Spectral Convolution Research Articles

Enhancing framelet GCNs with generalized p-Laplacian regularization

Graph neural networks (GNNs) have achieved remarkable results for various graph learning tasks. However, one of the recent challenges for GNNs is to adapt to different types of graph inputs, such as heterophilic graph datasets in which linked nodes are more likely to contain a different class of labels and features. Accordingly, an ideal GNN model should adaptively accommodate all types of graph datasets with different labeling distributions. In this paper, we tackle this challenge by proposing a regularization framework on graph framelet with the regularizer induced from graph p-Laplacian. By adjusting the value of p, the p-Laplacian based regularizer restricts the solution space of graph framelet into the desirable region based on the graph homophilic features. We propose an algorithm to effectively solve a more generalized regularization problem and prove that the algorithm imposes a (p-Laplacian based) spectral convolution and diagonal scaling operation to the framelet filtered node features. Furthermore, we analyze the denoising power of the proposed model and compare it with the predefined framelet denoising regularizer. Finally, we conduct empirical studies to show the prediction power of the proposed model in both homophily undirect and heterophily direct graphs with and without noises. Our proposed model shows significant improvements compared to multiple baselines, and this suggests the effectiveness of combining graph framelet and p-Laplacian.

SGCRNN: A ChebNet-GRU fusion model for eeg emotion recognition

The paper proposes a deep learning model based on Chebyshev Network Gated Recurrent Units, which is called Spectral Graph Convolution Recurrent Neural Network, for multichannel electroencephalogram emotion recognition. First, in this paper, an adjacency matrix capturing the local relationships among electroencephalogram channels is established based on the cosine similarity of the spatial locations of electroencephalogram electrodes. The training efficiency is improved by utilizing the computational speed of the cosine distance. This advantage enables our method to have the potential for real-time emotion recognition, allowing for fast and accurate emotion classification in real-time application scenarios. Secondly, the spatial and temporal dependence of the Spectral Graph Convolution Recurrent Neural Network for capturing electroencephalogram sequences is established based on the characteristics of the Chebyshev network and Gated Recurrent Units to extract the spatial and temporal features of electroencephalogram sequences. The proposed model was tested on the publicly accessible dataset DEAP. Its average recognition accuracy is 88%, 89.5%, and 89.7% for valence, arousal, and dominance, respectively. The experiment results demonstrated that the Spectral Graph Convolution Recurrent Neural Network method performed better than current models for electroencephalogram emotion identification. This model has broad applicability and holds potential for use in real-time emotion recognition scenarios.

Adaptive filters in Graph Convolutional Neural Networks

Over the last few years, the availability of an increasing data generated from non-Euclidean domains, which are usually represented as graphs with complex relationships, and Graph Neural Networks (GNN) have gained a high interest because of their potential in processing graph-structured data. In particular, there is a strong interest in performing convolution on graphs using an extension of the GNN architecture, generally referred to as Graph Convolutional Neural Networks (ConvGNN). Convolution on graphs has been achieved mainly in two forms: spectral and spatial convolutions. Due to the higher flexibility in exploring and exploiting the graph structure of data, there is recently an increasing interest in investigating the possibilities that the spatial approach can offer. The idea of finding a way to adapt the network behaviour to the inputs they process to maximize the total performances has aroused much interest in the neural networks literature over the years. This paper presents a novel method to adapt the behaviour of a ConvGNN to the input performing spatial convolution on graphs using input-specific filters, which are dynamically generated from nodes feature vectors. The experimental assessment confirms the capabilities of the proposed approach, achieving satisfying results using a low number of filters.

Graph classification via discriminative edge feature learning

Spectral graph convolutional neural networks (GCNNs) have been producing encouraging results in graph classification tasks. However, most spectral GCNNs utilize fixed graphs when aggregating node features while omitting edge feature learning and failing to get an optimal graph structure. Moreover, many existing graph datasets do not provide initialized edge features, further restraining the ability of learning edge features via spectral GCNNs. In this paper, we try to address this issue by designing an edge feature scheme and an add-on layer between every two stacked graph convolution layers in spectral GCNN. Both are lightweight while effective in filling the gap between edge feature learning and performance enhancement of graph classification. The edge feature scheme makes edge features adapt to node representations at different spectral graph convolution layers. The add-on layer helps adjust the edge features to an optimal graph structure. To test the effectiveness of our method, we take Euclidean positions as initial node features and extract graphs with semantic information from point cloud objects. The node features of our extracted graphs are more scalable for edge feature learning than most existing graph datasets (in one-hot encoded label format). Three new graph datasets are constructed based on ModelNet40, ModelNet10 and ShapeNet Part datasets. Experimental results show that our method outperforms state-of-the-art graph classification methods on the new datasets. Our code and the constructed graph datasets will be released to the community.

