|
|
|
题名
|
作者
|
年代
|
出处
|
被引量
|
| 1 | L_(1/2) regularization显示文摘In this paper we propose an L1 /2 regularizer which has a nonconvex penalty.The L 1/2 regularizer is shown to have many promising properties such as unbiasedness, sparsity and oracle properties.A reweighed iterative algorithm is proposed so that the solution of the L 1/2 regularizer can be solved through transforming it into the solution of a series of L 1 regularizers.The solution of the L 1/2 regularizer is more sparse than that of the L 1 regularizer, while solving the L 1/2 regularizer is much simpler than solving the L 0 regularizer.The experiments show that the L 1/2 regularizer is very useful and efficient, and can be taken as a representative of the Lp(0 < p < 1) regularizer. | XU ZongBen ZHANG Hai WANG Yao CHANG XiangYu LIANG Yong | 2010 | Science China(Information Sciences)2010，53，6： | 32 |
| 2 | Sparse SAR imaging based on L_(1/2) regularization显示文摘In this paper,a novel method for synthetic aperture radar(SAR)imaging is proposed.The approach is based on L1/2 regularization to reconstruct the scattering field,which optimizes a quadratic error term of the SAR observation process subject to the interested scene sparsity.Compared to the conventional SAR imaging technique,the new method implements SAR imaging effectively at much lower sampling rate than the Nyquist rate,and produces high-quality images with reduced sidelobes and increased resolution.Also,over the prevalent greedy pursuit and L1 regularization based SAR imaging methods,there are remarkable performance improvements of the new method.On one hand,the new method significantly reduces the number of measurements needed for reconstruction,as supported by a phase transition diagram study.On the other hand,the new method is more robust to the observation noise.These fundamental properties of the new method are supported and demonstrated both by simulations and real SAR data experiments. | ZENG JinShan FANG Jian XU ZongBen | 2012 | Science China(Information Sciences)2012，55，8： | 18 |
| 3 | Model-driven deep-learning显示文摘Deep learning has been widely recognized as the representative advances of machine learning or artificial intelligence in general nowadays[1,2].This can be attributed to the recent breakthroughs made by deep learning on a series of challenging applications.A deep-learning approach improves the accuracy rate of face recognition to be higher than99%,beating the human level[3].For speech recognition and machine translation,deep learning is approaching the performance level of a simultaneous in- | zongben xu jian sun | 2018 | National Science Review2018，5，1： | 11 |
| 4 | The learning performance of support vector machine classification based on Markov sampling显示文摘The previously known frameworks describing the consistency of support vector machine classification(SVMC) algorithm are usually based on the assumption of independent and identically distributed(i.i.d.) samples.In this paper we go far beyond these classical frameworks by studying the consistency of SVMC algorithm with uniformly ergodic Markov chain samples based on linear prediction models.We establish the bound on the consistency of SVMC algorithm with uniformly ergodic Markov chain samples,and show that SVMC algorithm with uniformly ergodic Markov chain samples is consistent.Inspired by the idea from Markov chain Monto Carlo(MCMC) methods,we introduce a new Markov sampling algorithm for classification to generate uniformly ergodic Markov chain samples from large data set,and present numerical studies on simulated data and benchmark repository using SVMC algorithm. | ZOU Bin PENG ZhiMing XU ZongBen | 2013 | Science China(Information Sciences)2013，56，3： | 9 |
| 5 | Convergence of multi-block Bregman ADMM for nonconvex composite problems显示文摘The alternating direction method with multipliers(ADMM) is one of the most powerful and successful methods for solving various composite problems. The convergence of the conventional ADMM(i.e.,2-block) for convex objective functions has been stated for a long time, and its convergence for nonconvex objective functions has, however, been established very recently. The multi-block ADMM, a natural extension of ADMM, is a widely used scheme and has also been found very useful in solving various nonconvex optimization problems. It is thus expected to establish the convergence of the multi-block ADMM under nonconvex frameworks. In this paper, we first justify the convergence of 3-block Bregman ADMM. We next extend these results to the N-block case(N≥3), which underlines the feasibility of multi-block ADMM applications in nonconvex settings. Finally, we present a simulation study and a real-world application to support the correctness of the obtained theoretical assertions. | Fenghui WANG Wenfei CAO Zongben XU | 2018 | Science China(Information Sciences)2018，61，12： | 9 |
