Spectral Convolution Research Articles

Depthwise Separable ResNet in the MAP Framework for Hyperspectral Image Classification

To build small and efficient neural networks for hyperspectral image (HSI) classification, this letter presents a depthwise separable residual neural network (ResNet). This approach, motivated by the popular MobileNet architecture, decomposes the traditional spatial-spectral convolution operation into a spatial-independent pointwise spectral convolution and a spectral-independent depthwise spatial convolution. It allows the separation of spectral and spatial information in HSI and also greatly reduces the network size to prevent the overfitting issue. To better preserve the class boundaries and edges, the proposed ResNet is integrated into a maximum a posteriori (MAP) framework to allow the use of the conditional random field (CRF) model. The experiment results on benchmark HSI scene demonstrate that the proposed ResNet compares favorably with several popular deep learning HSI classifiers and that the ResNet-CRF approach achieves higher accuracy and better boundaries among neighboring classes.

A successive flux estimation method for rapid g-function construction of small to large-scale ground heat exchanger

This paper presents a modification of the successive flux estimation algorithm of Pasquier and Marcotte (2013) [1] for computation of the so-called g-functions of small to large-scale ground heat exchanger fields. Fast calculation times are obtained by spectral convolution of the incremental flux signal and the borehole transfer function in an iterative scheme. An initial guess that is close to the solution and easily computable is also suggested for fast convergence. Further gains are obtained through the preprocessing of the transfer functions and the sub-sampling of the g-function. The proposed method was compared against the original successive flux estimation method, as well as two other rapid methods in the literature. Results show that the algorithm proposed in this work is by far the fastest and can generate a 40 year g-function of a large ground heat exchanger field composed of 400 randomly positioned boreholes in less than 4 s. The proposed approach is general and can manage fields composed of different number of boreholes and configurations.

DS-GCNs: Connectome Classification using Dynamic Spectral Graph Convolution Networks with Assistant Task Training.

Functional connectivity (FC) matrices measure the regional interactions in the brain and have been widely used in neurological brain disease classification. A brain network, also named as connectome, could form a graph structure naturally, the nodes of which are brain regions and the edges are interregional connectivity. Thus, in this study, we proposed novel graph convolutional networks (GCNs) to extract efficient disease-related features from FC matrices. Considering the time-dependent nature of brain activity, we computed dynamic FC matrices with sliding windows and implemented a graph convolution-based LSTM (long short-term memory) layer to process dynamic graphs. Moreover, the demographics of patients were also used as additional outputs to guide the classification. In this paper, we proposed to utilize the demographic information as extra outputs and to share parameters among three networks predicting subject status, gender, and age, which serve as assistant tasks. We tested the performance of the proposed architecture in ADNI II dataset to classify Alzheimer's disease patients from normal controls. The classification accuracy, sensitivity, and specificity reach 90.0%, 91.7%, and 88.6%, respectively, on ADNI II dataset.

Information transfer via temporal convolution in nonlinear optics

Nonlinear parametric processes involving ultrashort pulses are typically carried out in time domain, which mathematically corresponds to a convolution of their frequency spectra. In contrast, this spectral convolution changes into a multiplication operation when performing the nonlinear interaction in frequency domain. Here, we extend the scope of frequency-domain nonlinear optics by demonstrating its ability to perform a temporal convolution. Through this approach, nonlinear optical operations that are inaccessible in time domain can be realised: specific optical information can be coherently advanced by picoseconds within a pulse sequence—a newly generated second harmonic pulse carries the amplitude and phase information of two input pulses. This central pulse is isolated when using an input field consisting of two cross-polarized input pulses in combination with type-II second harmonic generation. The effects of nonlinear temporal convolution can be viewed from the aspect of signal processing and pulse shaping, where the nonlinear interaction in the parametric crystal plays the role of a dynamic linear optical filter—in contrast to conventional static filters—with a shaping mask instantaneously adapting to the laser field.

