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.

A robust clustering algorithm for underdetermined blind separation of sparse sources

In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for underdetermined blind separation of sparse sources with unknown number of sources in the presence of noise. It uses the robust competitive agglomeration （RCA） algorithm to estimate the source number and the mixing matrix, and the source signals then are recovered by using the interior point linear programming. Simulation results show good performance of the proposed algorithm for underdetermined blind sources separation （UBSS）.

Robust least squares projection twin SVM and its sparse solution

Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.

Metasample-Based Robust Sparse Representation for Tumor Classification

In this paper, based on sparse representation classification and robust thought, we propose a new classifier, named MRSRC (Metasample Based Robust Sparse Representation Classificatier), for DNA microarray data classification. Firstly, we extract Metasample from trainning sample. Secondly, a weighted matrix W is added to solve an l1-regular- ized least square problem. Finally, the testing sample is classified according to the sparsity coefficient vector of it. The experimental results on the DNA microarray data classification prove that the proposed algorithm is efficient.

Adaptive Sparse Group Variable Selection for a Robust Mixture Regression Model Based on Laplace Distribution

The traditional estimation of Gaussian mixture model is sensitive to heavy-tailed errors;thus we propose a robust mixture regression model by assuming that the error terms follow a Laplace distribution in this article. And for the variable selection problem in our new robust mixture regression model, we introduce the adaptive sparse group Lasso penalty to achieve sparsity at both the group-level and within-group-level. As numerical experiments show, compared with other alternative methods, our method has better performances in variable selection and parameter estimation. Finally, we apply our proposed method to analyze NBA salary data during the period from 2018 to 2019.

Parametrically Optimal, Robust and Tree-Search Detection of Sparse Signals

We consider sparse signals embedded in additive white noise. We study parametrically optimal as well as tree-search sub-optimal signal detection policies. As a special case, we consider a constant signal and Gaussian noise, with and without data outliers present. In the presence of outliers, we study outlier resistant robust detection techniques. We compare the studied policies in terms of error performance, complexity and resistance to outliers.

Vehicle Representation and Classification of Surveillance Video Based on Sparse Learning

We cast vehicle recognition as problem of feature representation and classification, and introduce a sparse learning based framework for vehicle recognition and classification in this paper. After objects captured with a GMM background subtraction program, images are labeled with vehicle type for dictionary learning and decompose the images with sparse coding （SC）, a linear SVM trained with the SC feature for vehicle classification. A simple but efficient active learning stategy is adopted by adding the false positive samples into previous training set for dictionary and SVM model retraining. Compared with traditional feature representation and classification realized with SVM, SC method achieves dramatically improvement on classification accuracy and exhibits strong robustness. The work is also validated on real-world surveillance video.

L1/2 -Regularized Quantile Method for Sparse Phase Retrieval

The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L1/2-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.

Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties

This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties.To characterize the random-field uncertainties with a reduced set of random variables,the Karhunen-Lo`eve(K-L)expansion is adopted.The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization.Under dividing the design domain,the volume fraction of each preset gradient layer is extracted.Based on the ordered solid isotropic microstructure with penalization(Ordered-SIMP),a functionally graded multi-material interpolation model is formulated by individually optimizing each preset gradient layer.The periodic constraint setting of the gradient layer is achieved by redistributing the average element compliance in sub-regions.Then,the method of moving asymptotes(MMA)is introduced to iteratively update the design variables.Several numerical examples are presented to verify the validity and applicability of the proposed method.The results demonstrate that the periodic functionally graded multi-material topology can be obtained under different numbers of sub-regions,and robust design structures are more stable than that indicated by the deterministic results.

Sparse rail network robustness analysis:Functional vulnerability levels of accidents resulting from human errors

Transportation network vulnerability analysis has developed increasingly in the last decade with the goal to identify the most critical locations against incidences.In this domain,many of the previous researches have focused on congested urban networks;however,there is still a need to consider regional and interurban sparse rail networks,specifically those networks in developing countries.In such sparse rail networks,there are limited possibilities to redirect trains if a link is disrupted,there might be less possibility of finding redundant alternative routes,and network failures are usually accompanied by a phenomenon called‘unsatisfied demand.’The study reported in this paper stemmed from research aimed to design precautionary actions for a developing country’s sparse railway system.Our study framework deemed to find the most vulnerable part of an inter-urban sparse rail network using a network scan approach,which found the consequences of network disruptions.A number of criteria were defined to determine the total cost including unsatisfied demand and additional transportation costs due to disruptions.The results showed that how well the process of the vulnerability analysis,considering the features of both supply and demand sides,can be a guide for railway authorities in applying system safety measures.