| 6 | The essential ability of sparse reconstruction of different compressive sensing strategies显示文摘We show the essential ability of sparse signal reconstruction of different compressive sensing strategies,which include the L1 regularization,the L0 regularization(thresholding iteration algorithm and OMP algorithm),the Lq(0 < q ≤ 1) regularizations,the Log regularization and the SCAD regularization.Taking phase diagram as the basic tool for analysis,we find that(i) the solutions of the L0 regularization using hard thresholding algorithm and OMP algorithm are similar to those of the L1 regularization;(ii) the Lq regularization with the decreasing value of q,the Log regularization and the SCAD regularization can attain sparser solutions than the L1 regularization;(iii) the L1/2 regularization can be taken as a representative of the Lq(0 < q < 1) regularizations.When 1/2 < q < 1,the L1/2 regularization always yields the sparsest solutions and when 0 < q < 1/2 the performance of the regularizations takes no significant difference.The results of this paper provide experimental evidence for our previous work. | ZHANG Hai LIANG Yong GOU HaiLiang XU ZongBen | 2012 | Science China(Information Sciences)2012，55，11： | 7 |
| 7 | Robust sparse principal component analysis显示文摘The model for improving the robustness of sparse principal component analysis(PCA)is proposed in this paper.Instead of the l2-norm variance utilized in the conventional sparse PCA model,the proposed model maximizes the l1-norm variance,which is less sensitive to noise and outlier.To ensure sparsity,lp-norm(0 p 1)constraint,which is more general and effective than l1-norm,is considered.A simple yet efficient algorithm is developed against the proposed model.The complexity of the algorithm approximately linearly increases with both of the size and the dimensionality of the given data,which is comparable to or better than the current sparse PCA methods.The proposed algorithm is also proved to converge to a reasonable local optimum of the model.The efficiency and robustness of the algorithm is verified by a series of experiments on both synthetic and digit number image data. | ZHAO Qian MENG DeYu XU ZongBen | 2014 | Science China(Information Sciences)2014，57，9： | 5 |
| 8 | Hierarchical clustering driven by cognitive features显示文摘For data sets of arbitrary shapes and densities,the existing clusterings have much space to be improved to obtain better results.In this paper,clustering is considered as a cognitive problem,and cognitive features are of vital importance to clustering.In combination with psychological experiment,we propose three cognitive features of clustering and model them as a flexible similarity measurement.Meanwhile a new clustering framework is put forward to integrate the cognitive features by employing the similarity measurement.The two attractive advantages are its low complexity and fitness for various types of data sets,such as data sets of diferent shapes and densities.Some synthetic and real data sets are employed to exhibit the superiority of the new clustering algorithm. | LI ChunZhong XU ZongBen QIAO Chen LUO Tao | 2014 | Science China(Information Sciences)2014，57，1： | 4 |
