Complex-valued Neural Networks Research Articles

Global Receptive Field Designed Complex-Valued Convolutional Neural Network Equalizer for Optical Fiber Communications

In this paper, an improved complex-valued convolutional neural network (CvCNN) structure to be placed at the received side is proposed for nonlinearity compensation in a coherent optical system. This complex-valued global convolutional kernel-assisted convolutional neural network equalizer (CvGNN) has been verified in terms of Q-factor performance and complexity compared to seven other related nonlinear equalizers based on both the 64 QAM experimental platform and the QPSK numerical platform. The global convolution operation of the proposed CvGNN is more suitable for the calculation process of perturbation coefficients, and the global receptive field can also be more effective at extracting effective information from perturbation feature maps. The introduction of CvCNN can directly focus on the complex-valued perturbation feature maps themselves without separately processing the real and imaginary parts, which is more in line with the waveform-dependent physical characteristics of optical signals. Based on the experimental platform, compared with the real-valued neural network with small convolutional kernel (RvCNNC), the proposed CvGNNC improves the Q-factor by ∼2.95 dB at the optimal transmission power, while reducing the time complexity by ∼44.7%.

Frequency and phase correction of GABA-edited magnetic resonance spectroscopy using complex-valued convolutional neural networks

PurposeTo determine the significance of complex-valued inputs and complex-valued convolutions compared to real-valued inputs and real-valued convolutions in convolutional neural networks (CNNs) for frequency and phase correction (FPC) of GABA-edited magnetic resonance spectroscopy (MRS) data. MethodsAn ablation study using simulated data was performed to determine the most effective input (real or complex) and convolution type (real or complex) to predict frequency and phase shifts in GABA-edited MEGA-PRESS data using CNNs. The best CNN model was subsequently compared using both simulated and in vivo data to two recently proposed deep learning (DL) methods for FPC of GABA-edited MRS. All methods were trained using the same experimental setup and evaluated using the signal-to-noise ratio (SNR) and linewidth of the GABA peak, choline artifact, and by visually assessing the reconstructed final difference spectrum. Statistical significance and effect size were assessed using the Wilcoxon signed rank test. ResultsThe ablation study showed that using complex values for the input represented by real and imaginary channels in our model input tensor, with complex convolutions was most effective for FPC. Overall, in the comparative study using simulated data, our CC-CNN model (that received complex-valued inputs with complex convolutions) outperformed the other models as evaluated by the mean absolute error. ConclusionOur results indicate that the optimal CNN configuration for GABA-edited MRS FPC uses a complex-valued input and complex convolutions. Overall, this model outperformed existing DL models.

DeepOTF: Learning Equations-constrained Prediction for Electromagnetic Behavior

High-quality passive devices are becoming increasingly important for the development of mobile devices and telecommunications, but obtaining such devices through simulation and analysis of electromagnetic (EM) behavior is time-consuming. To address this challenge, artificial neural network (ANN) models have emerged as an effective tool for modeling EM behavior, with NeuroTF being a representative example. However, these models are limited by the specific form of the transfer function, leading to discontinuity issues and high sensitivities. Moreover, previous methods have overlooked the physical relationship between distributed parameters, resulting in unacceptable numeric errors in the conversion results. To overcome these limitations, we propose two different neural network architectures: DeepOTF and ComplexTF. DeepOTF is a data-driven deep operator network for automatically learning feasible transfer functions for different geometric parameters. ComplexTF utilizes complex-valued neural networks to fit feasible transfer functions for different geometric parameters in the complex domain while maintaining causality and passivity. Our approach also employs an Equations-constraint Learning scheme to ensure the strict consistency of predictions and a dynamic weighting strategy to balance optimization objectives. The experimental results demonstrate that our framework shows superior performance than baseline methods, achieving up to 1700 × higher accuracy.

Almost Sure Stability of Complex-Valued Complex Networks: A Noise-Based Delayed Coupling Under Random Denial-of-Service Attacks.

