2D shape deformation using nonlinear least squares optimization

This paper presents a novel 2D shape deformation algorithm based on nonlinear least squares optimization. The algorithm aims to preserve two local shape properties: the Laplacian coordinates of the boundary curve and the local area of the shape interior, which are together represented in a non-quadratic energy function. An iterative Gauss–Newton method is used to minimize this nonlinear energy function. The result is an interactive shape deformation system that can achieve physically plausible results that are difficult to achieve with previous linear least squares methods. In addition to this algorithm that preserves local shape properties, we also introduce a scheme to preserve the global area of the shape, which is useful for deforming incompressible objects.     

基于偏最小二乘回归的性别识别

在现有研究中,人脸图像往往局限于简单的受控场景,忽略了自然场景中光照、姿态、表情等因素的影响.针对此问题,重点研究了自然场景下的性别识别问题,并提出了基于偏最小二乘回归(PLS)的性别识别算法.在人脸特征提取阶段,提出了一种新的特征描述算子多尺度方差局部二元模式(MBV-LBP),并与多尺度局部二元模式(MB-LBP)结合作为最终的人脸特征表示,采用PLS模型同时完成特征降维和性别识别,简化了计算过程.通过在LFW数据库和一个Web人脸图像库上进行实验,实验结果表明了算法的优越性.     

An iterative algorithm for least squares problem in quaternionic quantum theory

Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AXB=E that is appropriate when there is error in the matrix E. In this paper, by means of real representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, which is different from that in [T. Jiang, L. Chen, Algebraic algorithms for least squares problem in quaternionic quantum theory, Comput. Phys. Comm. 176 (2007) 481-485; T. Jiang, M. Wei, Equality constrained least squares problem over quaternion field, Appl. Math. Lett. 16 (2003) 883-888], and derive an iterative method for finding the minimum-norm solution of the QLS problem in quaternionic quantum theory.     

Interactive mesh deformation using equality-constrained least squares

Mesh deformation techniques that preserve the differential properties have been intensively studied. In this paper, we propose an equality-constrained least squares approach for stably deforming mesh models while approximately preserving mean curvature normals and strictly satisfying other constraints such as positional constraints. We solve the combination of hard and soft constraints by constructing a typical least squares system using QR decomposition. A well-known problem of hard constraints is over-constraints. We show that the equality-constrained least squares approach is useful for resolving such over-constrained situations. In our framework, the rotations of mean curvature normals are treated using the logarithms of unit quaternions in . During deformation, mean curvature normals can be rotated while preserving their magnitudes. In addition, we introduce a new modeling constraints called rigidity constraints and show that rigidity constraints can effectively preserve the shapes of feature regions during deformation. Our framework achieves good performance for interactive deformation of mesh models.     

Face recognition using partial least squares components

The paper considers partial least squares (PLS) as a new dimension reduction technique for the feature vector to overcome the small sample size problem in face recognition. Principal component analysis (PCA), a conventional dimension reduction method, selects the components with maximum variability, irrespective of the class information. So PCA does not necessarily extract features that are important for the discrimination of classes. PLS, on the other hand, constructs the components so that the correlation between the class variable and themselves is maximized. Therefore PLS components are more predictive than PCA components in classification. The experimental results on Manchester and ORL databases show that PLS is to be preferred over PCA when classification is the goal and dimension reduction is needed.     

An iterative algorithm for a least squares solution of a matrix equation

In this article, we propose an iterative algorithm to compute the minimum norm least-squares solution of AXB+CYD=E, based on a matrix form of the algorithm LSQR for solving the least squares problem. We then apply this algorithm to compute the minimum norm least-squares centrosymmetric solution of min _X ‖AXB?E‖ _F . Numerical results are provided to verify the efficiency of the proposed method.     

Learning-based super resolution using kernel partial least squares

In this paper, we propose a learning-based super resolution approach consisting of two steps. The first step uses the kernel partial least squares (KPLS) method to implement the regression between the low-resolution (LR) and high-resolution (HR) images in the training set. With the built KPLS regression model, a primitive super-resolved image can be obtained. However, this primitive HR image loses some detailed information and does not guarantee the compatibility with the LR one. Therefore, the second step compensates the primitive HR image with a residual HR image, which is the subtraction of the original and primitive HR images. Similarly, the residual LR image is obtained from the down-sampled version of the primitive HR and original LR image. The relation of the residual LR and HR images is again modeled with KPLS. Integration of the primitive and the residual HR image will achieve the final super-resolved image. The experiments with face, vehicle plate, and natural scene images demonstrate the effectiveness of the proposed approach in terms of visual quality and selected image quality metrics.     

