Graph Wavelet Research Articles

MagNet: Multilevel Dynamic Wavelet Graph Neural Network for Multivariate Time Series Classification

Multivariate time series classification (MTSC) is a fundamental data mining task, which is widely applied in the fields like health care and energy management. However, the existing MTSC methods are mostly adapted from univariate versions and model the static patterns among series in the time domain. We argue they fail to capture the inter-dependencies across variables and rarely consider the unique dynamic features in multilevel frequencies, which are susceptible to signal noise and lack sufficient feature extraction capability to achieve satisfactory classification accuracy. To address these issues, we propose a novel M ultilevel dyn a mic wavelet g raph neural Net work called MagNet, which effectively captures inherent temporal-frequency dependencies in multivariate time series data in a global view, facilitating the information flow among interrelated variables and leveraging learnable graph neural networks (GNNs) to uncover dynamic frequency dependencies. We propose an orthogonal temporal convolution layer that utilizes soft orthogonal losses to constrain features learned at different frequency components to reduce feature redundancy. Additionally, we introduce a hierarchical graph coarsening operator to address the flat learning challenges in traditional GNNs. Our dynamic wavelet graph neural network and hierarchical coarsening enable deep model stacking and end-to-end learning. Extensive experiments on 30 UEA benchmarks demonstrate that our method outperforms the state-of-the-art baselines in the MTSC tasks.

Deep Learning for Parkinson's Disease Diagnosis: A Graph Neural Network (GNN) Based Classification Approach with Graph Wavelet Transform (GWT) Using Protein-Peptide Datasets.

Background: An important neurological disorder of Parkinson's Disease (PD) is characterized by motor and non-motor activity of the patients. Empirical condition of the patient: PD assessment uses the Movement Disorder Society Unified Parkinson's Rating Scale part III (MDS-UPDRS-III) measures for identifying the prediction of PD. Due to the unstable value of the measurement, the PD prediction and tracking lead to a lower prediction rate. Methods: To overcome this limitation, this paper proposed the Graph Wavelet Transform (GWT) based weighted feature extraction along with the Graph Neutral Network (GNN) classification. The main contribution of this research is (i) The weighted correlation between the data is calculated by GWT for effective prediction of PD. (ii) Machine learning algorithms were trained to predict Parkinson's disease based on these patterns. In this research, we developed a new model called Graph Neural Network (GNN) to predict PD tremors' MDS-UPDRS-III score using input data. To strengthen PD research and enable the construction of individualized treatment plans, these linked networks work together to methodically examine the data and find significant discoveries. Results: The proposed approach for predicting PD severity (motor- and MDS_UPDRS) has a mean squared error of 0.1796 and a root mean squared error of 0.2845, according to the experimental data. The prediction accuracy is increased by 27.66%, 54.11%, and 0.71%, correspondingly, when compared with the most effective State-of-the-Art methods of DNN, ANFIS + SVR, and Mixed MLP models. Conclusion: In conclusion, this proves that the proposed strategy is more effective at making predictions.

Non-intrusive fault detection in shipboard power systems using wavelet graph neural networks

Naval shipboard power systems (SPS) are rapidly embracing electrification, resulting in loads that generate pulsation currents and encounter substantial transients. However, conventional time-based features alone are inadequate for effectively monitoring and safeguarding these loads against faults. This highlights the critical requirement for advanced machine learning based methods to discern and differentiate between the various transient stages within the load profile. In this paper, we propose a Wavelet Graph Neural Network (WGNN) model for non-intrusive fault detection in SPS. The fault detection system leverages the dynamic model of the SPS to train and test performance with varying fault scenarios. The underlying structure and the interdependence among component states in the SPS network are effectively captured using the WGNN model, resulting in accuracies over 99% for intrusive fault detection and 97% for non-intrusive fault detection. The developed WGNN model has also shown to be robust in the presence of pulse loads and noise, achieving an accuracy of over 95%. At the end, a real-time simulation of the proposed method is validated on a hardware-in-the-loop system, guaranteeing the high fidelity and low latency of the proposed approach. These findings validate the effectiveness of the proposed WGNN model for fault detection and real-world applications in SPS.