This article is concerned with stability for stochastic complex-valued delayed complex networks under random denial-of-service (RDoS) attacks. Different from the existing literature on the stability of stochastic complex-valued systems that concentrate on moment stability, we investigate almost sure stability (ASS), where noise plays a stabilizing role. It is noted that, besides the vertex systems influenced by noise, the interactions among vertices are also at the mercy of noise. As a consequence, an innovative noise-based delayed coupling (NDC) in the presence of RDoS attacks is proposed first to accomplish the stability of complex-valued networks, where the RDoS attacks have a certain probability of triumphantly interfering with communications at active intervals of attackers. Namely, RDoS attacks considered are randomly launched at active periods, which is more realistic. In terms of the Lyapunov method and stochastic analysis theory, an almost sure exponential stability (ASES) criterion of the system discussed straightforwardly is developed by constructing a delay-free auxiliary system, while removing the traditional assumption of moment stability. The criterion strongly linked with topological structure, RDoS frequency, attack successful probability, and noise intensity reveals that the higher the noise intensity, the faster the convergence rate is for the stability of the network. In light of the criterion established, we present an algorithm that can be employed to analyze the tolerable attack parameters and the upper bound of the coupling delays, under the prerequisite of guaranteeing the stability of the network. Eventually, the theoretical results are applied to inertial complex-valued neural networks (ICNNs) and an illustrative example is presented to substantiate the efficiency of the theoretical works.

IMAGE CLASSIFICATION OF VINE LEAF DISEASES USING COMPLEX-VALUED NEURAL NETWORK

Leaf diseases are a serious challenge in the agricultural industry affecting crop quality and yield especially in grapevines. Early recognition and classification of grape leaf diseases is crucial to enable farmers to take appropriate preventive measures in maintaining the health of their crops. The research utilized an innovative approach based on Complex-Valued Neural Network (CVNN) to address the problem. Using Complex-Valued Neural Network (CVNN) this research seeks to identify and classify grape leaf diseases through a series of experiments. A total of 100 images divided into 4 classes namely Black Rot, ESCA, Leaf Blight, and Healthy were collected to train the model. The results show that the trained CVNN model successfully achieved a training accuracy of 100% and a testing accuracy of 97%, demonstrating excellent performance in classifying grape leaf diseases. This states that the proposed approach has great potential to be an effective tool in helping growers manage their vineyards more efficiently and effectively. The developed image processing method is expected to be applied in designing a system to perform image classification of diseases on grape leaves.

Quasi-Projective Synchronization of Discrete-Time Fractional-Order Complex-Valued BAM Fuzzy Neural Networks via Quantized Control

In this paper, we ponder a kind of discrete-time fractional-order complex-valued fuzzy BAM neural network. Firstly, in order to guarantee the quasi-projective synchronization of the considered networks, an original quantitative control strategy is designed. Next, by virtue of the relevant definitions and properties of the Mittag-Leffler function, we propose a novel discrete-time fractional-order Halanay inequality, which is more efficient for disposing of the discrete-time fractional-order models with time delays. Then, based on the new lemma, fractional-order h-difference theory, and comparison principle, we obtain some easy-to-verify synchronization criteria in terms of algebraic inequalities. Finally, numerical simulations are provided to check the accuracy of the proposed theoretical results.

Research on Communication Signal Modulation Recognition Based on a CCLDNN

In this paper, a new automatic modulation recognition (AMR) method named CCLDNN (complex-valued convolution long short-term memory deep neural network) is proposed. It is designed to significantly improve the recognition accuracy of modulation modes in low signal-to-noise ratio (SNR) environments. The model integrates the advantages of existing mainstream neural networks. The phase and amplitude information of complex signals is effectively captured through a complex module in the input layer. The Squeeze-and-Excitation (SE) attention mechanism, Bi-LSTM layer, and deep convolutional layer are introduced in the feature extraction layer to gradually enhance feature expression. Among these, the introduction of LSTM enables the model to capture the sequence dependence of signals, and the application of the SE attention mechanism further improves the model’s ability to focus on key features. Tests using the RadioML2016.10a dataset show that the model performs well at multiple SNR levels, achieving an average recognition accuracy of more than 80% over an SNR range of 0 dB to 18 dB. However, under the condition of a low SNR from −20 dB to −2 dB, the model still maintains a high recognition ability. The advanced CCLDNN method shows great deep learning potential in solving practical communication problems.