Retracted: Research on the Spectral Domain Graph Convolution Collaborative Filtering Algorithm Based on Reinforcement Learning and Chebyshev

Retracted: Research on the Spectral Domain Graph Convolution Collaborative Filtering Algorithm Based on Reinforcement Learning and Chebyshev

MS3Net: Multiscale stratified-split symmetric network with quadra-view attention for hyperspectral image classification

Recently, hyperspectral image (HSI) classification has become a promising research direction in remote sensing image processing. Many HSI classification methods have been proposed based on convolutional neural networks (CNNs) and attention mechanisms (AMs). However, most current CNN-based methods only consider extracting features at a single scale in HSI, which may ignore the delicate features of some objects. Moreover, present AMs primarily focus on one feature dimension, such as spatial or channel attention, while disregarding dimension interaction. To conquer the above issues, a novel multiscale stratified-split symmetric network with quadra-view attention, namely MS3Net, is proposed for HSI classification. Generally, the proposed MS3Net has a dual-stream symmetric pipeline, which can better extract HSI's spectral signatures and spatial features. Specifically, the proposed MS3Net consists of three modules: a multiscale feature extraction module, a feature enhancement module, and a feature fusion module. Firstly, a stratified-split module is designed to extract multiscale spectral and spatial features. In addition, to reduce the complexity of the model, we designed pseudo-3-D spectral and spatial convolution to replace the traditional 3-D convolution operation. Secondly, a novel quadra-view attention module is proposed, guiding the model to focus on important features from multiple dimensions. Finally, the selective kernel feature fusion module is introduced, which can dynamically integrate spectral and spatial features. Experimental results on four benchmark HSI datasets with different scenes and resolutions confirm the visual and quantitative superiority of the proposed MS3Net over the state-of-the-art related methods in this research direction.

A spectral graph convolution for signed directed graphs via magnetic Laplacian

Signed directed graphs contain both sign and direction information on their edges, providing richer information about real-world phenomena compared to unsigned or undirected graphs. However, analyzing such graphs is more challenging due to their complexity, and the limited availability of existing methods. Consequently, despite their potential uses, signed directed graphs have received less research attention. In this paper, we propose a novel spectral graph convolution model that effectively captures the underlying patterns in signed directed graphs. To this end, we introduce a complex Hermitian adjacency matrix that can represent both sign and direction of edges using complex numbers. We then define a magnetic Laplacian matrix based on the adjacency matrix, which we use to perform spectral convolution. We demonstrate that the magnetic Laplacian matrix is positive semi-definite (PSD), which guarantees its applicability to spectral methods. Compared to traditional Laplacians, the magnetic Laplacian captures additional edge information, which makes it a more informative tool for graph analysis. By leveraging the information of signed directed edges, our method generates embeddings that are more representative of the underlying graph structure. Furthermore, we showed that the proposed method has wide applicability for various graph types and is the most generalized Laplacian form. We evaluate the effectiveness of the proposed model through extensive experiments on several real-world datasets. The results demonstrate that our method outperforms state-of-the-art techniques in signed directed graph embedding.

Fourier domain structural relationship analysis for unsupervised multimodal change detection

Change detection on multimodal remote sensing images has become an increasingly interesting and challenging topic in the remote sensing community, which can play an essential role in time-sensitive applications, such as disaster response. However, the modal heterogeneity problem makes it difficult to compare the multimodal images directly. This paper proposes a Fourier domain structural relationship analysis framework for unsupervised multimodal change detection (FD-MCD), which exploits both modality-independent local and nonlocal structural relationships. Unlike most existing methods analyzing the structural relationship in the original domain of multimodal images, the three critical parts in the proposed framework are implemented on the (graph) Fourier domain. Firstly, a local frequency consistency metric calculated in the Fourier domain is proposed to determine the local structural difference. Then, the nonlocal structural relationship graphs are constructed for pre-change and post-change images. The two graphs are then transformed to the graph Fourier domain, and high-order vertex information is modeled for each vertex by graph spectral convolution, where the Chebyshev polynomial is applied as the transfer function to pass K-hop local neighborhood vertex information. The nonlocal structural difference map is obtained by comparing the filtered graph representations. Finally, an adaptive fusion method based on frequency-decoupling is designed to effectively fuse the local and nonlocal structural difference maps. Experiments conducted on five real datasets with different modality combinations and change events show the effectiveness of the proposed framework.