Cross-modal and multimodal data analysis based on functional mapping of spectral descriptors and manifold regularization

Multimodal manifold modeling methods extend spectral geometry-aware data analysis to incorporate learning from multiple related and complementary modalities. However, most methods assume an equal number of homogeneous data samples in each modality and partial correspondences between modalities as prior knowledge. This work introduces two new multimodal modeling methods. The first method introduces a comprehensive framework for handling multimodal information in heterogeneous data without requiring specific prior knowledge. To achieve this, we begin by extracting local descriptors using spectral graph wavelet signatures (SGWS) to identify manifold localities. Then, we propose a manifold regularization framework that incorporates functional mapping between SGWS descriptors (FMBSD) to determine pointwise correspondences. The second method involves manifold regularized multimodal classification based on pointwise correspondences (M2CPC). This method addresses the challenge of multiclass classification in multimodal heterogeneous data by determining correspondences between modalities using the FMBSD method. Experimental results evaluating the FMBSD method on three widely used cross-modal retrieval datasets and evaluating the M2CPC method on three benchmark multimodal multiclass classification datasets demonstrate their effectiveness and superiority over state-of-the-art methods.

Explainable Graph Wavelet Denoising Network for Intelligent Fault Diagnosis.

Deep learning (DL)-based intelligent fault diagnosis methods have greatly promoted the development of the field of fault diagnosis due to their powerful feature extraction ability for handling massive monitoring data. However, most of them still suffer from the following three limitations. First, many existing DL-based intelligent diagnosis methods cannot extract proper discriminative features from signals with strong noise. Second, the interactions or relationships between signals are ignored, while they mainly focus on extracting temporal features from the signal. Third, owing to their black-box nature, the learned features lack interpretability, which hinders their application in the industry. To tackle these issues, an explainable graph wavelet denoising network (GWDN) is proposed to achieve intelligent fault diagnosis under noisy working conditions in this article. In GWDN, the collected signals are first transformed into graph-structured data to consider the interactions among signals. Then, the graph wavelet denoising convolution (GWDConv) is proposed based on the discrete graph wavelet frame, which allows GWDN to achieve multiscale feature extraction for graph-structured data and realize signal denoising. Extensive experiments are implemented to verify the efficacy of the proposed GWDN, and the experimental results show that GWDN can achieve state-of-the-art performance among the comparison methods. Besides, by using the square envelope spectrum to analyze the extracted features of GWDConv, we find that it can well retain the fault-related components of the signal and realize signal denoising, which further proves that GWDN is explainable.

Graph domain adaptation with localized graph signal representations

In this paper we propose a domain adaptation algorithm designed for graph domains. Given a source graph with many labeled nodes and a target graph with few or no labeled nodes, we aim to estimate the target labels by making use of the similarity between the characteristics of the variation of the label functions on the two graphs. Our assumption about the source and the target domains is that the local behavior of the label function, such as its spread and speed of variation on the graph, bears resemblance between the two graphs. We estimate the unknown target labels by solving an optimization problem where the label information is transferred from the source graph to the target graph based on the prior that the projections of the label functions onto localized graph bases be similar between the source and the target graphs. In order to efficiently capture the local variation of the label functions on the graphs, spectral graph wavelets are used as the graph bases. Experimentation on various data sets shows that the proposed method yields quite satisfactory classification accuracy compared to reference domain adaptation methods.

Geometric Multimodal Deep Learning With Multiscaled Graph Wavelet Convolutional Network.