Noise equalization scheme based on probabilistic shaping and complex-valued ANN for dual-polarization continuous spectrum NFDM system with high-order modulation formats

In dual-polarization continuous spectrum nonlinear frequency division multiplexing (DP-CS NFDM) systems, the presence of noise destroys the independence between subcarriers in the nonlinear spectral domain (NSD). Additionally, as the modulation order and the number of subcarriers increase, the signal power increases and the effect of noise on the performance of the system becomes more severe. In this paper, we propose a noise equalization scheme based on probabilistic shaping (PS) and complex-valued neural network (c-ANN) for dual-polarization transmission CS NFDM system with high-power signals. The scheme utilizes PS to reduce the distribution probability of high-power constellation points of the signal with high-order modulation format, to decrease the peak-to-average power ratio of the continuous spectrum subcarriers and the average power of the signal, which can achieve the suppression and equalization of the amplifier spontaneous emission (ASE) noise and the processing noise. In addition, the scheme uses the c-ANN to effectively reduce the correlation between subcarriers caused by the noise and improve the system performance. The effectiveness of the proposed scheme is verified in the DP-CS NFDM system, and the simulation results show that the Q-factor gain is enhanced by roughly 1.1 dB and 0.8 dB for the number of subcarriers of 128 and 256, respectively, compared to the classic nonlinear Fourier transform (NFT) scheme. Among them, with different noise figure (NF) and satisfying the 7% forward error correction (FEC) threshold, the 512QAM signal with an entropy of 8 after equalization increase the transmission distance by 80 km longer than that of uniform 256QAM signals for the number of subcarriers of 128. Compared with the joint scheme based on PS and real-valued neural network (r-ANN), this scheme has better equalization performance at the same complexity, and the complexity can be reduced by 50% under the same performance.

A hybrid complex spectral conjugate gradient learning algorithm for complex-valued data processing

Complex-valued neural networks (CVNNs) have become a powerful modelling tool for complex-valued data processing. Because most of the critical points of CVNNs are saddle points, the gradient-based learning algorithms for CVNNs enjoy more chances to reach the global minima while suffering from slow convergence. To this end, we propose a hybrid complex spectral conjugate gradient learning algorithm for fast training CVNNs in this paper. The proposed algorithm combines the scaled negative gradient with a Barzilai–Borwein stepsize and an optimized conjugate term to define a new training direction, thus providing an accurate approximation of the second-order curvature of the objective function. The complex Wolfe conditions are employed to adaptively determine the optimal training stepsize. Under mild conditions, the descent property of the training direction and the convergence of the proposed algorithm are theoretically established. Simulation results on a number of benchmark complex-valued data processing problems demonstrate the efficiency of the proposed algorithm.

Intelligent Analysis of E-commerce Reviews based on Complex-Valued Spatio-temporal Graph Convolutional Neural Network Optimized Tyrannosaurus Optimization Algorithm

Intelligent analysis of E-commerce reviews based on multimodal social media big data using applies the benefit of innovative artificial intelligence method, especially deep learning algorithms, to study and realize web-based product consider and social network data connected to e-commerce. In this manuscript, Intelligent Analysis of E-commerce reviews based on Complex-Valued Spatio-temporal Graph Convolutional Neural Network Optimized Tyrannosaurus Optimization Algorithm (IAER-CVSGCNN-TOA)is proposed for Intelligent Analysis of E-commerce Reviews. The input data are collected from E-commerce big Dataset. Then data are pre-processing utilizing federated neural collaborative filtering (FNCF) to remove the noise and clean the data. The pre-processed data is provided to the CVSGCNN is used for intelligent analysis of e-commerce reviews. In general, CVSGCNN does no express adapting optimization approaches to determine optimal parameters to ensure accurate prediction. Hence, proposed to utilize the Tyrannosaurus Optimization Algorithm enhancement CVSGCNN for intelligent analysis of e-commerce reviews. The proposed IAER-CVSGCNN-TOA method is implemented on python. Then performance of proposed technique is analyzed with other existing techniques. The proposed technique attains 30.26%, 28.70% and 46.25% higher accuracy, 20.53%, 32.60%, and 53.43% higher precision, 25.23%, 23.15%, and 22.33%higher recall, 25.75%, 44.30% and 53.70%higher specificity comparing with the existing methods such as a Retracted: Online Troll Reviewer Detection Utilizing Deep Learning Methods (IAER-CNN), Developing an Intelligent System and DL Algorithms for Sentiment Analysis of E-Commerce Product Reviews(IAER-LSTM), Intelligent Perception System of Big Data Decision in Cross-Border e-Commerce Depend on Data Fusion(IAER-DFN) respectively.