Dynamic detection of acoustic wave generated by polarization maintaining Brillouin random fiber laser

The intrinsic spectral width and intensity dynamics of the acoustic wave generated by the Brillouin random fiber laser were characterized experimentally for the first time. These are important to the understanding of the dynamic noise properties of random fiber lasers based on stimulated Brillouin scattering. We demonstrate that the spectra of the acoustic wave in the gain medium are determined by the spectral convolution of pump light and its Stokes light, which is further an influential factor on the narrow linewidth of the random fiber laser resulting from the distributed feedback of coherent Rayleigh scattering. The power of probe light is weak to ensure the minimum disturbance to the random fiber laser. In the time domain, the intensity of the reflected probe light exhibits a similar output property to that the Brillouin random fiber laser with Gaussian probability distribution when both narrow linewidth lasers (on the order of several kHz) are used as pump light and probe light. In contrast, stochastic noise features with an exponential probability distribution are introduced to the intensity dynamics of the reflected probe light when the linewidth of pump light or probe light is several MHz. The phase noise and intensity noise of the reflected probe light prove that acoustic wave generation and detection is based on a four wave mixing process, which enhances our understanding of the wave coupling in random fiber lasers and gives us a new perspective to understand the fundamental physics of the random lasing process and its noise property.

Spectral Convolution Feature-Based SPD Matrix Representation for Signal Detection Using a Deep Neural Network.

Convolutional neural networks have powerful performances in many visual tasks because of their hierarchical structures and powerful feature extraction capabilities. SPD (symmetric positive definition) matrix is paid attention to in visual classification, because it has excellent ability to learn proper statistical representation and distinguish samples with different information. In this paper, a deep neural network signal detection method based on spectral convolution features is proposed. In this method, local features extracted from convolutional neural network are used to construct the SPD matrix, and a deep learning algorithm for the SPD matrix is used to detect target signals. Feature maps extracted by two kinds of convolutional neural network models are applied in this study. Based on this method, signal detection has become a binary classification problem of signals in samples. In order to prove the availability and superiority of this method, simulated and semi-physical simulated data sets are used. The results show that, under low SCR (signal-to-clutter ratio), compared with the spectral signal detection method based on the deep neural network, this method can obtain a gain of 0.5–2 dB on simulated data sets and semi-physical simulated data sets.

Graph Markov network for traffic forecasting with missing data

Traffic forecasting is a classical task for traffic management and it plays an important role in intelligent transportation systems. However, since traffic data are mostly collected by traffic sensors or probe vehicles, sensor failures and the lack of probe vehicles will inevitably result in missing values in the collected raw data for some specific links in the traffic network. Although missing values can be imputed, existing data imputation methods normally need long-term historical traffic state data. As for short-term traffic forecasting, especially under edge computing and online prediction scenarios, traffic forecasting models with the capability of handling missing values are needed. In this study, we consider the traffic network as a graph and define the transition between network-wide traffic states at consecutive time steps as a graph Markov process. In this way, missing traffic states can be inferred step by step and the spatial–temporal relationships among the roadway links can be incorporated. Based on the graph Markov process, we propose a new neural network architecture for spatial–temporal data forecasting, i.e. the graph Markov network (GMN). By incorporating the spectral graph convolution operation, we also propose a spectral graph Markov network (SGMN). The proposed models are compared with baseline models and tested on three real-world traffic state datasets with various missing rates. Experimental results show that the proposed GMN and SGMN can achieve superior prediction performance in terms of both accuracy and efficiency. Besides, the proposed models’ parameters, weights, and predicted results are comprehensively analyzed and visualized.

