A robust subband adaptive filter algorithm for sparse and block-sparse systems identification

This paper presents a new subband adaptive filter(SAF)algorithm for system identification scenario under impulsive interference,named generalized continuous mixed p-norm SAF(GCMPN-SAF)algorithm.The proposed algorithm uses a GCMPN cost function to combat the impul-sive interference.To further accelerate the convergence rate in the sparse and the block-sparse system identification processes,the proportionate versions of the proposed algorithm,the L0-norm GCMPN-SAF(L0-GCMPN-SAF)and the block-sparse GCMPN-SAF(BSGCMPN-SAF)algorithms are also developed.Moreover,the convergence analysis of the proposed algorithm is provided.Simulation results show that the proposed algorithms have a better performance than some other state-of-the-art algorithms in the literature with respect to the convergence rate and the tracking capability.

Joint Multi-Domain Channel Estimation Based on Sparse Bayesian Learning for OTFS System

Since orthogonal time-frequency space(OTFS)can effectively handle the problems caused by Doppler effect in high-mobility environment,it has gradually become a promising candidate for modulation scheme in the next generation of mobile communication.However,the inter-Doppler interference(IDI)problem caused by fractional Doppler poses great challenges to channel estimation.To avoid this problem,this paper proposes a joint time and delayDoppler(DD)domain based on sparse Bayesian learning(SBL)channel estimation algorithm.Firstly,we derive the original channel response(OCR)from the time domain channel impulse response(CIR),which can reflect the channel variation during one OTFS symbol.Compare with the traditional channel model,the OCR can avoid the IDI problem.After that,the dimension of OCR is reduced by using the basis expansion model(BEM)and the relationship between the time and DD domain channel model,so that we have turned the underdetermined problem into an overdetermined problem.Finally,in terms of sparsity of channel in delay domain,SBL algorithm is used to estimate the basis coefficients in the BEM without any priori information of channel.The simulation results show the effectiveness and superiority of the proposed channel estimation algorithm.

特征增强的Sparse Transformer目标跟踪算法

针对Transformer的自注意力机制计算量大、容易被背景分心,导致有效信息抓取不足,从而降低跟踪性能的问题,提出特征增强的Sparse Transformer目标跟踪算法。基于孪生网络骨干进行特征提取;特征增强模块利用多尺度特征图生成的上下文信息,增强目标局部特征;利用Sparse Transformer的最相关特性生成目标聚焦特征,并嵌入位置编码提升跟踪定位的精度。提出的跟踪模型以端到端的方式进行训练,在OTB100,VOT2018和LaSOT等5个数据集上进行了大量实验,实验结果表明所提算法取得了较好的跟踪性能,实时跟踪速度为34帧/s。

Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

A Two-Layer Encoding Learning Swarm Optimizer Based on Frequent Itemsets for Sparse Large-Scale Multi-Objective Optimization

Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.

THE SPARSE REPRESENTATION RELATED WITH FRACTIONAL HEAT EQUATIONS

This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre(generalized Poisson equation).As a first step,the method expands the initial data function into a sparse series of the fundamental solutions with fast convergence,and,as a second step,makes use of the semigroup or the reproducing kernel property of each of the expanding entries.Experiments show the effectiveness and efficiency of the proposed series solutions.

Sparse Reconstructive Evidential Clustering for Multi-View Data

Although many multi-view clustering(MVC) algorithms with acceptable performances have been presented, to the best of our knowledge, nearly all of them need to be fed with the correct number of clusters. In addition, these existing algorithms create only the hard and fuzzy partitions for multi-view objects,which are often located in highly-overlapping areas of multi-view feature space. The adoption of hard and fuzzy partition ignores the ambiguity and uncertainty in the assignment of objects, likely leading to performance degradation. To address these issues, we propose a novel sparse reconstructive multi-view evidential clustering algorithm(SRMVEC). Based on a sparse reconstructive procedure, SRMVEC learns a shared affinity matrix across views, and maps multi-view objects to a 2-dimensional humanreadable chart by calculating 2 newly defined mathematical metrics for each object. From this chart, users can detect the number of clusters and select several objects existing in the dataset as cluster centers. Then, SRMVEC derives a credal partition under the framework of evidence theory, improving the fault tolerance of clustering. Ablation studies show the benefits of adopting the sparse reconstructive procedure and evidence theory. Besides,SRMVEC delivers effectiveness on benchmark datasets by outperforming some state-of-the-art methods.

