A partial least-squares regression approach to land use studies in the Suzhou-Wuxi-Changzhou region

In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically independent. But in fact, they have the tendency to be dependent, a phenomenon known as multicollinearity, especially in the cases of few observations. In this paper, a Partial Least-Squares （PLS） regression approach is developed to study relationships between land use and its influencing factors through a case study of the Suzhou-Wuxi-Changzhou region in China. Multicollinearity exists in the dataset and the number of variables is high compared to the number of observations. Four PLS factors are selected through a preliminary analysis. The correlation analyses between land use and influencing factors demonstrate the land use character of rural industrialization and urbanization in the Suzhou-Wuxi-Changzhou region, meanwhile illustrate that the first PLS factor has enough ability to best describe land use patterns quantitatively, and most of the statistical relations derived from it accord with the fact. By the decreasing capacity of the PLS factors, the reliability of model outcome decreases correspondingly.

PARTIAL LEAST-SQUARES(PLS)REGRESSION AND SPECTROPHOTOMETRY AS APPLIED TO THE ANALYSIS OF MULTICOMPONENT MIXTURES

The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by traditional spectrophotometric methods.In this paper,the partial least-squares(PLS)regression is applied to the simultaneous determination of these compounds in mixtures by UV spectrophtometry without any pretreatment of the samples.Ten synthetic mixture samples are analyzed by the proposed method.The mean recoveries are 99.4%,996%,100.2%,99.3% and 99.1%,and the relative standard deviations(RSD) are 1.87%,1.98%,1.94%,0.960% and 0.672%,respectively.

Characterizing and estimating rice brown spot disease severity using stepwise regression,principal component regression and partial least-square regression

Detecting plant health conditions plays a key role in farm pest management and crop protection. In this study, measurement of hyperspectral leaf reflectance in rice crop (Oryzasativa L.) was conducted on groups of healthy and infected leaves by the fungus Bipolaris oryzae (Helminthosporium oryzae Breda. de Hann) through the wavelength range from 350 to 2 500 nm. The percentage of leaf surface lesions was estimated and defined as the disease severity. Statistical methods like multiple stepwise regression, principal component analysis and partial least-square regression were utilized to calculate and estimate the disease severity of rice brown spot at the leaf level. Our results revealed that multiple stepwise linear regressions could efficiently estimate disease severity with three wavebands in seven steps. The root mean square errors (RMSEs) for training (n=210) and testing (n=53) dataset were 6.5% and 5.8%, respectively. Principal component analysis showed that the first principal component could explain approximately 80% of the variance of the original hyperspectral reflectance. The regression model with the first two principal components predicted a disease severity with RMSEs of 16.3% and 13.9% for the training and testing dataset, respec-tively. Partial least-square regression with seven extracted factors could most effectively predict disease severity compared with other statistical methods with RMSEs of 4.1% and 2.0% for the training and testing dataset, respectively. Our research demon-strates that it is feasible to estimate the disease severity of rice brown spot using hyperspectral reflectance data at the leaf level.

On-Line Batch Process Monitoring Using Multiway Kernel Partial Least Squares

An approach for batch processes monitoring and fault detection based on multiway kernel partial least squares(MKPLS) was presented.It is known that conventional batch process monitoring methods,such as multiway partial least squares(MPLS),are not suitable due to their intrinsic linearity when the variations are nonlinear.To address this issue,kernel partial least squares(KPLS) was used to capture the nonlinear relationship between the latent structures and predictive variables.In addition,KPLS requires only linear algebra and does not involve any nonlinear optimization.In this paper,the application of KPLS was extended to on-line monitoring of batch processes.The proposed batch monitoring method was applied to a simulation benchmark of fed-batch penicillin fermentation process.And the results demonstrate the superior monitoring performance of MKPLS in comparison to MPLS monitoring.

Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics

This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.