Deep spectral convolution network for hyperspectral image unmixing with spectral library

Spectral unmixing is an important task for hyperspectral remote sensing image processing, which infers the pure spectral signatures (endmembers) in hyperspectral image (HSI) and their corresponding fractions (abundances). Recently, deep learning has become a powerful tool for HSI analysis, such as HSI classification and HSI super-resolution. In this paper, we propose a new unmixing algorithm that uses the convolutional neural network (CNN) for hyperspectral data incorporating spectral library, which can be applied for a series of HSIs after training. The proposed deep spectral convolution network extracts features and then executes the estimating process from these extracted spectral characteristics to acquire the fractional abundances on a fixed spectral library. Meanwhile, considering the incorporation of spectral library, a deeper convolutional network has been adopted to achieve better results. Moreover, we construct a new loss function, which includes pixel reconstruction error, abundance sparsity, and abundance cross-entropy to train the aforementioned network in an end-to-end manner. Experiments on both simulated and real HSIs indicate the advantage of the proposed method, which can obviously enhance the abundance estimation accuracy.

Mixed 2D/3D Convolutional Network for Hyperspectral Image Super-Resolution

Deep learning-based hyperspectral image super-resolution (SR) methods have achieved great success recently. However, there are two main problems in the previous works. One is to use the typical three-dimensional convolution analysis, resulting in more parameters of the network. The other is not to pay more attention to the mining of hyperspectral image spatial information, when the spectral information can be extracted. To address these issues, in this paper, we propose a mixed convolutional network (MCNet) for hyperspectral image super-resolution. We design a novel mixed convolutional module (MCM) to extract the potential features by 2D/3D convolution instead of one convolution, which enables the network to more mine spatial features of hyperspectral image. To explore the effective features from 2D unit, we design the local feature fusion to adaptively analyze from all the hierarchical features in 2D units. In 3D unit, we employ spatial and spectral separable 3D convolution to extract spatial and spectral information, which reduces unaffordable memory usage and training time. Extensive evaluations and comparisons on three benchmark datasets demonstrate that the proposed approach achieves superior performance in comparison to existing state-of-the-art methods.

Every node counts: Self-ensembling graph convolutional networks for semi-supervised learning

Graph convolutional network (GCN) provides a powerful means for graph-based semi-supervised tasks. However, as a localized first-order approximation of spectral graph convolution, the classic GCN can not take full advantage of unlabeled data, especially when the unlabeled node is far from labeled ones. To capitalize on the information from unlabeled nodes to boost the training for GCN, we propose a novel framework named Self-Ensembling GCN (SEGCN), which marries GCN with Mean Teacher – a powerful self-ensemble learning mechanism for semi-supervised task. SEGCN contains a student model and a teacher model. As a student, it not only learns to correctly classify the labeled nodes, but also tries to be consistent with the teacher on unlabeled nodes in more challenging situations, such as a high dropout rate and graph corrosion. As a teacher, it averages the student model weights and generates more accurate predictions to lead the student. In such a mutual-promoting process, both labeled and unlabeled samples can be fully utilized for backpropagating effective gradients to train GCN. In a variety of semi-supervised classification benchmarks, i.e. Citeseer, Cora, Pubmed and NELL, we validate that the proposed method matches the state of the arts in the classification accuracy. The code is publicly available at https://github.com/RoyalVane/SEGCN.

A Lightweight Spectral–Spatial Feature Extraction and Fusion Network for Hyperspectral Image Classification

Hyperspectral image (HSI) classification accuracy has been greatly improved by employing deep learning. The current research mainly focuses on how to build a deep network to improve the accuracy. However, these networks tend to be more complex and have more parameters, which makes the model difficult to train and easy to overfit. Therefore, we present a lightweight deep convolutional neural network (CNN) model called S2FEF-CNN. In this model, three S2FEF blocks are used for the joint spectral–spatial features extraction. Each S2FEF block uses 1D spectral convolution to extract spectral features and 2D spatial convolution to extract spatial features, respectively, and then fuses spectral and spatial features by multiplication. Instead of using the full connected layer, two pooling layers follow three blocks for dimension reduction, which further reduces the training parameters. We compared our method with some state-of-the-art HSI classification methods based on deep network on three commonly used hyperspectral datasets. The results show that our network can achieve a comparable classification accuracy with significantly reduced parameters compared to the above deep networks, which reflects its potential advantages in HSI classification.