Fixed-time synchronization of complex-valued neural networks for image protection and 3D point cloud information protection

This paper studies the fixed-time synchronization (FDTS) of complex-valued neural networks (CVNNs) based on quantized intermittent control (QIC) and applies it to image protection and 3D point cloud information protection. A new controller was designed which achieved FDTS of the CVNNs, with the estimation of the convergence time not dependent on the initial state. Our approach divides the neural network into two real-valued systems and then combines the framework of the Lyapunov method to give criteria for FDTS. Applying synchronization to image protection, the image will be encrypted with a drive system sequence and decrypted with a response system sequence. The quality of image encryption and decryption depends on the synchronization error. Meanwhile, the depth image of the object is encrypted and then the 3D point cloud is reconstructed based on the decrypted depth image. This means that the 3D point cloud information is protected. Finally, simulation examples verify the efficacy of the controller and the synchronization criterion, giving results for applications in image protection and 3D point cloud information protection.

Synthesis of soundfields through irregular loudspeaker arrays based on convolutional neural networks

Most soundfield synthesis approaches deal with extensive and regular loudspeaker arrays, which are often not suitable for home audio systems, due to physical space constraints. In this article, we propose a technique for soundfield synthesis through more easily deployable irregular loudspeaker arrays, i.e., where the spacing between loudspeakers is not constant, based on deep learning. The input are the driving signals obtained through a plane wave decomposition-based technique. While the considered driving signals are able to correctly reproduce the soundfield with a regular array, they show degraded performances when using irregular setups. Through a complex-valued convolutional neural network (CNN), we modify the driving signals in order to compensate the errors in the reproduction of the desired soundfield. Since no ground truth driving signals are available for the compensated ones, we train the model by calculating the loss between the desired soundfield at a number of control points and the one obtained through the driving signals estimated by the network. The proposed model must be retrained for each irregular loudspeaker array configuration. Numerical results show better reproduction accuracy with respect to the plane wave decomposition-based technique, pressure-matching approach, and linear optimizers for driving signal compensation.

An Effective Strategy for Sentiment Analysis Based on Complex-Valued Embedding and Quantum Long Short-Term Memory Neural Network

Sentiment analysis aims to study, analyse and identify the sentiment polarity contained in subjective documents. In the realm of natural language processing (NLP), the study of sentiment analysis and its subtask research is a hot topic, which has very important significance. The existing sentiment analysis methods based on sentiment lexicon and machine learning take into account contextual semantic information, but these methods still lack the ability to utilize context information, so they cannot effectively encode context information. Inspired by the concept of density matrix in quantum mechanics, we propose a sentiment analysis method, named Complex-valued Quantum-enhanced Long Short-term Memory Neural Network (CQLSTM). It leverages complex-valued embedding to incorporate more semantic information and utilizes the Complex-valued Quantum-enhanced Long Short-term Memory Neural Network for feature extraction. Specifically, a complex-valued neural network based on density matrix is used to capture interactions between words (i.e., the correlation between words). Additionally, the Complex-valued Quantum-enhanced Long Short-term Memory Neural Network, which is inspired by the quantum measurement theory and quantum long short-term memory neural network, is developed to learn interactions between sentences (i.e., contextual semantic information). This approach effectively encodes semantic dependencies, which reflects the dispersion of words in the embedded space of sentences and comprehensively captures interactive information and long-term dependencies among the emotional features between words. Comparative experiments were performed on four sentiment analysis datasets using five traditional models, showcasing the effectiveness of the CQLSTM model.

