非线性偏最小二乘建模方法及在近红外光谱建模上的应用

偏最小二乘算法(PLS)是常用的线性光谱建模方法。针对汽油在线调合中具有非线性特点的辛烷值、干点等属性应用PLS方法建立模型误差较大问题,本文提出了残差-递阶偏最小二乘的建模方法,该方法对已经提取成分后的自变量中剩余的信息再提取主成分,并将该主成分作为新的自变量参与回归建模。仿真验证结果表明:残差-递阶偏最小二乘方法建立的模型中验证集的样本数据误差均在正负0.2之间。残差-递阶偏最小二乘方法与偏最小二乘、递阶偏最小二乘叫-PLS)两种方法比较,残差-递阶偏最小二乘建立的模型有的更高的精度和模型适应性。     

结合两种回归模型的图像插值算法研究

为了更好地保护图像的局部结构和提高图像插值算法的鲁棒性,结合基于几何对偶性的普通最小二乘和基于非局部均方的加权最小二乘来统计稳态区域形态,并基于该模型提出了一种改进的图像插值算法。算法首先采用非局部均方估计加权最小二乘模型系数,同时用核岭回归作为正则化项进行系数修正,考虑到核岭回归的有偏性,将基于边缘的普通最小二乘模型作为正则化项引进图像插值算法中,并对正则化参数进行自适应调整。与采用单一回归分析的插值算法相比较,该算法不但有效抑制了插值图像的边缘模糊和锯齿现象,而且插值结果具有较高的峰值信噪比和结构相似度。     

PLS-LSSVM模型在锌净化中的应用

在锌净化除钴过程中,生产数据存在噪声且变量间具有多重相关性,从而难以准确预测钴离子浓度。为此,采用偏最小二乘方法去除数据中的噪声,降低各参数间的多重相关性。通过为不同时期的样本数据赋予不同的权值,提高了最小二乘支持向量机(LSSVM)模型预测的准确性。利用改进的粒子群优化算法优化选择LSSVM模型的惩罚因子和核函数参数,以避免人为选择参数的盲目性。仿真结果表明,PLS- LSSVM模型的预测精度高于偏最小二乘回归和LSSVM。     

偏最小二乘法中主成分数确定的新方法

目的：合理地确定偏最小二乘法中的主成分数,方法：基于对 加权原理建立了适用于矩阵元素缺损数据的加权偏小二乘算法,将此算法应用于按矩阵元素分组的交互证实（Cross-validation),根据最大熵原理采用方差平方和σ2（自变量短阵残差的平方和／自由度）作为主成分数的判据,结果与结论：通过对Monte-Carlo法产生的多组分光光度数据进行计算,与常规的偏最小二乘法相比更加符合理论值,表明本算法较好地解决了偏最小二乘法中主成分数的确定问题。     

基于广义惩罚加权最小二乘的低剂量CT重建方法

针对低剂量CT成像问题,本文提出了一个基于广义惩罚加权最小二乘的低剂量CT重建方法,并在一定条件下建立了算法的全局收敛性定理.首先对投影数据进行统计建模构建广义加权最小二乘保真项,并且将二次先验信息引入投影数据的恢复过程中,从而达到抑制噪声的目的 ,最后使用经典的滤波反投影算法对恢复后的投影数据进行解析重建.实验结果表...     

融入深度学习的偏最小二乘优化方法

偏最小二乘在多元变量分析中得到了广泛的应用。但偏最小二乘方法内部采用主成分分析,不能充分表达数据的非线性特征,对非线性数据的预测精度较低。提出了一种融入深度学习的偏最小二乘优化方法,该方法利用深度学习的稀疏自编码器对特征空间提取非线性结构,将提取的特征成分取代偏最小二乘中的成分,从而形成能适应非线性的模型。分别采用大承气汤、麻杏石甘汤、葛根芩连汤和UCI数据集的数据进行分析处理,实验结果表明,融入深度学习的偏最小二乘优化方法能较好反映中医药数据的特征。     