Robustness Assessment of Asynchronous Advantage Actor-Critic Based on Dynamic Skewness and Sparseness Computation: A Parallel Computing View

Reinforcement learning as autonomous learning is greatly driving artificial intelligence(AI)development to practical applications.Having demonstrated the potential to significantly improve synchronously parallel learning,the parallel computing based asynchronous advantage actor-critic(A3C)opens a new door for reinforcement learning.Unfortunately,the acceleration's influence on A3C robustness has been largely overlooked.In this paper,we perform the first robustness assessment of A3C based on parallel computing.By perceiving the policy's action,we construct a global matrix of action probability deviation and define two novel measures of skewness and sparseness to form an integral robustness measure.Based on such static assessment,we then develop a dynamic robustness assessing algorithm through situational whole-space state sampling of changing episodes.Extensive experiments with different combinations of agent number and learning rate are implemented on an A3C-based pathfinding application,demonstrating that our proposed robustness assessment can effectively measure the robustness of A3C,which can achieve an accuracy of 83.3%.

局部鲁棒预处理的DME干扰抑制方法

全球定位系统(Global Positioning System, GPS) L5/北斗B2/Galilea E5是全球卫星导航系统(Global Navigation Satellite System, GNSS)的重要组成部分,为民用航空提供与生命安全相关的应用服务.然而L5/B2/E5信号处于受保护的航空无线电导航服务(Aeronautical Radio Navigation Service, ARNS)频段内(962~1213 MHz),同时工作在该频段内的还有民用航空导航系统测距机(Distance Measuring Equipment, DME)等. DME发射的大功率脉冲信号会对L5/B2/E5等卫星导航信号造成干扰,使得接收机无法正常捕获卫星信号或导致跟踪环路失锁.传统的DME干扰抑制方法通过在干扰稀疏域,如时域、频域和时频混合域进行DME干扰置零,这会在抑制干扰的同时完全消除与干扰重叠的卫星信号.为了降低DME干扰抑制对卫星信号的损失,本文提出基于鲁棒统计理论的局部鲁棒预处理的DME干扰抑制方法,根据DME干扰所在的稀疏域特性提取出存在干扰的信号片段后,应用非高斯分布下的鲁棒统计理论对提取出的数据样本进行鲁棒预处理,从而在抑制干扰的同时降低对卫星信号的影响.实验结果表明本文所提出的稀疏域局部鲁棒预处理的DME干扰抑制方法的性能优于相应的传统稀疏域方法,输出捕获因子比传统稀疏域方法提高1~2 dB.

阵元位置互质的线性阵列:阵列校正和波束形成

该文研究了阵元位置互质的线性阵列(CLA)的阵列校正和波束形成问题。在假设CLA天线单元部分校准的条件下,基于同时干扰定位与阵列校正(SILAC)技术,设计了一种适用于CLA的阵列校正和波束形成方法:CLA-SILAC-INCM算法。从理论上分析证明了,当CLA中包含有L_c≥3个完全校准的天线单元,使用SILAC技术可以高精度无模糊地实现干扰源角度和阵列天线幅相误差估计,并在此基础上完成干扰噪声协方差矩阵(INCM)重建和波束形成最优权向量构造。通过仿真实验验证了,提出的CLA-SILAC-INCM算法具有比其他常用算法更好的性能,尤其是信噪比接近干噪比时,CLA-SILAC-INCM算法的优势更为明显。

基于稳健估计的稀疏网格积分滤波算法及其在捷联惯导系统对准中的应用

为有效解决捷联惯性导航系统对准过程中异常量测对状态估计精度的影响,该文提出一种基于稳健估计的稀疏网格积分滤波算法(RESGQF)。该文给出了精度为3级的稀疏网格采样点规则,引入稳健估计算法,构建针对对准系统各状态分量偏差的权重函数。基于稀疏网格积分滤波(SGQF)算法框架,利用权重矩阵实时对量测噪声进行更新,从而降低异常量测对系统状态的影响。通过模拟飞行器动机座空中对准过程,对比在复杂噪声环境下不同滤波方法的性能,证明所提算法提升了系统鲁棒性。

基于混合稀疏ICCP的联合抗差重力匹配定位方法

针对经典最近等值线迭代(ICCP)算法因重力异常测量误差导致匹配精度下降甚至失效的问题,提出联合抗差匹配算法以提高匹配精度及可靠性。首先,分析了匹配点集间的匹配残差在高斯噪声影响下呈非高斯分布,为抑制其影响,采用l_(p)范数代替l_(2)范数计算匹配残差,并利用匹配残差重调野值点以获得有效的匹配区域。在此基础上,提出混合稀疏ICCP算法,并利用其进行粗匹配,然后将粗匹配后的位置作为惯导系统(INS)指示位置,再使用经典ICCP算法进行精匹配,获得更高的定位精度。仿真结果表明,考虑重力异常测量误差的情况下,重力联合抗差匹配算法的误差最大值小于1 n mile,导航精度较传统ICCP算法提升60%以上,提升了算法的鲁棒性和匹配精度。