Learning Graph Representations With Maximal Cliques.

Non-Euclidean property of graph structures has faced interesting challenges when deep learning methods are applied. Graph convolutional networks (GCNs) can be regarded as one of the successful approaches to classification tasks on graph data, although the structure of this approach limits its performance. In this work, a novel representation learning approach is introduced based on spectral convolutions on graph-structured data in a semisupervised learning setting. Our proposed method, COnvOlving cLiques (COOL), is constructed as a neighborhood aggregation approach for learning node representations using established GCN architectures. This approach relies on aggregating local information by finding maximal cliques. Unlike the existing graph neural networks which follow a traditional neighborhood averaging scheme, COOL allows for aggregation of densely connected neighboring nodes of potentially differing locality. This leads to substantial improvements on multiple transductive node classification tasks.

An Adaptive Kernels Layer for Deep Neural Networks Based on Spectral Analysis for Image Applications.

As the pixel resolution of imaging equipment has grown larger, the images' sizes and the number of pixels used to represent objects in images have increased accordingly, exposing an issue when dealing with larger images using the traditional deep learning models and methods, as they typically employ mechanisms such as increasing the models' depth, which, while suitable for applications that have to be spatially invariant, such as image classification, causes issues for applications that relies on the location of the different features within the images such as object localization and change detection. This paper proposes an adaptive convolutional kernels layer (AKL) as an architecture that adjusts dynamically to images' sizes in order to extract comparable spectral information from images of different sizes, improving the features' spatial resolution without sacrificing the local receptive field (LRF) for various image applications, specifically those that are sensitive to objects and features locations, using the definition of Fourier transform and the relation between spectral analysis and convolution kernels. The proposed method is then tested using a Monte Carlo simulation to evaluate its performance in spectral information coverage across images of various sizes, validating its ability to maintain coverage of a ratio of the spectral domain with a variation of around 20% of the desired coverage ratio. Finally, the AKL is validated for various image applications compared to other architectures such as Inception and VGG, demonstrating its capability to match Inception v4 in image classification applications, and outperforms it as images grow larger, up to a 30% increase in accuracy in object localization for the same number of parameters.

Empirical mode decomposition-based multi-scale spectral graph convolution network for abnormal electricity consumption detection

Empirical mode decomposition-based multi-scale spectral graph convolution network for abnormal electricity consumption detection

Multi-order hypergraph convolutional networks integrated with self-supervised learning

AbstractHypergraphs, as a powerful representation of information, effectively and naturally depict complex and non-pair-wise relationships in the real world. Hypergraph representation learning is useful for exploring complex relationships implicit in hypergraphs. However, most methods focus on the 1-order neighborhoods and ignore the higher order neighborhood relationships among data on the hypergraph structure. These often result in underutilization of hypergraph structure. In this paper, we exploit the potential of higher order neighborhoods in hypergraphs for representation and propose a Multi-Order Hypergraph Convolutional Network Integrated with Self-supervised Learning. We first encode the multi-channel network of the hypergraph by a high-order spectral convolution operator that captures the multi-order representation of nodes. Then, we introduce an inter-order attention mechanism to preserve the low-order neighborhood information. Finally, to extract valid embedding in the higher order neighborhoods, we incorporate a self-supervised learning strategy based on maximizing mutual information in the multi-order hypergraph convolutional network. Experiments on several hypergraph datasets show that the proposed model is competitive with state-of-the-art baselines, and ablation studies show the effectiveness of higher order neighborhood development, the inter-order attention mechanism, and the self-supervised learning strategy.