二维非负偏最小二乘在人脸识别中的应用

传统的基于统计的子空间学习算法如主成分分析,通过学习只能得到一系列特征脸,忽略了人脸识别中重要的局部信息（如眼睛、鼻子）。而利用到类别信息的算法如线性判别分析,也会因为小样本问题而有所影响。为了解决这些问题,结合二维偏最小二乘与非负矩阵分解的非负性思想提出二维非负偏最小二乘(Two-Dimensional Nonnegative Partial Least Squares,2DNPLS)算法。其核心思想是在提取人脸特征时加入了非负性约束,使得2DNPLS不仅拥有偏最小二乘算法加入类别信息带来的分类效果,还保留了图像矩阵的内部结构信息,而且还使得到的基矩阵具有非负的局部的可解释性。在ORL,Yale人脸库中的实验结果表明,该算法从时间上和识别率上均优于人脸识别的主流算法。     

非线性特征提取和LSSVM在化工过程故障诊断中应用

提出利用非线性特征提取（核主成分分析（KPCA）和核独立成分分析）消除数据的不相关性,降低维数。核主成分分析利用核函数把输入数据映射到特征空间,进行线性主成分分析计算提取特征;核独立成分分析在KPCA白化空间进行线性独立成分分析（ICA）变换提取独立成分。提取的特征作为最小二乘支持向量机分类器的输入,构建融合非线性特征提取和最小二乘支持向量机的智能故障分类方法。研究了该方法应用到某石化企业润滑油生产过程的故障诊断中的有效性和可行性。     

基于深度去噪核映射的长期预测模型

针对最小二乘支持向量机核函数结构较浅对其长期预测模型精度的限制,采用深度学习中逐层特征提取的思想,提出基于深度去噪核映射的最小二乘支持向量机长期预测模型.该模型通过深度核网络的逐层变换,将样本数据映射到深度特征空间,从而有效提高其长期预测的精度.此外,为了提高模型对含高噪声数据的拟合性能,将去噪算法融入深度核网络的训练过程中,并通过反向传播算法对核网络参数进行整体微调.标准数据集及实际工业数据的仿真实验结果表明,所提方法能够有效提取数据中蕴含的特征信息,提高预测模型的精度.     

融合随机森林的偏最小二乘法及其中医药数据分析

偏最小二乘方法在多元线性回归建模中存在着诸多优势,但其本质还是线性回归,难以满足中医药非线性的特性。而随机森林构建的回归模型是由多个多元线性片段构成,对非线性数据有良好的拟合效果。本文提出了一种融合随机森林的偏最小二乘方法,该方法主要是利用PLS不断提取主成分并累计,利用随机森林算法将这些主成分分别与原始被解释变量不断构建多棵决策树,直到满足精度条件为止。分别采用麻杏石甘汤君药止咳、平喘和UCI数据集的数据进行分析处理,实验结果表明,融合随机森林的偏最小二乘分析方法对中医药数据有很好的适应性。     

A Fast Heuristic Global Learning Algorithm for Multilayer Neural Networks

This paper presents a novel Heuristic Global Learning (HER-GBL) algorithm for multilayer neural networks. The algorithm is based upon the least squares method to maintain the fast convergence speed, and the penalized optimization to solve the problem of local minima. The penalty term, defined as a Gaussian-type function of the weight, is to provide an uphill force to escape from local minima. As a result, the training performance is dramatically improved. The proposed HER-GBL algorithm yields excellent results in terms of convergence speed, avoidance of local minima and quality of solution.     

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。     

局部近邻标准化偏最小二乘的多模态间歇过程故障检测

本文针对多模态间歇过程数据多中心和模态方差差异明显的问题,提出了一种基于局部近邻标准化偏最小二乘方法.首先,采用统计模量方法处理间歇过程数据,再利用局部近邻标准化方法将统计模量后的训练数据进行高斯化处理,建立偏最小二乘监控模型,确定控制限;然后,同样对统计模量后的测试数据进行局部近邻标准化处理,再计算测试数据的高斯偏最小二乘监控指标,进行过程监视及故障检测.最后,通过数值实例和青霉素发酵过程验证方法有效性.实验结果表明所提方法解决了故障样本近邻集跨模态问题,对多模态数据具有更好的故障检测能力.     

