Spectral Graph Wavelet Research Articles

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.

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.

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.

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.

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.

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

Enhancing e-commerce recommendations with a novel scale-aware spectral graph wavelets framework

Enhancing e-commerce recommendations with a novel scale-aware spectral graph wavelets framework

Spectral graph wavelet packets frames

Spectral graph wavelet packets frames

Network time series forecasting using spectral graph wavelet transform

We propose a novel method for forecasting network time series that occur in graphs or networks. Our approach is based on a spectral graph wavelet transform (SGWT) that provides the localized behavior of graph signals around each node. The proposed method improves forecasting performance over other existing methods. In particular, the advantages of the proposed method stand out when signals observed on a graph are inhomogeneous or non-stationary. We demonstrate the strength of the proposed approach through real-world data analysis. This analysis uses two network time series datasets: the daily number of people getting on and off the Seoul Metropolitan Subway, and daily Covid-19 confirmed cases reported in South Korea. We further conduct a simulation study to evaluate the effectiveness of the proposed method.

Multi-dimensional spectral graph wavelet transform

In this paper, we introduce the two-dimensional spectral graph wavelet transform (SGWT) of discrete functions defined on weighted Cartesian product graphs. The graphs we consider are undirected, non-planar, and can be cyclic with no multiple loops and no multiple edges. We build this transform with the help of spectral decomposition of $$N_1N_2 \times N_1N_2$$ Laplacian matrix $$\mathcal {L}$$ of the Cartesian product graph $$G=G_1\square G_2$$ , where $$N_1N_2$$ is the number of vertices of the Cartesian product graph. We have established the inversion formula for SGWT for continuous scale parameters $$s_1$$ and $$s_2$$ . By sampling the scale parameters at discrete values, we obtain discrete SGWT coefficients at different scales and vertices. We have obtained the frame bounds of the frame formed by the set of scaling and wavelet coefficients. Further, we have proved the localization result which holds for both normalized and non-normalized form of Laplacian. Towards the end, we have given the implementation details of SGWT through an example to show how to calculate the graph wavelet coefficients.

Undersampled MRI reconstruction based on spectral graph wavelet transform

Compressed sensing magnetic resonance imaging (CS-MRI) has exhibited great potential to accelerate magnetic resonance imaging if an image can be sparsely represented. How to sparsify the image significantly affects the reconstruction quality of images. In this paper, a spectral graph wavelet transform (SGWT) is introduced to sparsely represent magnetic resonance images in iterative image reconstructions. The SGWT is achieved by extending the traditional wavelets transform to the signal defined on the vertices of the weighted graph, i.e. the spectral graph domain. This SGWT uses only the connectivity information encoded in the edge weights, and does not rely on any other attributes of the vertices. Therefore, SGWT can be defined and calculated for any domain where the underlying relations between data locations can be represented by a weighted graph. Furthermore, we present a Chebyshev polynomial approximation algorithm for fast computing this SGWT transform. The l1 norm regularized CS-MRI reconstruction model is introduced and solved by the projected iterative soft-thresholding algorithm to verify its feasibility. Numerical experiment results demonstrate that our proposed method outperforms several state-of-the-art sparsify transforms in terms of suppressing artifacts and achieving lower reconstruction errors on the tested datasets.

Efficient multi-scale community search method based on spectral graph wavelet

Efficient multi-scale community search method based on spectral graph wavelet

Harmonic analysis on directed graphs and applications: From Fourier analysis to wavelets

We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph (digraphs) of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random walk operator as a non-orthogonal Fourier-type basis for functions over digraphs. We find a frequency interpretation by linking the variation of the eigenvectors of the random walk operator obtained from their Dirichlet energy to the real part of their associated eigenvalues. From this Fourier basis, we can proceed further and build multi-scale analyses on digraphs. We propose both a redundant wavelet transform and a decimated wavelet transform as an extension of spectral graph wavelets and diffusion wavelets framework respectively for digraphs. The development of our harmonic analysis on digraphs thus leads us to consider both semi-supervised learning problems and signal modeling problems on graphs applied to digraphs highlighting the efficiency of our framework.

Functions Approximation by Spectral Graph Wavelets

Approximating function by using Spectral Graph Wavelets is an interesting direction in approximation theory. We essential to well choosing the space of functions that are approximated by Spectral Graph Wavelets. spaces of functions are fantastic choices to study It is more interesting to take the value . In this paper , new formulas of Spectral Graph Wavelets were constructed and proved to get good rates of approximation. Fundamental properties of Graph Wavelets transform ( GWT) are studied, such as, inversion , scaling Limit and approximation Wavelets. Finally , existence of best approximation can be concluded here for Graph functions in terms of SGWT.

