三维荧光光谱的多维偏最小二乘建模方法

将偏最小二乘方法（PLS）推广到高维的多维偏最小二乘方法（N-PLS）由于同时考虑自变量矩阵和应变量矩阵的信息,可以有效解决高维数据的建模问题,并具有较好的模型预测和推广能力。本文研究了三维荧光光谱的多维偏最小二乘建模方法,根据样本序列、激发光谱、发射光谱构造出三维立体数据,并应用N-PLS建立校正模型。对水中的有机污染物浓度综合指标COD、TOC的建模实验,表明了在建模精度方面N-PLS方法优越于常规PLS和平行因子法。     

Orthogonal least squares regression with tunable kernels

A novel technique is proposed to construct sparse regression models based on the orthogonal least squares method with tunable kernels. The proposed technique tunes the centre vector and diagonal covariance matrix of individual regressors by incrementally minimising the training mean square error using a guided random search algorithm, and it offers a state-of-the-art method for constructing very sparse models that generalise well.     

基于区间选择偏最小二乘法回归分析的煎炸老油鉴别模型

煎炸老油属于地沟油之一,长时间食用会对身体健康造成严重危害。本文首先对食用金龙鱼菜籽油过度煎炸10次,分别提取光谱信息中特征吸收峰（323、391、443nm）处的光谱吸收值。然后建立区间选择偏最小二乘法模型,提取最佳区间为5,最佳因子为7的波长区间,验证区间预测相关系数达到0．998。最后建立PKS回归方程Y1,Y2,Y3,通过交叉有效性验证Q22=-0．3461〈0．0975。提取成分t1、t2。分别得到回归方程的实际值与预测值相关系数为：323nm处,r=0．8478;391nm处,r=0．9754;443nm处,r=0．9285。     

On a least squares predictive-transform modeling methodology

A deterministic least squares (LS) predictive-transform (PT) multichannel modeling framework is presented. In a manner analogous to the development of minimum mean square error (MSE) PT, the LS PT signal model is obtained as an inherent byproduct of an optimized predictive-transform signal source “encoder”, thereby preserving the direct integration of specific data compression concepts into the basic modeling procedure that have proven very useful in the application of minimum MSE PT to coding, detection, estimation, and control. Fundamental properties of the LS PT signal model are presented, and a recursive least squares (RLS) PT modeling procedure is developed. In addition to subsuming conventional RLS signal modeling as a special case and the presence of an integrated transformation mechanism, RLS PT offers greater flexibility when independent “fading memory” weighting of both the first- and second-order sample moments is desired. Sufficient conditions for the convergence of the RLS PT parameters to their minimum MSE PT counterparts are developed. In addition, the zero mean constraint (either deterministic or stochastic) imposed on the LS PT signal model's innovation sequence is shown to provide a mechanism for mitigating the deleterious effects of a singular or near-singular data correlation matrix     

Multichannel ARMA modeling by least squares circular latticefiltering

The paper makes an attempt to develop least squares lattice algorithms for the ARMA modeling of a linear, slowly time-varying, multichannel system employing scalar computations only. Using an equivalent scalar, periodic ARMA model and a circular delay operator, the signal set for each channel is defined in terms of circularly delayed input and output vectors corresponding to that channel. The orthogonal projection of each current output vector on the subspace spanned by the corresponding signal set is then computed in a manner that allows independent AR and MA order recursions. The resulting lattice algorithm can be implemented in a parallel architecture employing one processor per channel with the data flowing amongst them in a circular manner. The evaluation of the ARMA parameters from the lattice coefficients follows the usual step-up algorithmic approach but requires, in addition, the circulation of certain variables across the processors since the signal sets become linearly dependent beyond certain stages. The proposed algorithm can also be used to estimate a process from two correlated, multichannel processes adaptively allowing the filter orders for both the processes to be chosen independently of each other. This feature is further exploited for ARMA modeling a given multichannel time series with unknown, white input     

Comparison of the linear least squares and nonlinear least squares spheres

Two important, to scientists and engineers, sphere fitting procedures, namely the linear least squares (LLS) and the non-linear least squares (NLLS) methods and their general random-error analysis are described. The first-order random errors of the center coordinates and the radius of the fitted sphere using the above mentioned procedures are derived in detail under the assumption that the variance-covariance matrix exists for the random error vector. With the additional trivariate normal error distribution assumption, the Maximum Likelihood (ML) estimators and their standard deviations are also derived. The effectiveness of these procedures are studied through computer stimulation.     