Multimodal data provide complementary information of a natural phenomenon by integrating data from various domains with very different statistical properties. Capturing the intramodality and cross-modality information of multimodal data is the essential capability of multimodal learning methods. The geometry-aware data analysis approaches provide these capabilities by implicitly representing data in various modalities based on their geometric underlying structures. Also, in many applications, data are explicitly defined on an intrinsic geometric structure. Generalizing deep learning methods to the non-Euclidean domains is an emerging research field, which has recently been investigated in many studies. Most of those popular methods are developed for unimodal data. In this article, a multimodal graph wavelet convolutional network (M-GWCN) is proposed as an end-to-end network. M-GWCN simultaneously finds intramodality representation by applying the multiscale graph wavelet transform to provide helpful localization properties in the graph domain of each modality and cross-modality representation by learning permutations that encode correlations among various modalities. M-GWCN is not limited to either the homogeneous modalities with the same number of data or any prior knowledge indicating correspondences between modalities. Several semisupervised node classification experiments have been conducted on three popular unimodal explicit graph-based datasets and five multimodal implicit ones. The experimental results indicate the superiority and effectiveness of the proposed methods compared with both spectral graph domain convolutional neural networks and state-of-the-art multimodal methods.

A framework for collaborative multi-robot mapping using spectral graph wavelets

The exploration of large-scale unknown environments can benefit from the deployment of multiple robots for collaborative mapping. Each robot explores a section of the environment and communicates onboard pose estimates and maps to a central server to build an optimized global multi-robot map. Naturally, inconsistencies can arise between onboard and server estimates due to onboard odometry drift, failures, or degeneracies. The mapping server can correct and overcome such failure cases using computationally expensive operations such as inter-robot loop closure detection and multi-modal mapping. However, the individual robots do not benefit from the collaborative map if the mapping server provides no feedback. Although server updates from the multi-robot map can greatly alleviate the robotic mission strategically, most existing work lacks them, due to their associated computational and bandwidth-related costs. Motivated by this challenge, this paper proposes a novel collaborative mapping framework that enables global mapping consistency among robots and the mapping server. In particular, we propose graph spectral analysis, at different spatial scales, to detect structural differences between robot and server graphs, and to generate necessary constraints for the individual robot pose graphs. Our approach specifically finds the nodes that correspond to the drift’s origin rather than the nodes where the error becomes too large. We thoroughly analyze and validate our proposed framework using several real-world multi-robot field deployments where we show improvements of the onboard system up to 90% and can recover the onboard estimation from localization failures and even from the degeneracies within its estimation.

Multi-Source Information Fusion Based DLaaS for Traffic Flow Prediction

Traffic flow prediction is the key to transportation safety and efficiency. The advance in machine learning and deep learning has promoted the development of intelligent transportation systems. For example, the emergence of Deep Learning as a Service (DLaaS) has benefitted researchers a lot in dealing with large scale dataset and complex deep learning algorithms. In traffic forecasting, despite the success of deep learning-based models, there are still shortcomings, such as inadequate use of temporal and spatial traffic information, and indirect modeling of dependencies in traffic data. To address these challenges, we learn the transportation network in the form of a graph, and use graph wavelet as a key component to extract well-positioned features from the graph based on the transportation network. Compared with graph convolution, graph wavelets are very flexible and do not need to specify adjacent regions in the topological graph structure for feature extraction. At the same time, we propose to combine the multi-information fusion traffic control and guidance collaborative neural network and the results obtained are better than the benchmark algorithms. The results by comparison with several baseline methods show that our proposed method can outperform all the baseline methods.

SEA-GWNN: Simple and Effective Adaptive Graph Wavelet Neural Network

The utilization of wavelet-based techniques in graph neural networks (GNNs) has gained considerable attention, particularly in the context of node classification. Although existing wavelet-based approaches have shown promise, they are constrained by their reliance on pre-defined wavelet filters, rendering them incapable of effectively adapting to signals that reside on graphs based on tasks at hand. Recent research endeavors address this issue through the introduction of a wavelet lifting transform. However, this technique necessitates the use of bipartite graphs, causing a transformation of the original graph structure into a bipartite configuration. This alteration of graph topology results in the generation of undesirable wavelet filters, thereby undermining the effectiveness of the method. In response to these challenges, we propose a novel simple and effective adaptive graph wavelet neural network (SEA-GWNN) class that employs the lifting scheme on arbitrary graph structures while upholding the original graph topology by leveraging multi-hop computation trees. A noteworthy aspect of the approach is the focus on local substructures represented as acyclic trees, wherein the lifting strategy is applied in a localized manner. This locally defined lifting scheme effectively combines high-pass and low-pass frequency information to enhance node representations. Furthermore, to reduce computing costs, we propose to decouple the higher- order lifting operators and induce them from the lower-order structures. Finally, we benchmark our model on several real- world datasets spanning four distinct categories, including citation networks, webpages, the film industry, and large-scale graphs and the experimental results showcase the efficacy of the proposed SEA-GWNN.