PolSAR Image Classification with Active Complex-Valued Convolutional-Wavelet Neural Network and Markov Random Fields

PolSAR image classification has attracted extensive significant research in recent decades. Aiming at improving PolSAR classification performance with speckle noise, this paper proposes an active complex-valued convolutional-wavelet neural network by incorporating dual-tree complex wavelet transform (DT-CWT) and Markov random field (MRF). In this approach, DT-CWT is introduced into the complex-valued convolutional neural network to suppress the speckle noise of PolSAR images and maintain the structures of learned feature maps. In addition, by applying active learning (AL), we iteratively select the most informative unlabeled training samples of PolSAR datasets. Moreover, MRF is utilized to obtain spatial local correlation information, which has been proven to be effective in improving classification performance. The experimental results on three benchmark PolSAR datasets demonstrate that the proposed method can achieve a significant classification performance gain in terms of its effectiveness and robustness beyond some state-of-the-art deep learning methods.

Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.

Space-time domain equalization algorithm based on complex-valued neural network in a long-haul photonic-aided MIMO THz system.

The urgent demand for high-bandwidth wireless services in enhanced mobile broadband networks needs innovative solutions for mobile front-haul systems. The terahertz (THz) band offers a promising candidate for ultrahigh-capacity data transmission. This study investigates the integration of photonics-aided THz signal generation with MIMO and PDM technologies. We proposed a novel, to the best of our knowledge, space-time domain equalization algorithm based on MIMO-complex-valued neural networks (CVNN), which can preserve the signal phase and the relation between the X- and Y-polarization. We experimentally demonstrate the transmission of 60-GBaud PDM-QPSK and 30-GBaud PDM-16QAM signals over a 100-m 2 × 2 wireless MIMO link at 320 GHz with BER below 3.8 × 10-3 and 1.56 × 10-2 for QPSK and 16QAM signals, respectively. Compared with the MIMO-Volterra, our MIMO-CVNN has an advantage in terms of calculation complexity and decision accuracy due to its effective handling of phase information and inter-polarization relationships simultaneously.

On uniform stability and numerical simulations of complex valued neural networks involving generalized Caputo fractional order

The dynamics and existence results of generalized Caputo fractional derivatives have been studied by several authors. Uniform stability and equilibrium in fractional-order neural networks with generalized Caputo derivatives in real-valued settings, however, have not been extensively studied. In contrast to earlier studies, we first investigate the uniform stability and equilibrium results for complex-valued neural networks within the framework of a generalized Caputo fractional derivative. We investigate the intermittent behavior of complex-valued neural networks in generalized Caputo fractional-order contexts. Numerical results are supplied to demonstrate the viability and accuracy of the presented results. At the end of the article, a few open questions are posed.

Spectral transfer-learning-based metasurface design assisted by complex-valued deep neural network

Spectral transfer-learning-based metasurface design assisted by complex-valued deep neural network

Robust Stability of Semi-Markovian Complex-Valued Neural Networks with Generally Uncertain Transition Rates

Robust Stability of Semi-Markovian Complex-Valued Neural Networks with Generally Uncertain Transition Rates

Multistability analysis of complex-valued recurrent neural networks with sine and cosine activation functions

This paper is devoted to the multistability problem for complex-valued recurrent neural networks (CVRNNs) with a specific class of piecewise nonlinear activation functions. Firstly, a general class of piecewise nonlinear activation functions is presented to facilitate further analysis. Then, by resorting to the fixed point theorem and Lagrange’s mean value theorem, sufficient criteria are established which ascertain that the existence of (2k+1)2n equilibrium points. Meanwhile, it also verifies that (k+1)2n equilibrium points of the considered CVRNNs with a piecewise nonlinear activation function are stable, where k stands for a positive real number, which is associated with the frequency of sine and cosine functions. Moreover, the utilization of the activation functions provides a larger storage capacity in associative memory application. In the end of paper, three numerical examples are presented to demonstrate the feasibility and validity of the achieved theoretical results.