一种通过相续雷达成像构建目标三维像的算法

逆合成孔径雷达(ISAR)作为成像雷达技术之一,它是应用雷达波束对基于遥感目标的二维像进行观测.ISAR对相继像的观察就类似于采用摄像机捕捉移动的画面.在光学成像的领域里,将图像而成的二维速度变换称为"光速流"或者是"速度场".当摄像机与目标之间的相对运动是已知的时候,那么基于速度场的以相继运动图像来估计目标的三维形态是合理的.     

基于Laplacian特征映射的被动毫米波目标识别

针对传统被动毫米波金属目标识别方法中特征提取、选择的缺点,采用Laplacian特征映射流形学习算法发现了金属目标回波信号短时傅立叶谱中低维流形的存在,并研究了其特性。通过比较测试样本与正类样本低流形的匹配程度进行分类识别,与其他性降维及基于核的非线性降维算法相比,识别率更高,且对数据混叠分布鲁棒性好。     

流形核与LPP相结合的毛杆折痕识别方法

针对毛杆折痕难以检测问题,将非线性流形的思想引入到折痕识别领域。提出运用流形核函数与局部保持投影相结合的方法进行毛杆特征提取。首先基于区域图像构造协方差矩阵作为图像特征,利用仿射不变度量作为样本点的距离测度。然后通过定义的黎曼核函数选择流形上的近邻点,使得近邻点的选择符合数据呈非线性流形的假设,并结合数据类别信息构造相应的核矩阵。最后利用局部保持投影算法对毛杆图像进行降维。实验结果表明,本文算法能够有效克服光照不均和残余绒毛等外部因素影响,具有较好的稳健性和较高的识别率。     

基于共空间模式和均匀流形投影的运动想象脑电信号识别方法

运动想象脑电信号的识别与分类问题一直是脑机领域研究的热点问题。针对此问题,使用区别传统线性降维方法的流形学习方法,将共空间模式算法与均匀流形投影算法相结合,充分利用了脑电信号中的非线性特征,对运动想象脑电信号进行了特征提取和数据降维,并使用KNN分类器进行了分类,对分类效果做出了评价;将降维前后的数据分类结果进行对比,说明了数据降维的优点和必要性;进一步讨论了降维结果在数据可视化方面的表现。发现经过数据降维的特征数据的可视化效果明显优于未经过降维的数据,进一步提出了一种基于共空间模式和均匀流形投影的新型脑电信号识别方法,对进行脑电信号深度剖析。挖掘脑电信号非线性特征提供了参考价值,同时也在数据流形分布以及数据可视化的角度为运动想象脑电信号识别提供了新思路。     

自适应Chirplet信号分解用于ISAR目标三维转动检测

当ISAR目标作复杂的三维转动时,目标上各散射点的相位误差将与它们在目标上所处的位置有关,传统的相位聚焦方法难以采用统一的相位校正函数来进行补偿。为解决此问题,论文提出了一种基于自适应Chirplet信号分解的ISAR目标三维转动检测方法,该方法使用自适应Chirplet信号分解的快速算法来估计散射点子回波的相位信息,并根据两个散射点相位之间的非线性度来判断目标是否存在三维转动,从而只选择那些仅具有二维转动的数据段进行成像。仿真实验结果表明了它的有效性。     

基于监督式等距映射的人脸和表情识别

提出了一种基于监督式等距映射的人脸和表情识别方法,该方法能同时完成身份和表情的识别.首先,运用监督式等距映射,将训练集中的人脸表情图像投影到低维流形空间,在这个流形空间里,图像的投影不仅实现了按其身份的分离,同时在同身份图像的内部,又实现了按其表情的聚类.然后,用非线性投影,将待测图像嵌入到流形空间.最后,采用加权knn分类器,识别出它的身份和表情.在Coln-Kanade和JAFFE人脸库上的实验表明,该方法对人脸和表情的识别的准确率比较高.     

基于Gabor小波的人脸表情识别

提出通过提取人脸表情图像的Gabor特征,结合二次降维的方法,进行人脸表情识别.针对Gabor特征提取后维数变高,冗余很大的特点,先对高维特征进行采样,再引入二维PCA算法对Gabor特征进行选择,以达到降维的目的.然后采用基于模糊积分的多分类器联合的方法对7种表情进行融合识别.在JAFFE库上进行测试的结果验证了该算法的有效性,与2DPCA算法及传统特征提取算法相比,本文算法取得了较高的识别速度和精确度.该算法能更有效的提取反映表情状态的特征.     