A Novel Clutter Suppression Algorithm for Low-Slow-Small Targets Detecting Based on Sparse Adaptive Filtering

Passive detection of low-slow-small(LSS)targets is easily interfered by direct signal and multipath clutter,and the traditional clutter suppression method has the contradiction between step size and convergence rate.In this paper,a frequency domain clutter suppression algorithm based on sparse adaptive filtering is proposed.The pulse compression operation between the error signal and the input reference signal is added to the cost function as a sparsity constraint,and the criterion for filter weight updating is improved to obtain a purer echo signal.At the same time,the step size and penalty factor are brought into the adaptive iteration process,and the input data is used to drive the adaptive changes of parameters such as step size.The proposed algorithm has a small amount of calculation,which improves the robustness to parameters such as step size,reduces the weight error of the filter and has a good clutter suppression performance.

Ship recognition based on HRRP via multi-scale sparse preserving method

In order to extract the richer feature information of ship targets from sea clutter, and address the high dimensional data problem, a method termed as multi-scale fusion kernel sparse preserving projection(MSFKSPP) based on the maximum margin criterion(MMC) is proposed for recognizing the class of ship targets utilizing the high-resolution range profile(HRRP). Multi-scale fusion is introduced to capture the local and detailed information in small-scale features, and the global and contour information in large-scale features, offering help to extract the edge information from sea clutter and further improving the target recognition accuracy. The proposed method can maximally preserve the multi-scale fusion sparse of data and maximize the class separability in the reduced dimensionality by reproducing kernel Hilbert space. Experimental results on the measured radar data show that the proposed method can effectively extract the features of ship target from sea clutter, further reduce the feature dimensionality, and improve target recognition performance.

Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation

This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.

Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

Cambricon-QR:a sparse and bitwise reproducible quantized training accelerator

Quantized training has been proven to be a prominent method to achieve deep neural network training under limited computational resources.It uses low bit-width arithmetics with a proper scaling factor to achieve negligible accuracy loss.Cambricon-Q is the ASIC design proposed to efficiently support quantized training,and achieves significant performance improvement.However,there are still two caveats in the design.First,Cambricon-Q with different hardware specifications may lead to different numerical errors,resulting in non-reproducible behaviors which may become a major concern in critical applications.Second,Cambricon-Q cannot leverage data sparsity,where considerable cycles could still be squeezed out.To address the caveats,the acceleration core of Cambricon-Q is redesigned to support fine-grained irregular data processing.The new design not only enables acceleration on sparse data,but also enables performing local dynamic quantization by contiguous value ranges(which is hardware independent),instead of contiguous addresses(which is dependent on hardware factors).Experimental results show that the accuracy loss of the method still keeps negligible,and the accelerator achieves 1.61×performance improvement over Cambricon-Q,with about 10%energy increase.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.

Compressive Sensing Approach in Multicarrier Sparsely Indexing Modulation Systems

recently the indexed modulation(IM) technique in conjunction with the multi-carrier modulation gains an increasing attention. It conveys additional information on the subcarrier indices by activating specific subcarriers in the frequency domain besides the conventional amplitude-phase modulation of the activated subcarriers. Orthogonal frequency division multiplexing(OFDM) with IM(OFDM-IM) is deeply compared with the classical OFDM. It leads to an attractive trade-off between the spectral efficiency(SE) and the energy efficiency(EE). In this paper, the concept of the combinatorial modulation is introduced from a new point of view. The sparsity mapping is suggested intentionally to enable the compressive sensing(CS) concept in the data recovery process to provide further performance and EE enhancement without SE loss. Generating artificial data sparsity in the frequency domain along with naturally embedded channel sparsity in the time domain allows joint data recovery and channel estimation in a double sparsity framework. Based on simulation results, the performance of the proposed approach agrees with the predicted CS superiority even under low signal-to-noise ratio without channel coding. Moreover, the proposed sparsely indexed modulation system outperforms the conventional OFDM system and the OFDM-IM system in terms of error performance, peak-to-average power ratio(PAPR) and energy efficiency under the same spectral efficiency.

