are not always sufficient. To overcome these two issues, we proposed a novel root cause analysis (RCA) framework that integrates graph neural networks (GNNs) with graph structure learning (GSL) to infer hidden dependencies from available data. The learned dependencies are the graph structure utilized to predict the root cause machines or devices. We found that despite the fact that the data is often incomplete, the GSL model can infer fairly accurate hidden dependencies from data with a large number of nodes and generate informative graph representation for GNNs to identify the root cause. Our experimental results showed that higher accuracy of identifying a root cause and victim nodes can be achieved when the number of nodes in an environment is increased.

Graph structure learning (GSL) has emerged as a promising approach for optimizing graph structures to enhance downstream task performance. However, the quadratic complexity of GSL renders it impractical for large graphs, such as social networks. While several attempts have been made to mitigate the scalability issue of GSL, they struggle to ensure efficiency and expressiveness simultaneously. In this paper, we propose a novel scalable and expressive graph structure learning framework (SAVE-GSL), that models all-pair interactions with linear complexity. Specifically, we design cluster and expander sparse patterns for efficient expressiveness enhancement, and adaptively fuse them to generate the optimized graph. Moreover, leveraging these sparse patterns, we theoretically prove that SAVE-GSL is an efficient universal approximator of permutation-equivariant functions, providing a formal justification for its superior expressiveness. Extensive experiments demonstrate that SAVE-GSL outperforms state-of-the-art schemes in both efficiency and accuracy on social network datasets and other graph datasets of various scales.

Graph neural networks (GNNs) have a powerful ability to capture long-range spatial correlations in hyperspectral images (HSIs). However, existing GNN-based HSI classification methods are vulnerable to hand-crafted graphs, as the manner in which these graphs are constructed are often inappropriate and are likely to violate intrinsic graph properties, such as sparsity and low-rank. More importantly, the goal of HSI classification is to categorize each individual pixel into a land-cover class, but existing methods usually overuse global dependencies and ignore the importance of individualized spectral characteristics. Therefore, this paper proposes a Global-to-Local decoupling Graph network (GoLoG) to conduct HSI classification in a global-to-local framework, which jointly optimizes the graph structure and network parameters guided by both intrinsic graph properties and classification loss. Specifically, a novel global-to-local network framework with successive global and local graph convolutional stages is constructed. By decoupling global and local stages, global contextual information can be exploited, and the individualized information of each hyperspectral pixel can be emphasized for HSI classification. Second, a sparse and low-rank graph structure learning model is proposed to refine and renovate the initial-construct graph. Finally, to unify graph structure learning and network training, a joint alternating update algorithm is introduced to jointly optimize the sparse and low-rank graph structure learning model and the global-to-local network framework. Extensive experiments demonstrate that the proposed GoLoG has obvious advantages compared with other state-of-the-art HSI classification methods.

The success of graph neural networks (GNNs) has spurred numerous new works leveraging GNNs for modeling multivariate time series anomaly detection. Despite their achieved performance improvements, most of them only consider static graph to describe the spatial-temporal dependencies between time series. Moreover, existing works neglect the time and scale-changing structures of time series. In this work, we propose MDGAD, a novel multi-scale dynamic graph structure learning approach for time series anomaly detection. We design a multi-scale graph structure learning module that captures the complex correlations among time series, constructing an evolving graph at each scale. Meanwhile, an anomaly detector is used to combine bilateral prediction errors to detect abnormal data. Experiments conducted on two time series datasets demonstrate the effectiveness of MDGAD.

This study aims to improve the accuracy of weather predictions by discovering spatial correlations between Earth observations and atmospheric states. Existing numerical weather prediction (NWP) systems predict future atmospheric states at fixed locations, which are called NWP grid points, by analyzing previous atmospheric states and newly acquired Earth observations. However, the shifting locations of observations and the surrounding meteorological context induce complex, dynamic spatial correlations that are difficult for traditional NWP systems to capture, since they rely on strict statistical and physical formulations. To handle complicated spatial correlations, which change dynamically, we employ a spatiotemporal graph neural networks (STGNNs) with structure learning. However, structure learning has an inherent limitation that this can cause structural information loss and over-smoothing problem by generating excessive edges. To solve this problem, we regulate edge sampling by adaptively determining node degrees and considering the spatial distances between NWP grid points and observations. We validated the effectiveness of the proposed method (CloudNine-v2) using real-world atmospheric state and observation data from East Asia, achieving up to 15% reductions in RMSE over existing STGNN models. Even in areas with high atmospheric variability, CloudNine-v2 consistently outperformed baselines with and without structure learning.