High dimensional data clustering,with the inherent sparsity of data and the existence of noise,is a serious challenge for clustering algorithms.A new linear manifold clustering method was proposed to address this prob...High dimensional data clustering,with the inherent sparsity of data and the existence of noise,is a serious challenge for clustering algorithms.A new linear manifold clustering method was proposed to address this problem.The basic idea was to search the line manifold clusters hidden in datasets,and then fuse some of the line manifold clusters to construct higher dimensional manifold clusters.The orthogonal distance and the tangent distance were considered together as the linear manifold distance metrics. Spatial neighbor information was fully utilized to construct the original line manifold and optimize line manifolds during the line manifold cluster searching procedure.The results obtained from experiments over real and synthetic data sets demonstrate the superiority of the proposed method over some competing clustering methods in terms of accuracy and computation time.The proposed method is able to obtain high clustering accuracy for various data sets with different sizes,manifold dimensions and noise ratios,which confirms the anti-noise capability and high clustering accuracy of the proposed method for high dimensional data.展开更多
This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution ar...This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.展开更多
The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analy...The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.展开更多
The numerical manifold method(NMM)can be viewed as an inherent continuous-discontinuous numerical method,which is based on two cover systems including mathematical and physical covers.Higher-order NMM that adopts high...The numerical manifold method(NMM)can be viewed as an inherent continuous-discontinuous numerical method,which is based on two cover systems including mathematical and physical covers.Higher-order NMM that adopts higher-order polynomials as its local approximations generally shows higher precision than zero-order NMM whose local approximations are constants.Therefore,higherorder NMM will be an excellent choice for crack propagation problem which requires higher stress accuracy.In addition,it is crucial to improve the stress accuracy around the crack tip for determining the direction of crack growth according to the maximum circumferential stress criterion in fracture mechanics.Thus,some other enriched local approximations are introduced to model the stress singularity at the crack tip.Generally,higher-order NMM,especially first-order NMM wherein local approximations are first-order polynomials,has the linear dependence problems as other partition of unit(PUM)based numerical methods does.To overcome this problem,an extended NMM is developed based on a new local approximation derived from the triangular plate element in the finite element method(FEM),which has no linear dependence issue.Meanwhile,the stresses at the nodes of mathematical mesh(the nodal stresses in FEM)are continuous and the degrees of freedom defined on the physical patches are physically meaningful.Next,the extended NMM is employed to solve multiple crack propagation problems.It shows that the fracture mechanics requirement and mechanical equilibrium can be satisfied by the trial-and-error method and the adjustment of the load multiplier in the process of crack propagation.Four numerical examples are illustrated to verify the feasibility of the proposed extended NMM.The numerical examples indicate that the crack growths simulated by the extended NMM are in good accordance with the reference solutions.Thus the effectiveness and correctness of the developed NMM have been validated.展开更多
In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we ...In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.展开更多
With noncritical eigenvalues assumed to be campletely controllable stability and linear feedback stabiliz-ablity probems are attacked by the center manifold method, and a procedure had been established for the constru...With noncritical eigenvalues assumed to be campletely controllable stability and linear feedback stabiliz-ablity probems are attacked by the center manifold method, and a procedure had been established for the construction of linear feedback stabilizing law on the basis of noncritical eigenvalue assignment.展开更多
Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT)...Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.展开更多
局部线性嵌入(Local linear embedding,LLE)算法在挖掘高维空间的局部结构时,需要人工指定近邻点的个数,无法保证算法的特征提取能力。为了解决这个问题,提出了一种样本密度自适应的局部增强线性嵌入算法(Local enhanced linear embeddi...局部线性嵌入(Local linear embedding,LLE)算法在挖掘高维空间的局部结构时,需要人工指定近邻点的个数,无法保证算法的特征提取能力。为了解决这个问题,提出了一种样本密度自适应的局部增强线性嵌入算法(Local enhanced linear embedding algorithm with sample density adaptation,SDA-LELE)。首先,利用样本点与其近邻点之间的距离之和,衡量样本分布的稀疏稠密程度,从而自适应地选取近邻点个数。其次,采用局部增强算法,增加相邻样本间的权重,从而使样本在保持局部线性结构的同时也保持局部近邻结构,增强算法特征提取能力。最后,将算法应用在凯斯西储大学和东北石油大学轴承数据集上,并进行了可视化、Fisher信息等实验。实验结果表明,SDALELE算法比其他算法能提取出更多的显著特征,获得更好的降维效果。展开更多
针对电力机车牵引变流器中故障率最高的单相脉宽调制(pulse width modulation,PWM)整流器,提出一种流形学习算法融合多域特征的故障诊断方法。根据整流器在不同工作状态下的时域、频域和时频域特征构建多域特征向量;采用Hessian局部线...针对电力机车牵引变流器中故障率最高的单相脉宽调制(pulse width modulation,PWM)整流器,提出一种流形学习算法融合多域特征的故障诊断方法。根据整流器在不同工作状态下的时域、频域和时频域特征构建多域特征向量;采用Hessian局部线性嵌入(Hessian local linear embedding,HLLE)算法融合多域特征,根据故障样本数和聚类结果,解决高维数据中固有维数和最近邻数选取困难的问题,得到用于描述故障特征的最优低维特征向量,减少特征之间的冲突和冗余;采用支持向量机进行模式识别,实现对整流器的故障诊断。结果表明:对不同的输出电压,不同的训练和测试比,15种故障模式均具有较高的诊断率。与其他方法相比,本文方法具有较好的融合效果和较强的鲁棒性。展开更多
基金Project(60835005) supported by the National Nature Science Foundation of China
文摘High dimensional data clustering,with the inherent sparsity of data and the existence of noise,is a serious challenge for clustering algorithms.A new linear manifold clustering method was proposed to address this problem.The basic idea was to search the line manifold clusters hidden in datasets,and then fuse some of the line manifold clusters to construct higher dimensional manifold clusters.The orthogonal distance and the tangent distance were considered together as the linear manifold distance metrics. Spatial neighbor information was fully utilized to construct the original line manifold and optimize line manifolds during the line manifold cluster searching procedure.The results obtained from experiments over real and synthetic data sets demonstrate the superiority of the proposed method over some competing clustering methods in terms of accuracy and computation time.The proposed method is able to obtain high clustering accuracy for various data sets with different sizes,manifold dimensions and noise ratios,which confirms the anti-noise capability and high clustering accuracy of the proposed method for high dimensional data.