Kumaraswamy Wavelet for Heterophilic Scene Graph Generation

Graph neural networks (GNNs) has demonstrated its capabilities in the field of scene graph generation (SGG) by updating node representations from neighboring nodes. Actually it can be viewed as a form of low-pass filter in the spatial domain, which smooths node feature representation and retains commonalities among nodes. However, spatial GNNs does not work well in the case of heterophilic SGG in which fine-grained predicates are always connected to a large number of coarse-grained predicates. Blind smoothing undermines the discriminative information of the fine-grained predicates, resulting in failure to predict them accurately. To address the heterophily, our key idea is to design tailored filters by wavelet transform from the spectral domain. First, we prove rigorously that when the heterophily on the scene graph increases, the spectral energy gradually shifts towards the high-frequency part. Inspired by this observation, we subsequently propose the Kumaraswamy Wavelet Graph Neural Network (KWGNN). KWGNN leverages complementary multi-group Kumaraswamy wavelets to cover all frequency bands. Finally, KWGNN adaptively generates band-pass filters and then integrates the filtering results to better accommodate varying levels of smoothness on the graph. Comprehensive experiments on the Visual Genome and Open Images datasets show that our method achieves state-of-the-art performance.

Adaptive spectral graph wavelets for collaborative filtering

Adaptive spectral graph wavelets for collaborative filtering

Filter-Informed Spectral Graph Wavelet Networks for Multiscale Feature Extraction and Intelligent Fault Diagnosis.

Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to make better use of the inductive bias of the interdependencies between the different sensor measurements. However, there are some limitations with these GNN-based fault diagnosis methods. First, they lack the ability to realize multiscale feature extraction due to the fixed receptive field of GNNs. Second, they eventually encounter the over-smoothing problem with increase of model depth. Finally, the extracted features of these GNNs are hard to understand due to the black-box nature of GNNs. To address these issues, a filter-informed spectral graph wavelet network (SGWN) is proposed in this article. In SGWN, the spectral graph wavelet convolutional (SGWConv) layer is established upon the spectral graph wavelet transform, which can decompose a graph signal into scaling function coefficients and spectral graph wavelet coefficients. With the help of SGWConv, SGWN is able to prevent the over-smoothing problem caused by long-range low-pass filtering, by simultaneously extracting low-pass and band-pass features. Furthermore, to speed up the computation of SGWN, the scaling kernel function and graph wavelet kernel function in SGWConv are approximated by the Chebyshev polynomials. The effectiveness of the proposed SGWN is evaluated on the collected solenoid valve dataset and aero-engine intershaft bearing dataset. The experimental results show that SGWN can outperform the comparative methods in both diagnostic accuracy and the ability to prevent over-smoothing. Moreover, its extracted features are also interpretable with domain knowledge.

Behavior analysis for trajectory graph signal using graph wavelet transform

Behavior analysis for trajectory graph signal using graph wavelet transform

PointWavelet: Learning in Spectral Domain for 3-D Point Cloud Analysis.

With recent success of deep learning in 2-D visual recognition, deep-learning-based 3-D point cloud analysis has received increasing attention from the community, especially due to the rapid development of autonomous driving technologies. However, most existing methods directly learn point features in the spatial domain, leaving the local structures in the spectral domain poorly investigated. In this article, we introduce a new method, PointWavelet, to explore local graphs in the spectral domain via a learnable graph wavelet transform. Specifically, we first introduce the graph wavelet transform to form multiscale spectral graph convolution to learn effective local structural representations. To avoid the time-consuming spectral decomposition, we then devise a learnable graph wavelet transform, which significantly accelerates the overall training process. Extensive experiments on four popular point cloud datasets, ModelNet40, ScanObjectNN, ShapeNet-Part, and S3DIS, demonstrate the effectiveness of the proposed method on point cloud classification and segmentation.