飞机颤振模态参数辨识的频域广义整体最小二乘算法

采用一种适用于噪声环境的广义整体最小二乘算法,准确地辨识飞机的颠振模态参数．该算法结合有理传递函数模型,将带噪系统的辨识问题转化为广义整体最小二乘问题．利用线性的广义奇异值分解求解模型系数,避免了非线性优化的复杂计算．通过迭代法更新加权项,获得了接近于极大似然估计的辨识效果．最后利用试飞试验数据辨识飞机的模态参数,验证了该方法的有效性．     

A majorization algorithm for simultaneous parameter estimation in robust exploratory factor analysis

A new approach for fitting the exploratory factor analysis (EFA) model is considered. The EFA model is fitted directly to the data matrix by minimizing a weighted least squares (WLS) goodness-of-fit measure. The WLS fitting problem is solved by iteratively performing unweighted least squares fitting of the same model. A convergent reweighted least squares algorithm based on iterative majorization is developed. The influence of large residuals in the loss function is curbed using Huber’s criterion. This procedure leads to robust EFA that can resist the effect of outliers in the data. Applications to real and simulated data illustrate the performance of the proposed approach.     

Recursive exponentially weighted PLS and its applications to adaptive control and prediction

A new and fast recursive, exponentially weighted PLS algorithm which provides greatly improved parameter estimates in most process situations is presented. The potential of this algorithm is illustrated with two process examples: (i) adaptive control of a two by two simulated multivariable continuous stirred tank reactor; and (ii) updating of a prediction model for an industrial flotation circuit. The performance of the recursive PLS algorithm is shown to be much better than that of the recursive least squares algorithm. The main advantage of the recursive PLS algorithm is that it does not suffer from the problems associated with correlated variables and short data windows. During adaptive control, it provided satisfactory control when the recursive least squares algorithm experienced difficulties (i.e., ‘blew’ up) due to the ill-conditioned covariance matrix, (X^TX)_t. For the industrial soft sensor application, the new algorithm provided much improved estimates of all ten response variables.     

水下基于层级的约束加权最小二乘时差定位

针对距离无关定位算法与距离相关定位算法中定位精度的问题,分析了误差对定位性能的影响及影响误差的因素,在最小二乘定位算法的基础上,提出了一种基于层级结构的约束加权最小二乘时差定位算法。该算法利用AUV( Autonomous Underwater Vehicle)对水下节点进行分层,使得具有层级和深度信息的信标节点升降至未知节点所在平面,从而将三维定位转换为二维定位,降低了算法的复杂度,同时避免了距离未知节点较远的信标节点对定位的影响,提高了测距精度,使定位误差进一步降低。仿真结果表明,该算法在位置误差较小的情况下,可以明显地提高定位精度。     

A revisit to block and recursive least squares for parameter estimation

In this paper, the classical least squares (LS) and recursive least squares (RLS) for parameter estimation have been re-examined in the light of the present day computing capabilities. It has been demonstrated that for linear time-invariant systems, the performance of blockwise least squares (BLS) is always superior to that of RLS. In the context of parameter estimation for dynamic systems, the current computational capability of personal computers are more than adequate for BLS. However, for time-varying systems with abrupt parameter changes, standard blockwise LS may no longer be suitable due to its inefficiency in discarding “old” data. To deal with this limitation, a novel sliding window blockwise least squares approach with automatically adjustable window length triggered by a change detection scheme is proposed. Two types of sliding windows, rectangular and exponential, have been investigated. The performance of the proposed algorithm has been illustrated by comparing with the standard RLS and an exponentially weighted RLS (EWRLS) using two examples. The simulation results have conclusively shown that: (1) BLS has better performance than RLS; (2) the proposed variable-length sliding window blockwise least squares (VLSWBLS) algorithm can outperform RLS with forgetting factors; (3) the scheme has both good tracking ability for abrupt parameter changes and can ensure the high accuracy of parameter estimate at the steady-state; and (4) the computational burden of VLSWBLS is completely manageable with the current computer technology. Even though the idea presented here is straightforward, it has significant implications to virtually all areas of application where RLS schemes are used.     

Kernel continuum regression

The continuum regression technique provides an appealing regression framework connecting ordinary least squares, partial least squares and principal component regression in one family. It offers some insight on the underlying regression model for a given application. Moreover, it helps to provide deep understanding of various regression techniques. Despite the useful framework, however, the current development on continuum regression is only for linear regression. In many applications, nonlinear regression is necessary. The extension of continuum regression from linear models to nonlinear models using kernel learning is considered. The proposed kernel continuum regression technique is quite general and can handle very flexible regression model estimation. An efficient algorithm is developed for fast implementation. Numerical examples have demonstrated the usefulness of the proposed technique.