基金This work was supposed by the National Nature Science Foundation of China
文摘This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.
基金Hie-Tch Research and Development Program of China (2002AA723011)
文摘The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.
基金supported by the National Key R&D Program of China (Grant No.2018YFC0407002)the National Natural Science Foundation of China(Grant Nos.11502033 and 51879014)
文摘The numerical manifold method(NMM)can be viewed as an inherent continuous-discontinuous numerical method,which is based on two cover systems including mathematical and physical covers.Higher-order NMM that adopts higher-order polynomials as its local approximations generally shows higher precision than zero-order NMM whose local approximations are constants.Therefore,higherorder NMM will be an excellent choice for crack propagation problem which requires higher stress accuracy.In addition,it is crucial to improve the stress accuracy around the crack tip for determining the direction of crack growth according to the maximum circumferential stress criterion in fracture mechanics.Thus,some other enriched local approximations are introduced to model the stress singularity at the crack tip.Generally,higher-order NMM,especially first-order NMM wherein local approximations are first-order polynomials,has the linear dependence problems as other partition of unit(PUM)based numerical methods does.To overcome this problem,an extended NMM is developed based on a new local approximation derived from the triangular plate element in the finite element method(FEM),which has no linear dependence issue.Meanwhile,the stresses at the nodes of mathematical mesh(the nodal stresses in FEM)are continuous and the degrees of freedom defined on the physical patches are physically meaningful.Next,the extended NMM is employed to solve multiple crack propagation problems.It shows that the fracture mechanics requirement and mechanical equilibrium can be satisfied by the trial-and-error method and the adjustment of the load multiplier in the process of crack propagation.Four numerical examples are illustrated to verify the feasibility of the proposed extended NMM.The numerical examples indicate that the crack growths simulated by the extended NMM are in good accordance with the reference solutions.Thus the effectiveness and correctness of the developed NMM have been validated.
文摘In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.
文摘With noncritical eigenvalues assumed to be campletely controllable stability and linear feedback stabiliz-ablity probems are attacked by the center manifold method, and a procedure had been established for the construction of linear feedback stabilizing law on the basis of noncritical eigenvalue assignment.
基金supported by National Natural Science Foundation of China(No.61171145)Shanghai Educational Development Fundation(No.12ZZ083)
文摘Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.
文摘局部线性嵌入(Local linear embedding,LLE)算法在挖掘高维空间的局部结构时,需要人工指定近邻点的个数,无法保证算法的特征提取能力。为了解决这个问题,提出了一种样本密度自适应的局部增强线性嵌入算法(Local enhanced linear embedding algorithm with sample density adaptation,SDA-LELE)。首先,利用样本点与其近邻点之间的距离之和,衡量样本分布的稀疏稠密程度,从而自适应地选取近邻点个数。其次,采用局部增强算法,增加相邻样本间的权重,从而使样本在保持局部线性结构的同时也保持局部近邻结构,增强算法特征提取能力。最后,将算法应用在凯斯西储大学和东北石油大学轴承数据集上,并进行了可视化、Fisher信息等实验。实验结果表明,SDALELE算法比其他算法能提取出更多的显著特征,获得更好的降维效果。
文摘针对电力机车牵引变流器中故障率最高的单相脉宽调制(pulse width modulation,PWM)整流器,提出一种流形学习算法融合多域特征的故障诊断方法。根据整流器在不同工作状态下的时域、频域和时频域特征构建多域特征向量;采用Hessian局部线性嵌入(Hessian local linear embedding,HLLE)算法融合多域特征,根据故障样本数和聚类结果,解决高维数据中固有维数和最近邻数选取困难的问题,得到用于描述故障特征的最优低维特征向量,减少特征之间的冲突和冗余;采用支持向量机进行模式识别,实现对整流器的故障诊断。结果表明:对不同的输出电压,不同的训练和测试比,15种故障模式均具有较高的诊断率。与其他方法相比,本文方法具有较好的融合效果和较强的鲁棒性。
