基于多元曲线分辨-交替最小二乘-紫外光谱监控地黄炮制过程

称取若干地黄样品,用去离子水定容、超声震荡、过滤后测定紫外(UV)光谱.采用多元曲线分辨-交替最小二乘法(MCR-ALS)分析测得的UV光谱数据,提取出3种纯组分的UV光谱,并计算混合体系中其相对浓度.结果表明,从混合组分中提取的UV光谱可以用来将炮制过程中混合组分简单地定性,根据这些组分相对浓度升降的变化趋势,监控地黄炮制过程.确定炮制终点.MCR-ALS-UV法为监控地黄炮制过程及确定炮制终点提供了新途径.     

统一最小二乘规则的单幅图像超分辨算法

基于机器学习的超分辨方法是一个很有发展前景的单幅图像超分辨方法,稀疏表达和字典学习是其中的研究热点。针对比较耗时的字典训练与恢复精度不高图像重建,从减小低分辨率(LR)和高分辨率(HR)特征空间之间差异性的角度提出了一种使用迭代最小二乘字典学习算法(ILS-DLA),并使用锚定邻域回归(ANR)进行图像重建的单幅图像超分辨算法。迭代最小二乘法的整体优化过程极大地缩短了低分辨字典/高分辨字典的训练时间,它采用了与锚定邻域回归相同的优化规则,有效地保证了字典学习和图像重建在理论上的一致性。实验结果表明,所提算法的字典学习效果比K-均值奇异值分解(K-SVD)和Beta过程联合字典学习(BPJDL)等算法更高效,图像重建的效果也优于许多优秀的超分辨算法。     

最小二乘法集合成员辨识

该文研究集合成员辨识方法,并利用最小二乘法（LS method)进行集合成员辨识。这个方法的特点是辨识在时域进行,先利用小二乘法作为计算工具,辨识出实际系统的标称模型,然后求出可行参数集。本方法计算量小,可行参数集比文献[3]的要小。     

基于最小二乘法的数字水印方法

提出一种基于最小二乘法的数字水印方法。该方法通过对线性方程组数值求解的过程实现对数字水印的嵌入和提取,并通过纠错码提高数字水印对攻击的抵抗力。实验数据表明该方法对于多种对数字水印的攻击有相当强的抵抗能力,是一种有较好的鲁棒性的数字水印方法。     

最小二乘法分段直线拟合

曲线拟合是图像分析中非常重要的描述符号。最常用的曲线拟合方法是最小二乘法,然而一般的最小二乘法有一定的局限性,已经有不少学者对其进行了一些改进。进一步对最小二乘法进行改进,提出一种新的分段直线拟合算法来代替多项式曲线拟合,以达到简化数学模型的建立和减少计算的目的,使其能够更好地对点序列进行拟合。     

基于LU分解和交替最小二乘法的分布式奇异值分解推荐算法

针对当前分布式潜在因子推荐算法存在时间复杂度较高、运行时间较长的问题,文中提出基于LU分解和交替最小二乘法(ALS)的分布式奇异值分解推荐算法,利用ALS利于分布式求解目标函数的特点,提出网格状分布式粒度分割策略,获取相互独立不相关的特征向量.在更新特征矩阵时,使用LU分解求逆矩阵,加快算法的运行速度.在KDD CUP 2012 Track1中的腾讯微博数据集上的实验表明,文中算法在确保一定推荐精度的前提下,大幅提升推荐速度和算法效率.     

工程计算中最小二乘法的应用及研究

现代工业生产和工程计算中,往往需要对大量实验或调查数据进行分析、整理,寻求相关量之间的关系。拟合数据的最小二乘法是解决此类问题的常用手段。本文将对此方法从理论上进行分析并加以应用,比较计算结果给出数据拟合时要注意的两个问题。     

最小二乘法参数辨识及其微机实现

最小二乘法是系统参数辨识中最基本、最成熟的方法,在微机上实现最小二乘法辨识参数,使参数辨识和建模得到了从理论到实际应用的飞跃。     

最小二乘法在企业信用评估中的应用

本文介绍了数据拟舍的最小二乘法的基本概念,制定企业信用评分标准,利用数据拟合的最小二乘法,基于作者在福建工商系统工作中使用的案件违法数据,对企业进行信用评估。     

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.     

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.     

基于最小二乘法的高维目标减少算法

多目标进化算法在许多领域有广泛的应用,大部分文献都只针对二维与三维的测试问题,目标减少成为高维优化的热点之一．本文从决策者角度考虑冗余目标问题,提出了基于最小二乘法的目标减少算法（ORLSM）,该方法将每个目标函数分段拟合为若干条直线段,然后比较各直线段之间的斜率来确定最冗余目标对,进而确定冗余目标．同时针对目标减少前后个体支配关系的变化情况,提出了支配关系改变率的评价方法．通过3个测试函数,分别用逆世代距离（IGD）、支配关系改变率（CDR）和时间效率3个方面,对同类的两个算法进行了性能测试．结果表明,ORLSM在总体上具有最好的性能：CDR和IGD具有基本一致的评价结果．     

Fitting a least squares piecewise linear continuous curve in two dimensions

An optimal piecewise linear continuous fit to a given set of n data points D = {(x_i, y_i) : 1 ≤ i ≤ n} in two dimensions consists of a continuous curve defined by k linear segments {L₁, L₂,…,L_k} which minimizes a weighted least squares error function with weight w_i at (x_i, y_i), where k ≥ 1 is a given integer. A key difficulty here is the fact that the linear segment L_j, which approximates a subset of consecutive data points D_j ⊂ D in an optimal solution, is not necessarily an optimal fit in itself for the points D_j. We solve the problem for the special case k = 2 by showing that an optimal solution essentially consists of two least squares linear regression lines in which the weight w_j of some data point (x_j, y_j) is split into the weights λw_j and (1 − λ)w_j, 0 ≤ λ ≤ 1, for computations of these lines. This gives an algorithm of worst-case complexity O(n) for finding an optimal solution for the case k = 2.     

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.     

Curve-skeleton extraction using iterative least squares optimization

A curve skeleton is a compact representation of 3D objects and has numerous applications. It can be used to describe an object's geometry and topology. In this paper, we introduce a novel approach for computing curve skeletons for volumetric representations of the input models. Our algorithm consists of three major steps: 1) using iterative least squares optimization to shrink models and, at the same time, preserving their geometries and topologies, 2) extracting curve skeletons through the thinning algorithm, and 3) pruning unnecessary branches based on shrinking ratios. The proposed method is less sensitive to noise on the surface of models and can generate smoother skeletons. In addition, our shrinking algorithm requires little computation, since the optimization system can be factorized and stored in the pre-computational step. We demonstrate several extracted skeletons that help evaluate our algorithm. We also experimentally compare the proposed method with other well-known methods. Experimental results show advantages when using our method over other techniques.     

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.     

Almost sure convergence of least squares estimates for regular multivariate ARX systems

We establish almost sure convergence of least squares estimates for general multivariate ARX(p, s) systems, with stochastic input signal. Results of strong consistency and speed of convergence are obtained with a regularity assumption on the AR part of the system.     

Geometric properties of partial least squares for process monitoring

Projection to latent structures or partial least squares (PLS) produces output-supervised decomposition on input X, while principal component analysis (PCA) produces unsupervised decomposition of input X. In this paper, the effect of output Y on the X-space decomposition in PLS is analyzed and geometric properties of the PLS structure are revealed. Several PLS algorithms are compared in a geometric way for the purpose of process monitoring. A numerical example and a case study are given to illustrate the analysis results.