With the extensive application of large-scale array antennas,the increasing number of array elements leads to the increasing dimension of received signals,making it difficult to meet the real-time requirement of direc...With the extensive application of large-scale array antennas,the increasing number of array elements leads to the increasing dimension of received signals,making it difficult to meet the real-time requirement of direction of arrival(DOA)estimation due to the computational complexity of algorithms.Traditional subspace algorithms require estimation of the covariance matrix,which has high computational complexity and is prone to producing spurious peaks.In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements,this paper proposes a DOA estimation method based on Krylov subspace and weighted l_(1)-norm.The method uses the multistage Wiener filter(MSWF)iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace,further uses the measurement matrix to reduce the dimensionality of the signal subspace observation,constructs a weighted matrix,and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted l_(1)-norm to solve the target DOA.Simulation results show that the proposed method has high resolution under large array conditions,effectively suppresses spurious peaks,reduces computational complexity,and has good robustness for low signal to noise ratio(SNR)environment.展开更多
In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency est...In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency estimator is developed.Since the proposed method employs the weighted l_(1)-norm on the LP errors,it can be regarded as an extension of the l_(1)-generalized weighted linear predictor.Computer simulations are conducted in the environment of α-stable noise,indicating the superiority of the proposed algorithm,in terms of its robust to outliers and nearly optimal estimation performance.展开更多
As a way of training a single hidden layer feedforward network(SLFN),extreme learning machine(ELM)is rapidly becoming popular due to its efficiency.However,ELM tends to overfitting,which makes the model sensitive to n...As a way of training a single hidden layer feedforward network(SLFN),extreme learning machine(ELM)is rapidly becoming popular due to its efficiency.However,ELM tends to overfitting,which makes the model sensitive to noise and outliers.To solve this problem,L_(2,1)-norm is introduced to ELM and an L_(2,1)-norm robust regularized ELM(L_(2,1)-RRELM)was proposed.L_(2,1)-RRELM gives constant penalties to outliers to reduce their adverse effects by replacing least square loss function with a non-convex loss function.In light of the non-convex feature of L_(2,1)-RRELM,the concave-convex procedure(CCCP)is applied to solve its model.The convergence of L_(2,1)-RRELM is also given to show its robustness.In order to further verify the effectiveness of L_(2,1)-RRELM,it is compared with the three popular extreme learning algorithms based on the artificial dataset and University of California Irvine(UCI)datasets.And each algorithm in different noise environments is tested with two evaluation criterions root mean square error(RMSE)and fitness.The results of the simulation indicate that L_(2,1)-RRELM has smaller RMSE and greater fitness under different noise settings.Numerical analysis shows that L_(2,1)-RRELM has better generalization performance,stronger robustness,and higher anti-noise ability and fitness.展开更多
边界框回归分支是深度目标跟踪器的关键模块,其性能直接影响跟踪器的精度.评价精度的指标之一是交并比(Intersection over union,IoU).基于IoU的损失函数取代了l_(n)-norm损失成为目前主流的边界框回归损失函数,然而IoU损失函数存在2个...边界框回归分支是深度目标跟踪器的关键模块,其性能直接影响跟踪器的精度.评价精度的指标之一是交并比(Intersection over union,IoU).基于IoU的损失函数取代了l_(n)-norm损失成为目前主流的边界框回归损失函数,然而IoU损失函数存在2个固有缺陷:1)当预测框与真值框不相交时IoU为常量0,无法梯度下降更新边界框的参数;2)在IoU取得最优值时其梯度不存在,边界框很难收敛到IoU最优处.揭示了在回归过程中IoU最优的边界框各参数之间蕴含的定量关系,指出在边界框中心处于特定位置时存在多种尺寸不同的边界框使IoU损失最优的情况,这增加了边界框尺寸回归的不确定性.从优化两个统计分布之间散度的视角看待边界框回归问题,提出了光滑IoU(Smooth-IoU,SIoU)损失,即构造了在全局上光滑(即连续可微)且极值唯一的损失函数,该损失函数自然蕴含边界框各参数之间特定的最优关系,其唯一取极值的边界框可使IoU达到最优.光滑性确保了在全局上梯度存在使得边界框更容易回归到极值处,而极值唯一确保了在全局上可梯度下降更新参数,从而避开了IoU损失的固有缺陷.提出的光滑损失可以很容易取代IoU损失集成到现有的深度目标跟踪器上训练边界框回归,在LaSOT、GOT-10k、TrackingNet、OTB2015和VOT2018测试基准上所取得的结果,验证了光滑IoU损失的易用性和有效性.展开更多
In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong ...In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.展开更多
Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median...Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median zero. Define the minimum L_1norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:展开更多
无监督特征选择是机器学习和数据挖掘中的一种重要的降维技术。然而当前的无监督特征选择方法侧重于从数据的邻接矩阵中学习数据的流形结构,忽视非邻接数据对之间的关联。其次这些方法都假设数据实例具有独立同一性,但现实中的数据样本...无监督特征选择是机器学习和数据挖掘中的一种重要的降维技术。然而当前的无监督特征选择方法侧重于从数据的邻接矩阵中学习数据的流形结构,忽视非邻接数据对之间的关联。其次这些方法都假设数据实例具有独立同一性,但现实中的数据样本其来源是不同的,这样的假设就不成立。此外,在原始数据空间中特征重要性的衡量会受到数据和特征中的噪声影响。基于以上问题,本文提出了潜在多步马尔可夫概率的鲁棒无监督特征选择方法(unsupervised feature selection via multi-step Markov probability and latent representation,MMLRL),其思想是通过最大多步马尔可夫转移概率学习数据流形结构,然后通过对称非负矩阵分解模型学习数据的潜在表示,最后在数据的潜在表示空间中选择特征。同时在6个不同类型的数据集上验证了所提出算法的有效性。展开更多
In this paper,we consider the knot placement problem in B-spline curve approximation.A novel two-stage framework is proposed for addressing this problem.In the first step,the l_(∞,1)-norm model is introduced for the ...In this paper,we consider the knot placement problem in B-spline curve approximation.A novel two-stage framework is proposed for addressing this problem.In the first step,the l_(∞,1)-norm model is introduced for the sparse selection of candidate knots from an initial knot vector.By this step,the knot number is determined.In the second step,knot positions are formulated into a nonlinear optimization problem and optimized by a global optimization algorithm—the differential evolution algorithm(DE).The candidate knots selected in the first step are served for initial values of the DE algorithm.Since the candidate knots provide a good guess of knot positions,the DE algorithm can quickly converge.One advantage of the proposed algorithm is that the knot number and knot positions are determined automatically.Compared with the current existing algorithms,the proposed algorithm finds approximations with smaller fitting error when the knot number is fixed in advance.Furthermore,the proposed algorithm is robust to noisy data and can handle with few data points.We illustrate with some examples and applications.展开更多
For addressing impulse noise in images, this paper proposes a denoising algorithm for non-convex impulse noise images based on the l_(0) norm fidelity term. Since the total variation of the l_(0) norm has a better den...For addressing impulse noise in images, this paper proposes a denoising algorithm for non-convex impulse noise images based on the l_(0) norm fidelity term. Since the total variation of the l_(0) norm has a better denoising effect on the pulse noise, it is chosen as the model fidelity term, and the overlapping group sparse term combined with non-convex higher term is used as the regularization term of the model to protect the image edge texture and suppress the staircase effect. At the same time, the alternating direction method of multipliers, the majorization–minimization method and the mathematical program with equilibrium constraints were used to solve the model. Experimental results show that the proposed model can effectively suppress the staircase effect in smooth regions, protect the image edge details, and perform better in terms of the peak signal-to-noise ratio and the structural similarity index measure.展开更多
基金supported by the National Basic Research Program of China。
文摘With the extensive application of large-scale array antennas,the increasing number of array elements leads to the increasing dimension of received signals,making it difficult to meet the real-time requirement of direction of arrival(DOA)estimation due to the computational complexity of algorithms.Traditional subspace algorithms require estimation of the covariance matrix,which has high computational complexity and is prone to producing spurious peaks.In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements,this paper proposes a DOA estimation method based on Krylov subspace and weighted l_(1)-norm.The method uses the multistage Wiener filter(MSWF)iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace,further uses the measurement matrix to reduce the dimensionality of the signal subspace observation,constructs a weighted matrix,and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted l_(1)-norm to solve the target DOA.Simulation results show that the proposed method has high resolution under large array conditions,effectively suppresses spurious peaks,reduces computational complexity,and has good robustness for low signal to noise ratio(SNR)environment.