On the spectral line width broadening for simulation of the two-photon absorption cross-section of para-Nitroaniline in liquid environment

The calculated two-photon absorption (TPA) cross-section amplitude depends on the spectral line width (Γ) of the transition and there is not a consensus on the most appropriate way to obtain the Γ value. Usually it is arbitrarily defined or ambiguously estimated based on experimental data or using a transition energy variation determined from a quantum mechanics/molecular mechanics approach. In this study we compare different procedures to estimate Γ values and different methods of spectral convolution to simulate TPA cross-section for para-Nitroaniline (pNA) in liquid environment. The effects of the liquid environment on the nonlinear absorption were approximated using Monte Carlo and Born-Oppenheimer Molecular Dynamics as well as the commonly used Polarizable Continuum Model. The different procedures adopted here provided large difference in the calculated TPA amplitudes, mainly because of the underestimate/overestimate of the homogeneous and/or inhomogeneous contributions to the spectral line width. Based on these difficulties, we suggest a new procedure in which the value assigned to Γ is the one used to induce the total line width of the simulated TPA spectrum to reproduce the experimental one-photon absorption line width. Within this procedure the Γ value, which becomes a fitting parameter (Γfit), represents part of the homogeneous contribution to the spectral line width. Finally, although time dependent density functional theory calculations reproduced only reasonably well the energy of the lowest-energy π → π* transition of pNA, the fitting procedure here proposed provided the calculated TPA cross-section in good agreement with the available experimental data.

Graph Attention Networks With Local Structure Awareness for Knowledge Graph Completion

Graph neural networks have been proven to be very effective for representation learning of knowledge graphs. Recent methods such as SACN and CompGCN, have achieved the most advanced results in knowledge graph completion. However, previous efforts mostly rely on localized first-order approximations of spectral graph convolutions or first-order neighborhoods, ignoring the abundant local structures like cycles and stars. Therefore, the diverse semantic information beneath these structures is not well-captured, leaving opportunities for better knowledge representation which will finally help KGC. In this work, we propose LSA-GAT, a graph attention network with a novel neighborhood aggregation strategy for knowledge graph completion. The model can take special local structures into account, and derive a sophisticated representation covering both the semantic and structural information. Moreover, the LSA-GAT model is combined with a CNN-based decoder to form an encoder-decoder framework with a carefully designed training process. The experimental results show significant improvement of the proposed LSA-GAT compared to current state-of-the-art methods on FB15k-237 and WN18RR datasets.

Semi-Supervised Gated Spectral Convolution on a Directed Signed Network

A complex network is a powerful tool that enables a complex system in the real world to be represented as a network structure. Due to the heterogeneous edges and nodes implying rich semantic information, network representation has received considerable attention in both research and industrial domain. Over the recent years, the graph convolutional network (GCN) has provided a novel approach for learning network embeddings. However, this primarily supports undirected unsigned networks; that is, it cannot be directly applied to directed signed networks because it is challenging to effectively depict the direction and signs of edges in such models. In this paper, we therefore propose a method for semi-supervised gated spectral convolution in directed signed networks. We first extend the concept of the GCN to directed signed networks, which not only preserves the advantages of the traditional GCN but also properly describes the significance of the directions and signs of the edges. We then innovatively define sign (label) propagation rules in directed signed networks, rendering the networks semi-supervised. Furthermore, we enhance the balance theory to constrain the process of sign propagation to obtain network embedding with better interpretability. To satisfy the needs of large-scale complex networks, we propose a gating mechanism to adaptively forget sign information, which significantly reduces the time-space complexity of the sign propagation process. Finally, we compare the proposed method with state-of-the-art baselines using four real-world data sets for the classical link sign prediction task. Experimental results demonstrate that the proposed method is competitive.

Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecasting

Traffic forecasting is a particularly challenging application of spatiotemporal forecasting, due to the time-varying traffic patterns and the complicated spatial dependencies on road networks. To address this challenge, we learn the traffic network as a graph and propose a novel deep learning framework, Traffic Graph Convolutional Long Short-Term Memory Neural Network (TGC-LSTM), to learn the interactions between roadways in the traffic network and forecast the network-wide traffic state. We define the traffic graph convolution based on the physical network topology. The relationship between the proposed traffic graph convolution and the spectral graph convolution is also discussed. An L1-norm on graph convolution weights and an L2-norm on graph convolution features are added to the model’s loss function to enhance the interpretability of the proposed model. Experimental results show that the proposed model outperforms baseline methods on two real-world traffic state datasets. The visualization of the graph convolution weights indicates that the proposed framework can recognize the most influential road segments in real-world traffic networks.

Sound generation by a pair of co-rotating vortices using spectral acoustic analogy

The spectral acoustic analogy (AA) theory is used to study the acoustic generation by a pair of co-rotating vortices from the decomposition of wave packets. The use of a two-dimensional spectral AA formulation is based on the data obtained by conducting a direct simulation of unsteady compressible Navier-Stokes equations. By way of the spectral AA theory and convolution filtering operations, the role played by the wave packets of the vortices in the generation of the sound is thoroughly discussed. It is found that the far-field sound is generated by the linear superimposition of the interactions between the base flow and the remaining wave packets. Moreover, a notable wave packet of the co-rotating vortices, called the acoustic-related wave packet herein, is identified in the spectral domain, which not only contains all radiating components but also contributes to a discernible acoustic source. It potentially bridges the gap between the near-field wave packets and the far-field sound. The present methodology based on the spectral AA theory shows promise in providing insights into the mechanisms of sound generation in turbulent or unsteady vortical flows.

Two‐order graph convolutional networks for semi‐supervised classification

Currently, deep learning (DL) algorithms have achieved great success in many applications including computer vision and natural language processing. Many different kinds of DL models have been reported, such as DeepWalk, LINE, diffusionconvolutional neural networks, graph convolutional networks (GCN), and so on. The GCN algorithm is a variant of convolutional neural network and achieves significant superiority by using a one-order localised spectral graph filter. However, only a one-order polynomial in the Laplacian of GCN has been approximated and implemented, which ignores undirect neighbour structure information. The lack of rich structure information reduces the performance of the neural networks in the graph structure data. In this study, the authors deduce and simplify the formula of two-order spectral graph convolutions to preserve rich local information. Furthermore, they build a layerwise GCN based on this two-order approximation, i.e. two-order GCN (TGCN) for semi-supervised classification. With the two-order polynomial in the Laplacian, the proposed TGCN model can assimilate abundant localised structure information of graph data and then boosts the classification significantly. To evaluate the proposed solution, extensive experiments are conducted on several popular datasets including the Citeseer, Cora, and PubMed dataset. Experimental results demonstrate that the proposed TGCN outperforms the state-of-art methods.