Maximum likelihood, least squares, and penalized least squares for PET

The EM algorithm is the basic approach used to maximize the log likelihood objective function for the reconstruction problem in positron emission tomography (PET). The EM algorithm is a scaled steepest ascent algorithm that elegantly handles the nonnegativity constraints of the problem. It is shown that the same scaled steepest descent algorithm can be applied to the least squares merit function, and that it can be accelerated using the conjugate gradient approach. The experiments suggest that one can cut the computation by about a factor of 3 by using this technique. The results are applied to various penalized least squares functions which might be used to produce a smoother image.     

Human motion prediction using optimized sliding window polynomial fitting and recursive least squares

Human motion prediction is a critical issue in human-robot collaboration (HRC) tasks. In order to reduce thelocal error caused by the limitation of the capture range and sampling frequency of the depth sensor, a hybrid human motion prediction algorithm, optimized sliding window polynomial fitting and recursive least squares (OSWPF-RLS) was proposed. The OSWPF-RLS algorithm uses the human body joint data obtained under the HRC task as input, and uses recursive least squares (RLS) to predict the human movement trajectories within the time window. Then, the optimized sliding window polynomial fitting (OSWPF) is used to calculate the multi-step prediction value, and the increment of multi-step prediction value was appropriately constrained. Experimental results show that compared with the existing benchmark algorithms, the OSWPF-RLS algorithm improved the multi-     

Hysteresis modeling and compensation of a piezostage using least squares support vector machines

Hysteresis effect degrades the positioning accuracy of a piezostage, and hence the nonlinearity has to be suppressed for ultrahigh-precision positioning applications. This paper extends least squares support vector machines (LS-SVM) to the domain of hysteresis modeling and compensation for a piezostage driven by piezoelectric stack actuators. A LS-SVM model is proposed and trained by introducing the current input value and input variation rate as the input data set to formulate a one-to-one mapping. By adopting the radial basis function (RBF) as kernel function, the LS-SVM model only has two free hyperparameters, which are optimally tuned by resorting to Bayesian inference framework. The effectiveness of the presented model is verified as compared with two state-of-the-art approaches, namely, Bouc–Wen model and modified Prandtl–Ishlinskii (MPI) model. In addition, the LS-SVM inverse model based feedforward control combined with an incremental proportional–integral–derivative (PID) feedback control is designed to compensate the hysteresis nonlinearity. Experimental results show that the LS-SVM model based hybrid control scheme is superior to the Bouc–Wen model and MPI model based ones as well as either of the stand-alone controllers. The rate-dependent hysteresis is suppressed to a negligible level, which validates the effectiveness of the constructed controller. Owing to a simple procedure, the proposed LS-SVM based approach can be applied to modeling and control of other types of hysteretic systems as well.     

Fault analysis and research of wireless sensor network based on kernel partial least squares

With the development of intelligent and networked sensor technology,wireless sensor networks were widely used in human life and commercial fields,because wireless sensor network nodes usually only carry limited resources,it is prone to failures due to insufficient resources,the accurate and timely fault diagnosis of WSN nodes can ensure the reliability of information,thus improving the maintainability of WSN and prolonging the service life of WSN.A method of using kernel partial least squares has been proposed to predict the fault reasons,the method overcomes the defects of traditional linear regression method and the nonlinear high dimensional space for data analysis.Through many experiments,the method can absorb the characteristics of canonical correlation analysis and principal component analysis method,provide a more thorough and rich content analysi,that the reason of the fault can be predicted effectively.     

A new approach for nonlinear distortion correction in endoscopicimages based on least squares estimation

Images captured with a typical endoscope show spatial distortion, which necessitates distortion correction for subsequent analysis. In this paper, a new methodology based on least squares estimation is proposed to correct the nonlinear distortion in the endoscopic images. A mathematical model based on polynomial mapping is used to map the images from distorted image space onto the corrected image space. The model parameters include the polynomial coefficients, distortion center, and corrected center. The proposed method utilizes a line search approach of global convergence for the iterative procedure to obtain the optimum expansion coefficients. A new technique to find the distortion center of the image based on curvature criterion is presented. A dual-step approach comprising token matching and integrated neighborhood search is also proposed for accurate extraction of the centers of the dots contained in a rectangular grid, used for the model parameter estimation. The model parameters were verified with different grid patterns. The distortion-correction model is applied to several gastrointestinal images and the results are presented. The proposed technique provides high-speed response and forms a key step toward online camera calibration, which is required for accurate quantitative analysis of the images.     