文摘In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency estimator is developed.Since the proposed method employs the weighted l_(1)-norm on the LP errors,it can be regarded as an extension of the l_(1)-generalized weighted linear predictor.Computer simulations are conducted in the environment of α-stable noise,indicating the superiority of the proposed algorithm,in terms of its robust to outliers and nearly optimal estimation performance.
基金supported by the National Natural Science Foundation of China(51875457)the Key Research Project of Shaanxi Province(2022GY-050,2022GY-028)+1 种基金the Natural Science Foundation of Shaanxi Province of China(2022JQ-636,2022JQ-705,2021JQ-714)Shaanxi Youth Talent Lifting Plan of Shaanxi Association for Science and Technology(20220129)。
文摘As a way of training a single hidden layer feedforward network(SLFN),extreme learning machine(ELM)is rapidly becoming popular due to its efficiency.However,ELM tends to overfitting,which makes the model sensitive to noise and outliers.To solve this problem,L_(2,1)-norm is introduced to ELM and an L_(2,1)-norm robust regularized ELM(L_(2,1)-RRELM)was proposed.L_(2,1)-RRELM gives constant penalties to outliers to reduce their adverse effects by replacing least square loss function with a non-convex loss function.In light of the non-convex feature of L_(2,1)-RRELM,the concave-convex procedure(CCCP)is applied to solve its model.The convergence of L_(2,1)-RRELM is also given to show its robustness.In order to further verify the effectiveness of L_(2,1)-RRELM,it is compared with the three popular extreme learning algorithms based on the artificial dataset and University of California Irvine(UCI)datasets.And each algorithm in different noise environments is tested with two evaluation criterions root mean square error(RMSE)and fitness.The results of the simulation indicate that L_(2,1)-RRELM has smaller RMSE and greater fitness under different noise settings.Numerical analysis shows that L_(2,1)-RRELM has better generalization performance,stronger robustness,and higher anti-noise ability and fitness.
文摘宽度学习系统(broad learning system,BLS)因其特征提取能力强、计算效率高而被广泛应用于众多领域.然而,目前BLS主要用于单输出回归,当BLS存在多个输出时,BLS无法有效发掘多个输出权重之间的相关性,会导致模型预测性能的下降.鉴于此,通过Frobenius和L_(2,1)矩阵范数的联合约束,提出多输出宽度学习系统(multi-output broad learning system,MOBLS).首先,在原有BLS的基础上构建新的目标函数,将L2损失函数替换为L_(2,1)形式,L_(2)正则化项替换为Frobenius和L_(2,1)两项;然后,利用交替方向乘子法(alternating direction method of multipliers,ADMM)对新目标函数BLS的输出权重优化求解.利用11个公共数据集和1个实际过程数据集验证了所提系统的有效性.