Illegal activity detection on bitcoin transaction using deep learning

Forensic investigations increasingly leverage artificial intelligence (AI/ML) to identify illegal activities on bitcoin. bitcoin transactions have an original graph (network) structure, which is sophisticated and yet informative. However, machine learning applications on bitcoin have given limited attention to developing end-to-end deep learning frameworks that are modeled to exploit the bitcoin graph structure. To identify illegal transactions on bitcoin, the current paper extracts nineteen features from the bitcoin network and proposes a deep learning-based graph neural network model using spectral graph convolutions and transaction features. The proposed model is compared with two state-of-the-art techniques, viz., a graph attention network (GAT2) and an extreme gradient boosted decision tree (XGBOOST) trained on convoluted features for classification of illegal transactions on bitcoin. To understand the efficacy of the proposed model, a dataset is collected consisting of 13310125 transactions of 2059 entities having 3152202 bitcoin account addresses and belonging to 28 categories of users. Two sets of experiments are performed on the datasets: labeling transactions as legal or illegal (binary classification) and identifying the originator of the transaction to one of the twenty-eight types of entities (multi-class classification). For fast and accurate decisions, binary classification is appropriate, and for pinpointing the category of bitcoin users, a multi-class classifier is suitable. On both the tasks, the proposed models achieved a maximum of 92% accuracy, validating the methodology and suitability of the model for real-world deployment.

Diffused Convolutional Neural Network for Hyperspectral Image Super-Resolution

With the rapid development of deep convolutional neural networks, super-resolution (SR) in hyperspectral image (HSI) has achieved good results. Current methods generally use two dimensional (2D) convolution for feature extraction, but they cannot effectively extract spectral information. Although three dimensional (3D) convolution can better characterize feature structure of HSI, it will lead to parameter redundancy, model complexity and severe memory shortage. To address above problems, we propose a new hyperspectral image super-resolution method, named diffused convolutional neural network (DCNN). Specifically, spectral convolutions have been added into the enhanced convolutional neural (ECN) block, and a series of spectral convolutions is introduced in the residual network to learn features in the channel direction of different depths. Further, Histogram of Oriented Gradient (HOG) and Local Binary Pattern (LBP) are used to retain the shape and texture information of the image respectively, which can well represent the spatial structure of the object. In order to effectively make use of the extracted shallow and deep features, a feature fusion strategy is employed to reinforce the reconstruction efficiency. Besides, an image enhancement module has been developed to diffuse the super-resolution image into the image space. Extensive evaluations and comparisons show that our DCNN approach can not only recover the HSI data with richer details, but also achieve superiority over several state-of-the-art methods.

Spectral–Spatial Morphological Attention Transformer for Hyperspectral Image Classification

In recent years, convolutional neural networks (CNNs) have drawn significant attention for classification of hyperspectral images (HSIs). Due to their self-attention mechanism, the vision transformer (ViT) provides promising classification performance compared to CNNs. Many researchers have incorported ViT for HSI classification purposes. However, its performance can be further improved because the current version does not use spatial-spectral features. In this paper, we present a new morphological transformer (morphFormer) that implements a learnable spectral and spatial morphological network, where spectral and spatial morphological convolution operations are used (in conjunction with the attention mechanism) to improve the interaction between the structural and shape information of the HSI token and the CLS token. Experiments conducted on widely used HSIs demonstrate the superiority of proposed morphFormer over the classical CNN models and state-of-the-art transformer models. The source will be made available publicly at https://github.com/mhaut/morphFormer.

A Graph Convolutional Network Based on Univariate Neurodegeneration Biomarker for Alzheimer's Disease Diagnosis.

Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disease that is not easily detectable in the early stage. This study proposed an efficient method of applying a graph convolutional network (GCN) on the early prediction of AD. We proposed a univariate neurodegeneration biomarker (UNB) based GCN semi-supervised classification framework. We generated UNB by comparing the similarity of individual morphological atrophy pattern and the atrophy pattern of [Formula: see text] AD group according to the brain morphological abnormalities induced by AD. For the GCN semi-supervised classification model, we took the UNBs of individuals as the features of nodes and constructed the weight of edges according to the similarity of phenotypic information between individuals, which explored the essential features of individuals through spectral graph convolution. The attention module was constructed and embedded into the GCN framework, which may refine the input morphological features to highlight the main impact of AD on the cerebral cortex and weaken the instability caused by individual diversities, thereby identifying the significant ROIs affected by AD and improving the classification accuracy. We tested the UNB-GCN framework on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. The estimated minimum sample sizes were 156, 349 and 423 for the longitudinal [Formula: see text] AD, [Formula: see text] mild cognitive impairment (MCI) and [Formula: see text] cognitively unimpaired (CU) groups, respectively. And the proposed UNB-GCN framework combined with the attention module can effectively improve the classification performance with 93.90% classification accuracy for AD vs. CU and 82.05% for AD vs. MCI on the validation set. The proposed UNB measures were superior to the conventional volume measures in describing the AD-induced cerebral cortex morphological changes. And the UNB-GCN framework combined with attention module may effectively improve the classification performance between MCI subjects and AD patients. Clinical and Translational Impact Statement: This study aims to predict the early AD patients, so as to help clinicians develop effective interventions to delay the deterioration of AD symptoms.