Orthogonal vs. uncorrelated least squares discriminant analysis for feature extraction

In this paper, a new discriminant analysis for feature extraction is derived from the perspective of least squares regression. To obtain great discriminative power between classes, all the data points in each class are expected to be regressed to a single vector, and the basic task is to find a transformation matrix such that the squared regression error is minimized. To this end, two least squares discriminant analysis methods are developed under the orthogonal or the uncorrelated constraint. We show that the orthogonal least squares discriminant analysis is an extension to the null space linear discriminant analysis, and the uncorrelated least squares discriminant analysis is exactly equivalent to the traditional linear discriminant analysis. Comparative experiments show that the orthogonal one is more preferable for real world applications.     

Rotational fluid flow using a least squares collocation technique

A potential theory approach for incompressible viscous flow which leads to the biharmonic equation is first developed. A numerical least squares collocation technique using fundamental singular solutions of the biharmonic equation is then applied to a rotational flow problem with moving boundaries that produce discontinuous boundary conditions associated with the biharmonic. It is shown that the least squares technique smoothes out local disturbances in boundary data of the type which are likely to present difficulties to the more commonly used boundary element method. A compact computer program for the method and the results for the problem of a rectangular channel with one moving boundary are included along with an experimental verification of the results using the thin plate bending analogy.     

小波分析和偏最小二乘法相结合用于示波计时电位同时测定铅和铊中的研究

提出了基于小波分析和偏最小二乘(Partial Least Squares,PLS)基础上的化学计量学方法用于示波计时电位同时测定铅和铊的研究。利用小波变换可方便地从dE/dt-E信号中滤噪,提取与去极剂浓度变化有关的信号,获得利于多组分测定的示波图。该方法为示波过程分析奠定了一定的基础。     

基于最小二乘平滑算法的时变信道盲辨识

针对基展开模型的时变信道盲辨识问题,提出了联合阶数估计的最小二乘平滑算法.该算法充分利用其投影误差矩阵包含的时变信道阶数和系数信息,在信道辨识前先进行阶数精确估计,克服了该子空间类盲辨识方法对信道阶数敏感的缺点,改善了辨识效果;与线性预测类方法相比,该方法不需要知道输入信号的统计特性.理论推导和仿真结果验证了该算法的有效性.     

Stochastic adaptive control using a modified least squares algorithm

Recent papers on stochastic adaptive control have established global convergence for algorithms using a stochastic approximation iteration. However, to date, global convergence has not been established for algorithms incorporating a least squares iteration. This paper establishes global convergence for a slightly modified least squares stochastic adaptive control algorithm. It is shown that, with probability one, the algorithm will ensure that the system inputs and outputs are sample mean square bounded and the mean square output tracking error achieves its global minimum possible value for linear feedback control.     

Mixed operator problems using least squares finite element collocation

A finite element method based on least squares collocation on an element is formulated for problems of mixed type. The least squares method is developed using an incomplete quintic (C¹) element and overdetermined element collocation equations. Numerical experiments are conducted for the classical Tricomi equation, and the accuracy of computed solutions is examined at points in elliptic and hyperbolic subdomains.     

小波分析和偏最小二乘法相结合用于示波计时电位同时测定铅和铊中的研究

提出了基于小波分析和偏最小二乘（Partal Least Squares,PLS)基础上的化学计量学方法用于示波计时电位同时测定铅和铊的研究。利用小波变换可方便地从dE/dt-E信号中滤噪,提取与去极剂浓度变化有关的信号,获得利于多组分测定的示波图。该方法为示波过程分析奠定了一定的基础。     

一种用于数据校正的最小二乘与准最小二乘组合方法

过程系统的控制与优化要求可靠的过程数据。通过测量得到的过程数据含有随机误差和过失误差,采用数据校正技术可有效地减小过程测量数据的误差,从而提高过程控制与优化的准确性。针对传统基于最小二乘的数据校正方法:和基于准最小二乘的鲁棒数据校正方法:,分析了它们的优缺点,并提出了一种最小二乘与准最小二乘组合方法:。该方法:先采用准最小二乘估计器检测过失误差并剔除,然后再采用最小二乘估计器进行数据校正,可以综合前两种方法:各自的优点,使得数据校正结果:更加准确。将提出最小二乘与准最小二乘组合方法:应用于线性与非线性系统的数据校正中,通过校正结果:的比较说明此方法:的具有较好的过失误差检测能力和较准确的数据校正结果:。最后将此方法:应用于实际过程系统空气分离流程的数据校正中,结果:说明了此方法:的有效性。     

Approximate multi-objective optimization using conservative and feasible moving least squares method: application to automotive knuckle design

The original version of the moving least squares method (MLSM) does not always ensure solution feasibility for nonlinear and/or non-convex functions in the context of meta-model-based approximate optimization. The paper explores a new implementation of MLSM that ensures the conservative feasibility of Pareto optimal solutions in non-dominated sorting genetic algorithm (NSGA-II)-based approximate multi-objective optimization. We devised a ‘conservative and feasible MLSM’ (CF-MLSM) to realize the conservativeness and feasibility of multi-objective Pareto optimal solutions for both unconstrained and constrained problems. We verified the usefulness of our proposed approach by exploring strength-based sizing optimization of an automotive knuckle component under bump and brake loading constraints.