Biorthogonal Wavelet Based Algebraic Multigrid Preconditioners for Large Sparse Linear Systems

In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic multigrid context is based on lowpass filter version of Wavelet Transform. The robustness and efficiency of this new approach is tested by applying it to large sparse, unsymmetric and ill-conditioned matrices from Tim Davis collection of sparse matrices. Proposed preconditioners have potential in reducing cputime, operator complexity and storage space of algebraic multigrid V-cycle and meet the desired accuracy of solution compared with that of orthogonal wavelets.

Application of Atomic Sparse Decomposition to Feature Extraction of the Fault Signal in Small Current Grounding System

Applying the atomic sparse decomposition in the distribution network with harmonics and small current grounding to decompose the transient zero sequence current that appears after the single phase to ground fault occurred. Based on dictionary of Gabor atoms and matching pursuit algorithm, the method extracts the atomic components iteratively from the feature signals and translated them to damped sinusoidal components. Then we can obtain the parametrical and analytical representation of atomic components. The termination condition of decomposing iteration is determined by the threshold of the initial residual energy with the purpose of extract the features more effectively. Accordingly, the proposed method can extract the starting and ending moment of disturbances precisely as well as their magnitudes, frequencies and other features. The numerical examples demonstrate its effectiveness.

Fast Sparse Multipath Channel Estimation with Smooth L0 Algorithm for Broadband Wireless Communication Systems

Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficients are approximately zero or under noise floor. To exploit sparsity of multi-path channels (MPCs), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable;on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems be-cause of computational complexity. In this paper, we introduce a novel channel estimation strategy using smooth L0 (SL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm. We also give various simulations to verify the sensing training signal method.

A Fast Clustering Based Evolutionary Algorithm for Super-Large-Scale Sparse Multi-Objective Optimization

During the last three decades,evolutionary algorithms(EAs)have shown superiority in solving complex optimization problems,especially those with multiple objectives and non-differentiable landscapes.However,due to the stochastic search strategies,the performance of most EAs deteriorates drastically when handling a large number of decision variables.To tackle the curse of dimensionality,this work proposes an efficient EA for solving super-large-scale multi-objective optimization problems with sparse optimal solutions.The proposed algorithm estimates the sparse distribution of optimal solutions by optimizing a binary vector for each solution,and provides a fast clustering method to highly reduce the dimensionality of the search space.More importantly,all the operations related to the decision variables only contain several matrix calculations,which can be directly accelerated by GPUs.While existing EAs are capable of handling fewer than 10000 real variables,the proposed algorithm is verified to be effective in handling 1000000 real variables.Furthermore,since the proposed algorithm handles the large number of variables via accelerated matrix calculations,its runtime can be reduced to less than 10%of the runtime of existing EAs.

Vector Approximate Message Passing with Sparse Bayesian Learning for Gaussian Mixture Prior

Compressed sensing(CS)aims for seeking appropriate algorithms to recover a sparse vector from noisy linear observations.Currently,various Bayesian-based algorithms such as sparse Bayesian learning(SBL)and approximate message passing(AMP)based algorithms have been proposed.For SBL,it has accurate performance with robustness while its computational complexity is high due to matrix inversion.For AMP,its performance is guaranteed by the severe restriction of the measurement matrix,which limits its application in solving CS problem.To overcome the drawbacks of the above algorithms,in this paper,we present a low complexity algorithm for the single linear model that incorporates the vector AMP(VAMP)into the SBL structure with expectation maximization(EM).Specifically,we apply the variance auto-tuning into the VAMP to implement the E step in SBL,which decrease the iterations that require to converge compared with VAMP-EM algorithm when using a Gaussian mixture(GM)prior.Simulation results show that the proposed algorithm has better performance with high robustness under various cases of difficult measurement matrices.