A new recursive pseudo least squares algorithm for ARMA filteringand modeling. I

This study is based on the observation that if the bootstrapping is combined with different parameterizations of the ARMA (autoregressive moving average) process, then different linearized problems are obtained for the underlying nonlinear ARMA modeling problem. In this part, a specific parameterization termed the predictor space representation for an ARMA process, which decouples the estimation for the AR and the MA parameters, is used. A vector space formalism for the given data case is then defined, and the least-squares ARMA filtering problem is interpreted in terms of projection operations on some linear spaces. A new projection operator update formula, which is particularly suited for the underlying problem, is then used in conjunction with the vector space formalism to develop a computationally efficient pseudo-least-squares algorithm for ARMA filtering. It is noted that these recursions can be put in the form of a filter structure     

A new recursive pseudo least squares algorithm for ARMA filteringand modeling. II

For pt.I see ibid., vol.40, no.11, p.2766-74 (Nov. 1992). A recursive algorithm for ARMA (autoregressive moving average) filtering has been developed in a companion paper. These recursions are seen to have a lattice-like filter structure. The ARMA parameters, however, are not directly available from the coefficients of this filter. The problem of identification of the ARMA model from the coefficients of this filter is addressed here. Two new update relations for certain pseudoinverses are derived and used to obtain a recursive least squares algorithm for AR parameter estimation. Two methods for the estimation of the MA parameters are also presented. Numerical results demonstrate the usefulness of the proposed algorithms     

最小二乘与加权最小二乘空域矩阵滤波器设计

空域矩阵滤波器是一种新的信号处理技术,通过一个滤波矩阵与接收到的阵列数据相乘,可实现保留通带目标信号,抑制阻带干扰的目的.本文主要研究了最小二乘和加权最小二乘两类的空域矩阵滤波器.给出了空域滤波器设计基本原理,通过最优化问题得出了最优解.最小二乘空域矩阵滤波器是加权系数为1的加权加权最小二乘空域矩阵滤波器的特列.由加权最小二乘迭代仿真结果可以看出,迭代次数的增加使滤波器阻带响应极大值逐渐变小,可实现恒定阻带抑制效果,设计效率较高.     

基于改进的偏最小二乘法的LIBS钢液成分定量分析

为了研究激光诱导击穿光谱技术基体效应对其测量精确度的影响,采用改进的偏最小二乘法进行数据预测,以有效降低基体效应对待测元素的影响。通过与单变量定标和偏最小二乘模型定标进行对比研究可知,待测元素Mn和Si的定标曲线的拟合度分别从0.991和0.993提高到了0.996和0.997,对于验证样品的预测相对误差也分别从6.231%,6.912%下降到了5.510%和6.125%。结果表明,采用改进的偏最小二乘法可以有效减小基体效应,定标精度有较明显提高,对分析性能有了较大的提高。     

Selfperturbing recursive least squares algorithm with fast tracking capability

A novel recursive least squares (RLS) type algorithm with a selfperturbing action is devised. The algorithm possesses a fast tracking capability in itself because its adaptation gain is automatically revitalised through perturbation of the covariance update dynamics by the filter output error square when it encounters sudden parameter changes. Furthermore, the algorithm converges to the true parameter values in stationary environments.<>     

An introduction to the Gaussian least squares approximation and its application in signal processing and system modeling

At the end of the 18th century C.F. Gauss introduced the idea of least squares approximation. This idea is still of fundamental importance today, 200 years later, and has led to the development of many related techniques in signal processing and system modeling. In this paper, a tutorial discussion is given on least squares approximation. Related techniques are presented with examples. These include generalized Fourier analysis, deconvolution and linear prediction, all of which are shown to be closely related to Gauss's original idea.     

Fast sequential least squares design of FIR filters with linearphase

The authors propose a fast adaptive least-squares algorithm for linear-phase finite-impulse-response (FIR) filters. The algorithm requires 10m multiplications per data point where m is the filter order. This reduced computation stems from the fast adaptive forward-backward least-squares method. Both linear-phase cases i.e. with constant phase delay and with constant group delay, are examined. Simulation results demonstrate that the proposed algorithm is superior to the least-mean-squares gradient algorithm and the averaging scheme used for the modified fast Kalman algorithm     

Exponentially weighted least squares identification of time-varyingsystems with white disturbances

The paper is devoted to the stochastic analysis of recursive least squares (RLS) identification algorithms with an exponential forgetting factor. A persistent excitation assumption of a conditional type is made that does not prevent the regressors from being a dependent sequence. Moreover, the system parameter is modeled as the output of a random-walk type equation without extra constraints on its variance. It is shown that the estimation error can be split into two terms, depending on the parameter drift and the disturbance noise, respectively. The first term turns out to be proportional to the memory length of the algorithm, whereas the second is proportional to the inverse of the same quantity. Even though these dependence laws are well known in very special mathematical frameworks (deterministic excitation and/or independent observations), this is believed to be the first contribution where they are proven in a general dependent context. Some idealized examples are introduced in the paper to clarify the link between generality of assumptions and applicability of results in the developed analysis