Semisupervised Hyperspectral Image Classification Network Based on Pseudo-Label and Spatial–Spectral Convolution

Semisupervised Hyperspectral Image Classification Network Based on Pseudo-Label and Spatial–Spectral Convolution

A Low-cost Portable Interrogator for Dynamic Monitoring of Wavelength-Based Sensors

This paper proposes a low-cost portable interrogator for dynamic monitoring of wavelength-based fiber-optic sensors such as fiber Bragg gratings (FBGs) and Fabry-Perrot interferometers (FPIs). The interrogator is based on a compact solution involving a broadband light source and the spectral convolution between the sensor and a tunable filter. The filtered signal is then acquired by a photodetector where the optical-electrical conversion happens. Additionally, a microcontroller performs three actions: (i) controls the filter tuning, (ii) acquires the photodetector signal, and (iii) sends the data to a single-board computer (SBC). Lastly, the SBC performs further signal processing and displays the sensor data on a graphical user interface. The choice for hardware and software development combined allows for a lost-cost solution that supports monitoring of four channels simultaneously, real-time operation, compatibility with Windows and Linux-based operating systems, dynamic inputs for signal processing, wireless communication with low latency, and portability.

SPHARM-Net: Spherical Harmonics-Based Convolution for Cortical Parcellation.

We present a spherical harmonics-based convolutional neural network (CNN) for cortical parcellation, which we call SPHARM-Net. Recent advances in CNNs offer cortical parcellation on a fine-grained triangle mesh of the cortex. Yet, most CNNs designed for cortical parcellation employ spatial convolution that depends on extensive data augmentation and allows only predefined neighborhoods of specific spherical tessellation. On the other hand, a rotation-equivariant convolutional filter avoids data augmentation, and rotational equivariance can be achieved in spectral convolution independent of a neighborhood definition. Nevertheless, the limited resources of a modern machine enable only a finite set of spectral components that might lose geometric details. In this paper, we propose (1) a constrained spherical convolutional filter that supports an infinite set of spectral components and (2) an end-to-end framework without data augmentation. The proposed filter encodes all the spectral components without the full expansion of spherical harmonics. We show that rotational equivariance drastically reduces the training time while achieving accurate cortical parcellation. Furthermore, the proposed convolution is fully composed of matrix transformations, which offers efficient and fast spectral processing. In the experiments, we validate SPHARM-Net on two public datasets with manual labels: Mindboggle-101 (N=101) and NAMIC (N=39). The experimental results show that the proposed method outperforms the state-of-the-art methods on both datasets even with fewer learnable parameters without rigid alignment and data augmentation. Our code is publicly available at https://github.com/Shape-Lab/SPHARM-Net.

SC-CAN: Spectral Convolution and Channel Attention Network for Wheat Stress Classification

Biotic and abiotic plant stress (e.g., frost, fungi, diseases) can significantly impact crop production. It is thus essential to detect such stress at an early stage before visual symptoms and damage become apparent. To this end, this paper proposes a novel deep learning method, called Spectral Convolution and Channel Attention Network (SC-CAN), which exploits the difference in spectral responses of healthy and stressed crops. The proposed SC-CAN method comprises two main modules: (i) a spectral convolution module, which consists of dilated causal convolutional layers stacked in a residual manner to capture the spectral features; (ii) a channel attention module, which consists of a global pooling layer and fully connected layers that compute inter-relationship between feature map channels before scaling them based on their importance level (attention score). Unlike standard convolution, which focuses on learning local features, the dilated convolution layers can learn both local and global features. These layers also have long receptive fields, making them suitable for capturing long dependency patterns in hyperspectral data. However, because not all feature maps produced by the dilated convolutional layers are important, we propose a channel attention module that weights the feature maps according to their importance level. We used SC-CAN to classify salt stress (i.e., abiotic stress) on four datasets (Chinese Spring (CS), Aegilops columnaris (co(CS)), Ae. speltoides auchery (sp(CS)), and Kharchia datasets) and Fusarium head blight disease (i.e., biotic stress) on Fusarium dataset. Reported experimental results show that the proposed method outperforms existing state-of-the-art techniques with an overall accuracy of 83.08%, 88.90%, 82.44%, 82.10%, and 82.78% on CS, co(CS), sp(CS), Kharchia, and Fusarium datasets, respectively.