转子故障数据集降维的CKLPMDP算法研究

针对传统的数据降维方法难以兼顾局部流形结构和多流形判别结构学习的问题,提出一种相关熵测度核局部保持多流形判别投影算法(correntropy kernel locality preserving multi-manifold discriminant projection, CKLPMDP)的转子故障数据集降维方法。该方法的显著特点是采用相关熵测度监督近邻图的构建,首先将数据集映射到高维核空间,然后在核空间中综合考虑数据集的局部流形结构和多流形判别结构信息,提取出最优表征故障数据集的低维敏感特征矢量,采用三维图直观地显示出低维分类效果,并以低维敏感特征矢量输入K近邻分类器(K-nearest neighbor, KNN)中的辨识率和聚类分析中类间距S_b、类内距S_w作为衡量降维效果的指标。通过双跨转子实验台的振动信号数据集进行验证,与其他几种典型特征提取方法对比,该方法能更有效地提取出局部流形和多流形判别信息,在转子故障辨识中表现出更好的分类性能。     

带标志点的LTSA算法及其在轴承故障诊断中的应用

针对非监督式流形学习算法面临的增量式学习问题,提出一种带标志点的增量式局部切空间排列算法.该方法在局部切空间排列算法的基础上,利用最小角度回归算法从原始训练样本中选取标志点,以选取的标志点和新增样本建立所有样本的全局坐标矩阵,利用原始样本低维嵌入坐标和全局坐标矩阵对新增样本的低维嵌入坐标进行估计,并采用全局坐标矩阵特征值迭代方法更新所有样本的低维嵌入坐标.滚动轴承4种不同状态振动数据样本的增量式识别结果表明,本方法在实现局部切空间排列算法增量式学习的基础上,保持了对滚动轴承不同状态样本较高的类别可分性测度.     

一种改进的图像低维表示方法

目的解决当前方法需要对图像中的相应点手动标记界标,且局限于特定对象或形状变形的问题。方法提出一种可以同时实现图像颜色、外观和形态的图像低维表示算法。结果该算法通过将形态和外观的流形约束到低维子空间上,进一步降低了流形学习的采样复杂性。结论文中方法的性能远优于目前典型的稳健型光流算法和SIFT流算法。在图像编辑和关节学习关任务中取得了令人满意的定性结果。     

基于流形学习和K-最近邻分类器的旋转机械故障诊断方法

针对旋转机械故障诊断需人工干预、精度低、故障样本难以获取等问题,提出基于流形学习和K-最近邻分类器（KNNC）的故障诊断模型。提取振动信号多域信息熵以全面反映设备运行状态并构造高维特征集;利用正交邻域保持嵌入(ONPE)非线性流形学习算法的二次特征提取特性进行维数约简使特征具有更好的聚类特性;基于改进的更适用于小样本分类KNNC进行模式识别,用轴承故障诊断案例证明该模型的有效性。     

A local multiple proper generalized decomposition based on the partition of unity

It is well known that model order reduction techniques that project the solution of the problem at hand onto a low-dimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcome these difficulties (notably, an undesirable increase in the number of required modes in the solution), several solutions have been suggested. Among them, we can cite the use of nonlinear dimensionality reduction techniques or, alternatively, the employ of linear local reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented, which ensures this continuity by resorting to the paradigm of the partition of unity while employing proper generalized decompositions at each local patch.     

Local proper generalized decomposition

One of the main difficulties that a reduced‐order method could face is the poor separability of the solution. This problem is common to both a posteriori model order reduction (proper orthogonal decomposition, reduced basis) and a priori [proper generalized decomposition (PGD)] model order reduction. Early approaches to solve it include the construction of local reduced‐order models in the framework of POD. We present here an extension of local models in a PGD—and thus, a priori—context. Three different strategies are introduced to estimate the size of the different patches or regions in the solution manifold where PGD is applied. As will be noticed, no gluing or special technique is needed to deal with the resulting set of local reduced‐order models, in contrast to most proper orthogonal decomposition local approximations. The resulting method can be seen as a sort of a priori manifold learning or nonlinear dimensionality reduction technique. Examples are shown that demonstrate pros and cons of each strategy for different problems.     

Asymptotic stability of a stochastic delay equation

The investigation of a nonlinear stochastic delay equation with structural tool and regenerative time delays is presented. The conditions of Hopf bifurcation are computed in order to describe the regions of stability and instability. Explicit expressions characterizing the influence of nonlinear and stochastic perturbations, valid in the first order centre manifold approximation, are derived. In addition to this, we describe the underlying mathematical ideas of the centre manifold reduction of delay differential equations to ordinary differential equations for fixed time delays.     