| 9 | The essential order of approximation for nearly exponential type neural networks显示文摘For the nearly exponential type of feedforward neural networks (neFNNs), it is revealed the essential order of their approximation. It is proven that for any continuous function defined on a compact set of Rd, there exists a three-layer neFNNs with fixed number of hidden neurons that attain the essential order. When the function to be ap- proximated belongs to the α-Lipschitz family (0 < α ≤ 2), the essential order of approxi- mation is shown to be O(n?α) where n is any integer not less than the reciprocal of the predetermined approximation error. The upper bound and lower bound estimations on approximation precision of the neFNNs are provided. The obtained results not only char- acterize the intrinsic property of approximation of the neFNNs, but also uncover the im- plicit relationship between the precision (speed) and the number of hidden neurons of the neFNNs. | XU Zongben WANG Jianjun | 2006 | Science in China(Series F)2006，49，4： | 3 |
| 10 | Efficient DPCA SAR imaging with fast iterative spectrum reconstruction method显示文摘The displaced phase center antenna(DPCA)technique is an effective strategy to achieve wide-swath synthetic aperture radar(SAR)imaging with high azimuth resolution.However,traditionally,it requires strict limitation of the pulse repetition frequency(PRF)to avoid non-uniform sampling.Otherwise,any deviation could bring serious ambiguity if the data are directly processed using a matched filter.To break this limitation,a recently proposed spectrum reconstruction method is capable of recovering the true spectrum from the nonuniform samples.However,the performance is sensitive to the selection of the PRF.Sparse regularization based imaging may provide a way to overcome this sensitivity.The existing time-domain method,however,requires a large-scale observation matrix to be built,which brings a high computational cost.In this paper,we propose a frequency domain method,called the iterative spectrum reconstruction method,through integration of the sparse regularization technique with spectrum analysis of the DPCA signal.By approximately expressing the observation in the frequency domain,which is realized via a series of decoupled linear operations,the method performs SAR imaging which is then not directly based on the observation matrix,which reduces the computational cost from O(N2)to O(N log N)(where N is the number of range cells),and is therefore more efficient than the time domain method.The sparse regularization scheme,realized via a fast thresholding iteration,has been adopted in this method,which brings the robustness of the imaging process to the PRF selection.We provide a series of simulations and ground based experiments to demonstrate the high efficiency and robustness of the method.The simulations show that the new method is almost as fast as the traditional mono-channel algorithm,and works well almost independently of the PRF selection.Consequently,the suggested method can be accepted as a practical and efficient wide-swath SAR imaging technique. | FANG Jian ZENG JinShan XU ZongBen ZHAO Yao | 2012 | Science China(Information Sciences)2012，55，8： | 2 |
| 11 | Image restoration with shifting reflective boundary conditions显示文摘In signal and image processing,we want to recover a faithful representation of an original scene from blurred,noisy image data.This process can be transformed mathematically into solving a linear system with a blurring matrix.Particularly,the blurring matrix is determined from not only a point spread function(PSF),which defines how each pixel is blurred,but also boundary conditions(BCs),which specify our assumptions on the data outside the domain of consideration.In this paper,we first propose shifting reflective BCs which preserve the continuity at the boundaries and,therefore,reduce ringing effects in the restored image.A Kronecker product approximation of the corresponding blurring matrix is then provided,regardless of symmetry requirement of the PSF.Finally,we demonstrate the efficiency of our approximation in an SVD-based regularization method by several numerical examples. | HUANG Jie HUANG TingZhu ZHAO XiLe XU ZongBen | 2013 | Science China(Information Sciences)2013，56，6： | 2 |