A Differential Quadrature Based Approach for Volterra Partial Integro-Differential Equation with a Weakly Singular Kernel

Differential quadrature method is employed by numerous researchers due to its numerical accuracy and computational efficiency,and is mentioned as potential alternative of conventional numerical methods.In this paper,a differential quadrature based numerical scheme is developed for solving volterra partial integro-differential equation of second order having a weakly singular kernel.The scheme uses cubic trigonometric B-spline functions to determine the weighting coefficients in the differential quadrature approximation of the second order spatial derivative.The advantage of this approximation is that it reduces the problem to a first order time dependent integro-differential equation(IDE).The proposed scheme is obtained in the form of an algebraic system by reducing the time dependent IDE through unconditionally stable Euler backward method as time integrator.The scheme is validated using a homogeneous and two nonhomogeneous test problems.Conditioning of the system matrix and numerical convergence of the method are analyzed for spatial and temporal domain discretization parameters.Comparison of results of the present approach with Sinc collocation method and quasi-wavelet method are also made.

Application research on metal rheological forming of reproducing kernel partial method

The meshless method is a new numerical technology presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The process of cylinder compression was analyzed by using rigid-plastic meshless variational principle and programming reproducing kernel partial method(RKPM),the influence of node number,weight functions and size factor on the solution was discussed and the suitable range of size factor was obtained.Compared with the finite element method(FEM),the feasibility and validity of the method were verified,which proves a good supplement of FEM in this field and provides a good guidance for the application of meshless in actual engineering.

Using reproducing kernel for solving a class of partial differential equation with variable-coefficients

How to solve the partial differential equation has been attached importance to by all kinds of fields. The exact solution to a class of partial differential equation with variable-coefficient is obtained in reproducing kernel space. For getting the approximate solution, give an iterative method, convergence of the iterative method is proved. The numerical example shows that our method is effective and good practicability.

Solving Three Types of Satellite Gravity Gradient Boundary Value Problems by Least-Squares

The principle and method for solving three types of satellite gravity gradient boundary value problems by least-squares are discussed in detail. Also, kernel function expressions of the least-squares solution of three geodetic boundary value problems with the observations {Γ zz },{Γ xz , Γ yz} and {Γ xx -Γ yy ,2 Γxy}are presented. From the results of recovering gravity field using simulated gravity gradient tensor data, we can draw a conclusion that satellite gravity gradient integral formulas derived from least-squares are valid and rigorous for recovering the gravity field.

Near-Infrared Spectroscopy Coupled with Kernel Partial Least Squares-Discriminant Analysis for Rapid Screening Water Containing Malathion

Near-infrared spectroscopy coupled with kernel partial least squares-discriminant analysis was used to rapidly screen water containing malathion. In the wavenumber of 4348 cm-1 to 9091 cm-1, the overall correct classification rate of kernel partial least squares-discriminant analysis was 100% for training set, and 100% for test set, with the lowest concentration detected malathion residues in water being 1 μg·ml-1. Kernel partial least squares-discriminant analysis was able to have a good performance in classifying data in nonlinear systems. It was inferred that Near-infrared spectroscopy coupled with the kernel partial least squares-discriminant analysis had a potential in rapid screening other pesticide residues in water.

A Novel Extension of Kernel Partial Least Squares Regression

Based on continuum power regression(CPR) method, a novel derivation of kernel partial least squares(named CPR-KPLS) regression is proposed for approximating arbitrary nonlinear functions.Kernel function is used to map the input variables(input space) into a Reproducing Kernel Hilbert Space(so called feature space),where a linear CPR-PLS is constructed based on the projection of explanatory variables to latent variables(components). The linear CPR-PLS in the high-dimensional feature space corresponds to a nonlinear CPR-KPLS in the original input space. This method offers a novel extension for kernel partial least squares regression(KPLS),and some numerical simulation results are presented to illustrate the feasibility of the proposed method.

Adaptive Single Piecewise Interpolation Reproducing Kernel Method for Solving Fractional Partial Differential Equation

It is well-known that using the traditional reproducing kernel method(TRKM) for solving the fractional partial differential equation(FPDE) is very intractable. In this study, the adaptive single piecewise interpolation reproducing kernel method(ASPIRKM) is determined to solve the FPDE. This improved method not only improves the calculation accuracy, but also reduces the waste of time. Two numerical examples show that the ASPIRKM is a more time-saving numerical method than the TRKM.