Diffusion maps-based surrogate modeling: An alternative machine learning approach

In this work, an alternative machine learning methodology is proposed, which utilizes nonlinear manifold learning techniques in the frame of surrogate modeling. Under the assumption that the solutions of a parametrized physical system lie on a low-dimensional manifold embedded in a high-dimensional Euclidean space, the goal is to unveil the manifold's intrinsic dimensionality and use it for the construction of a surrogate model, which will be used as a cost-efficient emulator of the high-dimensional physical system. To this purpose, a computational framework based on the diffusion maps algorithm is put forth herein, where a set of system solutions is used to identify the geometry of a low-dimensional space called the diffusion maps space. This space is completely described by a low-dimensional basis, which is constructed from the eigenvectors and eigenvalues of a diffusion operator on the data. The proposed approach exploits the diffusion maps space's reduced dimensionality for the construction of locally clustered interpolation schemes between the parameter space, the diffusion maps space, and the solution space, which are cheap to evaluate and highly accurate. This way, the need to formulate and solve the governing equations of the system is eliminated. In addition, a sampling methodology is proposed based on the metric of the diffusion maps space to efficiently sample the parameter space, thus ensuring the quality of the surrogate model. Even though it is exploited herein in the premises of uncertainty quantification, this methodology is applicable to any other problem type that depends on some parametric space (ie, optimization, sensitivity analysis, etc). In the numerical examples, it is shown that the proposed surrogate model is capable of high levels of accuracy, as well as significant computational gains.     

基于核主元分析的头部姿势估计

现有头部姿势估计方法主要是基于几何分析和基于外现线性变换的方法,计算复杂、通用性不强.提出一种新的利用非线性的核变换算法进行姿势估计的方法,根据流形学习理论,不同姿势的高维人脸图像存在一低维流形结构,提取该流形结构可估计头部姿势.核主元分析是一种非线性降维算法,能够把这种流形结构嵌入到低维空间.利用核主元分析训练姿势估计曲线,然后把新图像投影到姿势曲线上,利用插值方法估计新投影点对应得姿势角度.核主元分析的方法克服了传统线性估计方法的缺点,实验证明该方法估计效果良好,并给出进一步提高估计效果的途径.     

Nonlinear manifold learning for meshfree finite deformation thin‐shell analysis

Calculations on general point‐set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges. The absence of a mesh makes it nontrivial to decide if two neighboring points in the three‐dimensional embedding are nearby or rather far apart on the manifold. Furthermore, the topology of surfaces is generally not that of an open two‐dimensional set, ruling out global parametrizations. We propose a general and simple numerical method analogous to the mathematical theory of manifolds, in which the point‐set surface is described by a set of overlapping charts forming a complete atlas. We proceed in four steps: (1) partitioning of the node set into subregions of trivial topology; (2) automatic detection of the geometric structure of the surface patches by nonlinear dimensionality reduction methods; (3) parametrization of the surface using smooth meshfree (here maximum‐entropy) approximants; and (4) gluing together the patch representations by means of a partition of unity. Each patch may be viewed as a meshfree macro‐element. We exemplify the generality, flexibility, and accuracy of the proposed approach by numerically approximating the geometrically nonlinear Kirchhoff–Love theory of thin‐shells. We analyze standard benchmark tests as well as point‐set surfaces of complex geometry and topology. Copyright © 2012 John Wiley & Sons, Ltd.     

Dimensionality reduction for metabolome data using PCA, PLS, OPLS, and RFDA with differential penalties to latent variables

Dimensionality reduction is an important technique for preprocessing of high-dimensional data. Because only one side of the original data is represented in a low-dimensional subspace, useful information may be lost. In the present study, novel dimensionality reduction methods were developed that are suitable for metabolome data, where observation varies with time. Metabolomics deal with this type of data, which are often obtained in microorganism fermentation processes. However, no dimensionality reduction method that utilizes information from the original data in a positive manner has been reported to date. The ordinary dimensionality reduction methods of principal component analysis (PCA), partial least squares (PLS), orthonormalized PLS (OPLS), and regularized Fisher discriminant analysis (RFDA) were extended by introducing differential penalties to the latent variables in each class. A nonlinear extension of this approach, using kernel methods, was also proposed in the form of kernel-smoothed PCA, PLS, OPLS, and FDA. Since all of these methods are formulated as generalized eigenvalue problems, the solutions can be computed easily. These methods were then applied to intracellular metabolite data of a xylose-fermenting yeast in ethanol fermentation. Visualization in the low-dimensional subspace suggests that smoothed PCA successfully preserves the information about the time course of observations during fermentation, and that RFDA can produce high separation among different strains.