Anomaly Detection in Hyperspectral Images Using Adaptive Graph Frequency Location.

Graph theory-based techniques have recently been adopted for anomaly detection in hyperspectral images (HSIs). However, these methods rely excessively on the relational structure within the constructed graphs and tend to downplay the importance of spectral features in the original HSI. To address this issue, we introduce graph frequency analysis to hyperspectral anomaly detection (HAD), which can serve as a natural tool for integrating graph structure and spectral features. We treat anomaly detection as a problem of graph frequency location, achieved by constructing a beta distribution-based graph wavelet space, where the optimal wavelet can be identified adaptively for anomaly detection. Initially, a high-dimensional, undirected, unweighted graph is built using the pixels in the HSI as vertices. By leveraging the observation of energy shifting to higher frequencies caused by anomalies, we can dynamically pinpoint the specific Beta wavelet associated with the anomalies' high-frequency content to accurately extract anomalies in the context of HSIs. Furthermore, we introduce a novel entropy definition to address the frequency location problem in an adaptive manner. Experimental results from seven real HSIs validate the remarkable detection performance of our newly proposed approach when compared to various state-of-the-art anomaly detection methods.

Perception-Guided Quality Metric of 3D Point Clouds Using Hybrid Strategy.

Full-reference point cloud quality assessment (FR-PCQA) aims to infer the quality of distorted point clouds with available references. Most of the existing FR-PCQA metrics ignore the fact that the human visual system (HVS) dynamically tackles visual information according to different distortion levels (i.e., distortion detection for high-quality samples and appearance perception for low-quality samples) and measure point cloud quality using unified features. To bridge the gap, in this paper, we propose a perception-guided hybrid metric (PHM) that adaptively leverages two visual strategies with respect to distortion degree to predict point cloud quality: to measure visible difference in high-quality samples, PHM takes into account the masking effect and employs texture complexity as an effective compensatory factor for absolute difference; on the other hand, PHM leverages spectral graph theory to evaluate appearance degradation in low-quality samples. Variations in geometric signals on graphs and changes in the spectral graph wavelet coefficients are utilized to characterize geometry and texture appearance degradation, respectively. Finally, the results obtained from the two components are combined in a non-linear method to produce an overall quality score of the tested point cloud. The results of the experiment on five independent databases show that PHM achieves state-of-the-art (SOTA) performance and offers significant performance improvement in multiple distortion environments. The code is publicly available at https://github.com/zhangyujie-1998/PHM.

Robust Visible-Infrared Person Re-Identification Based on Polymorphic Mask and Wavelet Graph Convolutional Network

Robust Visible-Infrared Person Re-Identification Based on Polymorphic Mask and Wavelet Graph Convolutional Network

Spectral Graph Wavelet Transform-Based Feature Representation for Automated Classification of Emotions From EEG Signal

Spectral Graph Wavelet Transform-Based Feature Representation for Automated Classification of Emotions From EEG Signal

Multiscale transforms for signals on simplicial complexes

Our previous multiscale graph basis dictionaries/graph signal transforms—Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen Transform (HGLET); Natural Graph Wavelet Packets (NGWPs); and their relatives—were developed for analyzing data recorded on vertices of a given graph. In this article, we propose their generalization for analyzing data recorded on edges, faces (i.e., triangles), or more generally κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-dimensional simplices of a simplicial complex (e.g., a triangle mesh of a manifold). The key idea is to use the Hodge Laplacians and their variants for hierarchical partitioning of a set of κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-dimensional simplices in a given simplicial complex, and then build localized basis functions on these partitioned subsets. We demonstrate their usefulness for data representation on both illustrative synthetic examples and real-world simplicial complexes generated from a co-authorship/citation dataset and an ocean current/flow dataset.