Convergence analysis for complementary-label learning with kernel ridge regression

Complementary-label learning(CLL)aims at finding a classifier via samples with complementary labels.Such data is considered to contain less information than ordinary-label samples.The transition matrix between the true label and the complementary label,and some loss functions have been developed to handle this problem.In this paper,we show that CLL can be transformed into ordinary classification under some mild conditions,which indicates that the complementary labels can supply enough information in most cases.As an example,an extensive misclassification error analysis was performed for the Kernel Ridge Regression(KRR)method applied to multiple complementary-label learning(MCLL),which demonstrates its superior performance compared to existing approaches.

ESTIMATORS AND SOME BEHAVIORS FORA PARTIALLY LINEAR MODEL WITH CENSORED DATA

This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.

Improved Kernel PLS-based Fault Detection Approach for Nonlinear Chemical Processes

In this paper, an improved nonlinear process fault detection method is proposed based on modified kernel partial least squares(KPLS). By integrating the statistical local approach(SLA) into the KPLS framework, two new statistics are established to monitor changes in the underlying model. The new modeling strategy can avoid the Gaussian distribution assumption of KPLS. Besides, advantage of the proposed method is that the kernel latent variables can be obtained directly through the eigen value decomposition instead of the iterative calculation, which can improve the computing speed. The new method is applied to fault detection in the simulation benchmark of the Tennessee Eastman process. The simulation results show superiority on detection sensitivity and accuracy in comparison to KPLS monitoring.

ESTIMATION FOR THE AYMPTOTIC VARIANCE OF PARAMETRIC ESTIMATES IN PARTIAL LINEAR MODEL WITH CENSORED DATA

Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).

Partial least squares regression for predicting economic loss of vegetables caused by acid rain

To predict the economic loss of crops caused by acid rain,we used partial least squares(PLS) regression to build a model of single dependent variable -the economic loss calculated with the decrease in yield related to the pH value and levels of Ca2+,NH4+,Na+,K+,Mg2+,SO42-,NO3-,and Cl-in acid rain. We selected vegetables which were sensitive to acid rain as the sample crops,and collected 12 groups of data,of which 8 groups were used for modeling and 4 groups for testing. Using the cross validation method to evaluate the performace of this prediction model indicates that the optimum number of principal components was 3,determined by the minimum of prediction residual error sum of squares,and the prediction error of the regression equation ranges from -2.25% to 4.32%. The model predicted that the economic loss of vegetables from acid rain is negatively corrrelated to pH and the concentrations of NH4+,SO42-,NO3-,and Cl-in the rain,and positively correlated to the concentrations of Ca2+,Na+,K+ and Mg2+. The precision of the model may be improved if the non-linearity of original data is addressed.

QSAR Studies on PCDD/Fs by Kernel PLS

QSPR models of PCDD/Fs were generated by means of kernel partial least squares. The molecular distance-edge vector method was used as descriptors to get model I for predicting PCDD/Fs retention behavior. The chlorinated positions were also used and model II was obtained. In studied cases, the predictive ability of the KPLS model is comparable or superior to those of PLS and ANN. The results indicate that KPLS can be used as an alternative powerful modeling tool for QSPR studies.

Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold

Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.

A Comparative Numerical Study of Parabolic Partial Integro-Differential Equation Arising from Convection-Diffusion

This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation(PIDE)with a weakly singular kernel.Cubic trigonometric B-spline(CTBS)functions are used for interpolation in both methods.The first method is CTBS based collocation method which reduces the PIDE to an algebraic tridiagonal system of linear equations.The other method is CTBS based differential quadrature method which converts the PIDE to a system of ODEs by computing spatial derivatives as weighted sum of function values.An efficient tridiagonal solver is used for the solution of the linear system obtained in the first method as well as for determination of weighting coefficients in the second method.An explicit scheme is employed as time integrator to solve the system of ODEs obtained in the second method.The methods are tested with three nonhomogeneous problems for their validation.Stability,computational efficiency and numerical convergence of the methods are analyzed.Comparison of errors in approximations produced by the present methods versus different values of discretization parameters and convection-diffusion coefficients are made.Convection and diffusion dominant cases are discussed in terms of Peclet number.The results are also compared with cubic B-spline collocation method.