Functions Approximation by Spectral Graph Wavelets

Functions Approximation by Spectral Graph Wavelets

Dynamic PET images denoising using spectral graph wavelet transform.

Positron emission tomography (PET) is a non-invasive molecular imaging method for quantitative observation of physiological and biochemical changes in living organisms. The quality of the reconstructed PET image is limited by many different physical degradation factors. Various denoising methods including Gaussian filtering (GF) and non-local mean (NLM) filtering have been proposed to improve the image quality. However, image denoising usually blurs edges, of which high frequency components are filtered as noises. On the other hand, it is well-known that edges in a PET image are important to detection and recognition of a lesion. Denoising while preserving the edges of PET images remains an important yet challenging problem in PET image processing. In this paper, we propose a novel denoising method with good edge-preserving performance based on spectral graph wavelet transform (SGWT) for dynamic PET images denoising. We firstly generate a composite image from the entire time series, then perform SGWT on the PET images, and finally reconstruct the low graph frequency content to get the denoised dynamic PET images. Experimental results on simulation and in vivo data show that the proposed approach significantly outperforms the GF, NLM and graph filtering methods. Compared with deep learning-based method, the proposed method has the similar denoising performance, but it does not need lots of training data and has low computational complexity.

Data-Wise Spatial Regional Consistency Re-Enhancement for Hyperspectral Image Classification

Effectively using rich spatial and spectral information is the core issue of hyperspectral image (HSI) classification. The recently proposed Diverse Region-based Convolutional Neural Network (DRCNN) achieves good results by weighted averaging the features extracted from several predefined regions, thus exploring the use of spatial consistency to some extent. However, such feature-wise spatial regional consistency enhancement does not effectively address the issue of wrong classifications at the edge of regions, especially when the edge is winding and rough. To improve the feature-wise approach, Data-wise spAtial regioNal Consistency re-Enhancement (“DANCE”) is proposed. Firstly, the HSIs are decomposed once using the Spectral Graph Wavelet (SGW) to enhance the intra-class correlation. Then, the image components in different frequency domains obtained from the weight map are filtered using a Gaussian filter to “debur” the non-smooth region edge. Next, the reconstructed image is obtained based on all filtered frequency domain components using inverse SGW transform. Finally, a DRCNN is used for further feature extraction and classification. Experimental results show that the proposed method achieves the goal of pixel level re-enhancement with image spatial consistency, and can effectively improve not only the performance of the DRCNN, but also that of other feature-wise approaches.

Localized Fourier analysis for graph signal processing

We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard Fourier analysis of $f$ relies on the study of functions $g(\mathcal{L})f$ for some filters $g$ on $I_\mathcal{L}$, the smallest interval containing the Laplacian spectrum ${\mathrm sp}(\mathcal{L}) \subset I_\mathcal{L}$. We show that for carefully chosen partitions $I_\mathcal{L} = \sqcup_{1\leq k\leq K} I_k$ ($I_k \subset I_\mathcal{L}$), there are many advantages in understanding the collection $(g(\mathcal{L}_{I_k})f)_{1\leq k\leq K}$ instead of $g(\mathcal{L})f$ directly, where $\mathcal{L}_I$ is the projected matrix $P_I(\mathcal{L})\mathcal{L}$. First, the partition provides a convenient modelling for the study of theoretical properties of Fourier analysis and allows for new results in graph signal analysis (\emph{e.g.} noise level estimation, Fourier support approximation). We extend the study of spectral graph wavelets to wavelets localized in the Fourier domain, called LocLets, and we show that well-known frames can be written in terms of LocLets. From a practical perspective, we highlight the interest of the proposed localized Fourier analysis through many experiments that show significant improvements in two different tasks on large graphs, noise level estimation and signal denoising. Moreover, efficient strategies permit to compute sequence $(g(\mathcal{L}_{I_k})f)_{1\leq k\leq K}$ with the same time complexity as for the computation of $g(\mathcal{L})f$.

3D Spectral Graph Wavelet Point Signatures in Pre-Processing Stage for Mobile Laser Scanning Point Cloud Registration in Unstructured Orchard Environments

3D Spectral Graph Wavelet Point Signatures in Pre-Processing Stage for Mobile Laser Scanning Point Cloud Registration in Unstructured Orchard Environments