文摘边界框回归分支是深度目标跟踪器的关键模块,其性能直接影响跟踪器的精度.评价精度的指标之一是交并比(Intersection over union,IoU).基于IoU的损失函数取代了l_(n)-norm损失成为目前主流的边界框回归损失函数,然而IoU损失函数存在2个固有缺陷:1)当预测框与真值框不相交时IoU为常量0,无法梯度下降更新边界框的参数;2)在IoU取得最优值时其梯度不存在,边界框很难收敛到IoU最优处.揭示了在回归过程中IoU最优的边界框各参数之间蕴含的定量关系,指出在边界框中心处于特定位置时存在多种尺寸不同的边界框使IoU损失最优的情况,这增加了边界框尺寸回归的不确定性.从优化两个统计分布之间散度的视角看待边界框回归问题,提出了光滑IoU(Smooth-IoU,SIoU)损失,即构造了在全局上光滑(即连续可微)且极值唯一的损失函数,该损失函数自然蕴含边界框各参数之间特定的最优关系,其唯一取极值的边界框可使IoU达到最优.光滑性确保了在全局上梯度存在使得边界框更容易回归到极值处,而极值唯一确保了在全局上可梯度下降更新参数,从而避开了IoU损失的固有缺陷.提出的光滑损失可以很容易取代IoU损失集成到现有的深度目标跟踪器上训练边界框回归,在LaSOT、GOT-10k、TrackingNet、OTB2015和VOT2018测试基准上所取得的结果,验证了光滑IoU损失的易用性和有效性.
基金Supported by the Natural Science Foundation of Beijing City of China (1042002)the Science and Technology Development Foundation of Education Committee of Beijing Citythe Special Expenditure of Excellent Person Education of Beijing(20041D0501515)
文摘In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.
基金Project supported by the National Natural Science Foundation of China and also supported by the U. S. Office of Naval Research and Air Force Office of Scientific Research.
文摘Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median zero. Define the minimum L_1norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:
文摘无监督特征选择是机器学习和数据挖掘中的一种重要的降维技术。然而当前的无监督特征选择方法侧重于从数据的邻接矩阵中学习数据的流形结构,忽视非邻接数据对之间的关联。其次这些方法都假设数据实例具有独立同一性,但现实中的数据样本其来源是不同的,这样的假设就不成立。此外,在原始数据空间中特征重要性的衡量会受到数据和特征中的噪声影响。基于以上问题,本文提出了潜在多步马尔可夫概率的鲁棒无监督特征选择方法(unsupervised feature selection via multi-step Markov probability and latent representation,MMLRL),其思想是通过最大多步马尔可夫转移概率学习数据流形结构,然后通过对称非负矩阵分解模型学习数据的潜在表示,最后在数据的潜在表示空间中选择特征。同时在6个不同类型的数据集上验证了所提出算法的有效性。
基金supported by the National Natural Science Foundation of China(Nos.11871447,11801393)the Natural Science Foundation of Jiangsu Province(No.BK20180831).
文摘In this paper,we consider the knot placement problem in B-spline curve approximation.A novel two-stage framework is proposed for addressing this problem.In the first step,the l_(∞,1)-norm model is introduced for the sparse selection of candidate knots from an initial knot vector.By this step,the knot number is determined.In the second step,knot positions are formulated into a nonlinear optimization problem and optimized by a global optimization algorithm—the differential evolution algorithm(DE).The candidate knots selected in the first step are served for initial values of the DE algorithm.Since the candidate knots provide a good guess of knot positions,the DE algorithm can quickly converge.One advantage of the proposed algorithm is that the knot number and knot positions are determined automatically.Compared with the current existing algorithms,the proposed algorithm finds approximations with smaller fitting error when the knot number is fixed in advance.Furthermore,the proposed algorithm is robust to noisy data and can handle with few data points.We illustrate with some examples and applications.
基金funded by National Nature Science Foundation of China,grant number 61302188。
文摘For addressing impulse noise in images, this paper proposes a denoising algorithm for non-convex impulse noise images based on the l_(0) norm fidelity term. Since the total variation of the l_(0) norm has a better denoising effect on the pulse noise, it is chosen as the model fidelity term, and the overlapping group sparse term combined with non-convex higher term is used as the regularization term of the model to protect the image edge texture and suppress the staircase effect. At the same time, the alternating direction method of multipliers, the majorization–minimization method and the mathematical program with equilibrium constraints were used to solve the model. Experimental results show that the proposed model can effectively suppress the staircase effect in smooth regions, protect the image edge details, and perform better in terms of the peak signal-to-noise ratio and the structural similarity index measure.