基于深度展开ADMM网络的稳健自适应波束形成

阵列通道间的幅相误差导致导向矢量失配,会严重退化自适应波束形成的性能。现有稳健自适应波束形成(RAB)方法通过引入最差导向矢量失配误差约束或联合估计幅相误差和波束形成器权值矢量,以改善波束形成性能,但这些方法的计算复杂度高,且在有限快拍下性能有限。为此,文中在深度展开框架下提出一种基于交替方向乘子法(ADMM)的RAB网络,以快速实现幅相误差和干扰协方差矩阵的联合估计。首先,建立存在阵列通道幅相误差时的干扰信号稀疏表示模型;然后,根据基于ADMM的幅相误差和干扰稀疏表示系数联合估计算法,设计一种深度展开ADMM(DU-ADMM)网络,该网络的输入为接收到达的干扰信号,输出为幅相误差和干扰稀疏表示系数;最后,利用该网络的输出重构出干扰加噪声协方差矩阵,并生成稳健自适应波束形成器。仿真结果表明,DU-ADMM网络可在单快拍场景下实现RAB,且能够以较少的网络层数更精确地估计出幅相误差,有效降低了计算量,同时可获得更高的输出信干噪比。

Block Principle Component Analysis with Lp-norm for Robust and Sparse Modelling

Block principle and pattern classification component analysis （BPCA） is a recently developed technique in computer vision In this paper, we propose a robust and sparse BPCA with Lp-norm, referred to as BPCALp-S, which inherits the robustness of BPCA-L1 due to the employment of adjustable Lp-norm. In order to perform a sparse modelling, the elastic net is integrated into the objective function. An iterative algorithm which extracts feature vectors one by one greedily is elaborately designed. The monotonicity of the proposed iterative procedure is theoretically guaranteed. Experiments of image classification and reconstruction on several benchmark sets show the effectiveness of the proposed approach.

基于稀疏差分调制的包装水印算法

在传统的包装印刷领域,印刷条码由于其易损坏、防伪能力弱、占用空间大以及解码时间长等缺点,影响了生产效率。针对这些问题,提出了一种基于稀疏差分调制(Sparse Differential Modulation,SDM)的高效包装水印算法。该技术采用人眼难以察觉但可以通过相机提取的水印嵌入到包装印刷图像中,具有抗破坏性、不易伪造和易于识别等特点。首先,对商品信息、生产日期、防伪标签等数字信息进行编码,生成水印块。通过在与设备无关的CIE Lab色彩空间中微调相应的像素来嵌入水印信息,从而实现了高度的不可感知性和安全性,同时采用了稀疏差分调制在嵌入阶段调制图像的单个通道,这在提取水印时有助于实现图像的精准配准和定位。实验结果表明该算法不仅适用于包装印刷图像的信息存储,也适用于版权保护等领域。

基于原子范数最小化的稀疏阵列稳健波束形成算法

为提高稀疏阵列在信号模型存在失配时的波束形成性能,提出一种基于原子范数最小化(Atomic Norm Minimization,ANM)的稳健波束形成算法。构建基于ANM的降噪问题模型,根据稀疏阵列的协方差矩阵结构将其转化为等价的半定规划问题,同时推导该问题的对偶问题以提高运行效率,求解得到阵列降噪后的接收数据和协方差矩阵。根据互质阵列的结构特性证明其空间谱的无模糊性,对所得的协方差矩阵直接使用多重信号分类算法获得入射信号的波达方向。利用虚拟填充技术得到与互质阵列孔径相同的均匀线性阵列的接收数据,最终获得阵列输出。通过计算机仿真实验,验证了所提算法的可行性和准确性,较其他被测算法输出的信干噪比至少提高1.5 dB。

基于GA-BP代理模型和稀疏多项式混沌展开的冲压稳健优化设计

为了开展冲压稳健优化设计,提出基于GA-BP代理模型和稀疏多项式混沌展开(sPCE)的优化设计方法。首先,根据生产现场实际情况,选取冲压工艺设计变量和成形质量指标,利用拉丁超立方采样(LHS)和CAE数值模拟获得冲压工艺样本点,在此基础上,综合遗传算法(GA)和反向传播神经网络(BP)构建GA-BP代理模型;然后,基于sPCE分析冲压成形质量对设计变量的不确定性响应,耦合上述GA-BP代理模型和sPCE不确定响应模型,建立冲压稳健优化模型;最后,运用非支配排序遗传算法(NSGA-II),在全冲压设计空间内求解稳健优化模型,并以某汽车A柱下加强板为例开展冲压稳健优化设计,结果表明:该方法可准确获得可行的最优稳健性工艺参数组合,能较好地应用于冲压稳定优化设计。