HesGCN: Hessian graph convolutional networks for semi-supervised classification

Manifold or local geometry of samples have been recognized as a powerful tool in machine learning areas, especially in the graph-based semi-supervised learning (GSSL) problems. Over recent decades, plenty of manifold assumption-based SSL algorithms (MSSL) have been proposed including graph embedding and graph regularization models, where the objective is to utilize the local geometry of data distributions. One of most representative MSSL approaches is graph convolutional networks (GCN), which effectively generalizes the convolutional neural networks to deal with the graphs with the arbitrary structures by constructing and fusing the Laplacian-based structure information. However, the null space of the Laplacian remains unchanged along the underlying manifold, it causes the poor extrapolating ability of the model. In this paper, we introduce a variant of GCN, i.e. Hessian graph convolutional networks (HesGCN). In particularly, we get a more efficient convolution layer rule by optimizing the one-order spectral graph Hessian convolutions. In addition, the spectral graph Hessian convolutions is a combination of the Hessian matrix and the spectral graph convolutions. Hessian gets a richer null space by the existence of its two-order derivatives, which can describe the intrinsic local geometry structure of data accurately. Thus, HesGCN can learn more efficient data features by fusing the original feature information with its structure information based on Hessian. We conduct abundant experiments on four public datasets. Extensive experiment results validate the superiority of our proposed HesGCN compared with many state-of-the-art methods.

HpLapGCN: Hypergraph p-Laplacian graph convolutional networks

Currently, the representation learning of a graph has been proved to be a significant technique to extract graph structured data features. In recent years, many graph representation learning (GRL) algorithms, such as Laplacian Eigenmaps (LE), Node2vec and graph convolutional networks (GCN), have been reported and have achieved great success on node classification tasks. The most representative GCN fuses the feature information and structure information of data, which aims to generalize convolutional neural networks (CNN) to learn data features with arbitrary structure. However, how to exactly express the structure information of data is still an enormous challenge. In this paper, we utilize hypergraph p-Laplacian to preserve the local geometry of samples and then propose an effective variant of GCN, i.e. hypergraph p-Laplacian graph convolutional networks (HpLapGCN). Since hypergraph p-Laplacian is a generalization of the graph Laplacian, HpLapGCN model shows great potential to learn more representative data features. In particular, we simplify and deduce a one-order approximation of spectral hypergraph p-Laplacian convolutions. Thus, we can get a more efficient layer-wise aggregate rule. Extensive experiment results on the Citeseer and Cora datasets prove that our proposed model achieves better performance compare with GCN and p-Laplacian GCN (pLapGCN).

Perrogator: A Portable Energy-Efficient Interrogator for Dynamic Monitoring of Wavelength-Based Sensors in Wearable Applications.

In this paper, we report the development of a portable energy-efficient interrogator (Perrogator) for wavelength-based optical sensors. The interrogator is based on a compact solution encompassing a white light source and the spectral convolution between the sensor and a tunable filter, which is acquired by a photodetector, where a microcontroller has two functions: (i) To control the filter tuning and to (ii) acquire the photodetector signal. Then, the data is sent to a single-board computer for further signal processing. Furthermore, the employed single-board computer has a Wi-Fi module, which can be used to send the sensors data to the cloud. The proposed approach resulted in an interrogator with a resolution as high as 3.82 pm (for 15.64 nm sweeping range) and maximum acquisition frequency of about 210 Hz (with lower resolution ~15.30 pm). Perrogator was compared with a commercial fiber Bragg grating (FBG) interrogator for strain measurements and good agreement between both devices was found (1.226 pm/µε for the commercial interrogator and 1.201 pm/µε for the proposed approach with root mean square error of 0.0144 and 0.0153, respectively), where the Perrogator has the additional advantages of lower cost, higher portability and lower energy consumption. In order to demonstrate such advantages in conjunction with the high acquisition frequency allowed us to demonstrate two wearable applications using the proposed interrogation device over FBG and Fabry-Perot interferometer (FPI) sensors. In the first application, an FBG-embedded smart textile for knee angle assessment was used to analyze the gait of a healthy person. Due to the capability of reconstructing the FBG spectra, it was possible to employ a technique based on the FBG wavelength shift and reflectivity to decouple the effects of the bending angle and axial strain on the FBG response. The measurement of the knee angle as well as the estimation of the angular and axial displacements on the grating that can be correlated to the variations of the knee center of rotation were performed. In the second application, a FPI was embedded in a chest band for simultaneous measurement of breath and heart rates, where good agreement (error below 5%) was found with the reference sensors in all analyzed cases.