| 12 | Efficient projected gradient methods for cardinality constrained optimization显示文摘Sparse optimization has attracted increasing attention in numerous areas such as compressed sensing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constrained optimization problems, which involves box constraints and a singly linear constraint. An efficient approach is provided for calculating the projection over the feasibility set after a careful analysis on the projection subproblem. Then we present several types of projected gradient methods for a general class of cardinality constrained optimization problems. Global convergence of the methods is established under suitable assumptions. Finally, we illustrate some applications of the proposed methods for signal recovery and index tracking.Especially for index tracking, we propose a new model subject to an adaptive upper bound on the sparse portfolio weights. The computational results demonstrate that the proposed projected gradient methods are efficient in terms of solution quality. | Fengmin Xu Yuhong Dai Zhihu Zhao Zongben Xu | 2019 | Science China Mathematics2019，62，2： | 2 |
| 13 | A NEW ALGORITHM FOR COMPUTING THE INVERSE AND GENERALIZED INVERSE OF THE SCALED FACTOR CIRCULANT MATRIX显示文摘为发现一个非退化的放大因素 circulant 矩阵的逆的一个新算法被欧几里得的算法介绍。扩展被做计算组逆和单个放大因素 circulant 矩阵的 Moore-Penrose 逆。数字例子被举表明建议算法的实现。 | Zhaolin Jiang Zongben Xu | 2008 | Journal of Computational Mathematics2008，26，1： | 2 |
| 14 | Some theorems of random operator equations 显示文摘 | Zhu Chuanxi Xu Zongben | 2002 | International Journal of Mathematics and Mathematical Sciences2002，30，9： | 2 |
| 15 | On the uniqueness of virtual substrate for metasurface in a dielectric half-space显示文摘In this paper,we study the uniqueness of a virtual substrate for periodic metallic elements in a dielectric half-space.When the periodic metallic elements are placed at the interface of different substrates,they can be regarded to be embedded into a virtual substrate whose thickness approaches zero.However,the process of the mathematical limit of the thickness seems to be independent of the choice of the virtual substrate.Thereby,it is necessary to verify whether the arbitrary virtual substrate holds for the case.It is theoretically verified that the permittivity of the virtual substrate should be unique in order to satisfy the physical boundary condition of the periodic metallic elements.The root of the phenomenon is that the mathematical limit gives the alternative means to approach the actual physical situation,but the actual physical situation determines the way how the mathematical limit approaches zero.Finally,for comparison,two different virtual substrates are designed to validate the theory,for alternative substrate,incidence angle,and metallic elements.Besides,the finding can also be used to simplify the analysis and design of the metasurface by converting the periodic metallic elements in a dielectric half-space to the same periodic metallic elements in a uniform substrate. | Xiaobo LIU Wei XUE Xiaoming CHEN Anxue ZHANG Qiang CHENG Zongben XU | 2022 | Science China(Information Sciences)2022，65，1： | 2 |
| 16 | Improving geo-desic distance estimation based on locally linear assumption 显示文摘 | Meng Deyu Yee Leung Xu Zongben | 2008 | Pattern Recognition Letters2008，29，7： | 1 |
| 17 | Lower estimation of approximation rate for neural networks显示文摘Let SFd and Πψ,n,d = { nj=1bjψ(ωj·x+θj) :bj,θj∈R,ωj∈Rd} be the set of periodic and Lebesgue’s square-integrable functions and the set of feedforward neural network (FNN) functions, respectively. Denote by dist (SF d, Πψ,n,d) the deviation of the set SF d from the set Πψ,n,d. A main purpose of this paper is to estimate the deviation. In particular, based on the Fourier transforms and the theory of approximation, a lower estimation for dist (SFd, Πψ,n,d) is proved. That is, dist(SF d, Πψ,n,d) (nlogC2n)1/2 . The obtained estimation depends only on the number of neuron in the hidden layer, and is independent of the approximated target functions and dimensional number of input. This estimation also reveals the relationship between the approximation rate of FNNs and the topology structure of hidden layer. | CAO FeiLong ZHANG YongQuan XU ZongBen | 2009 | Science in China(Series F)2009，52，8： | 1 |
| 18 | Seif-adjoint domains of products of differential expressions 显示文摘 | Wei Guangsheng Xu Zongben Sun Jun | 2001 | Journal of Defferential Equation2001，174，： | 1 |
| 19 | L1/2 Regularization: A Thresholding Representation Theory and a Fast Solver 显示文摘 | XU Zongben CHANG Xiangyu XU Fengmin | 2012 | IEEE Trans Neural Network and Learning Systems2012，23，7： | 1 |
| 20 | Image inpainting by patch propagation using patch sparsity显示文摘 | XU Zongben SUN Jian | 2010 | IEEE Transactions on Image Processing2010，19，5： | 1 |
您所在的机构暂未开通此部分的功能，请联系管理员