This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations...This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.展开更多
Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand...Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.展开更多
One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification ...One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.展开更多
In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering comp...In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.展开更多
In order to realize direct thrust control instead of conventional sensors-based control for aero-engine, a thrust estimator with high accuracy is designed by using the boosting technique to improve the performance of ...In order to realize direct thrust control instead of conventional sensors-based control for aero-engine, a thrust estimator with high accuracy is designed by using the boosting technique to improve the performance of least squares support vector regression （LSSVR）. There exist two distinct features compared with the conven- tional boosting technique： （1） Sampling without replacement is used to avoid numerical instability for modeling LSSVR. （2） To realize the sparseness of LSSVR and reduce the computational complexity, only a subset of the training samples is used to construct LSSVR. Thus, this boosting method for LSSVR is called the boosting sparse LSSVR （BSLSSVR）. Finally, simulation results show that BSLSSVR-based thrust estimator can satisfy the requirement of direct thrust control, i.e. , maximum absolute value of relative error of thrust estimation is not more than 5‰.展开更多
针对浮选过程变量滞后、耦合特征及建模样本数量少所导致精矿品位难以准确预测的问题,提出了一种基于改进麻雀搜索算法(Improved Sparrow Search Algorithm,ISSA)优化混核最小二乘支持向量机(Hybrid Kernel Least Squares Support Vecto...针对浮选过程变量滞后、耦合特征及建模样本数量少所导致精矿品位难以准确预测的问题,提出了一种基于改进麻雀搜索算法(Improved Sparrow Search Algorithm,ISSA)优化混核最小二乘支持向量机(Hybrid Kernel Least Squares Support Vector Machine,HKLSSVM)的浮选过程精矿品位预测方法.首先采集浮选现场载流X荧光品位分析仪数据作为建模变量并进行预处理,建立基于最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)的预测模型,以此构建新型混合核函数,将输入空间映射至高维特征空间,再引入改进麻雀搜索算法对模型参数进行优化,提出基于ISSA-HKLSSVM方法实现精矿品位预测,最后开发基于LabVIEW的浮选精矿品位预测系统对本文提出方法实际验证.实验结果表明,本文提出方法对于浮选过程小样本建模具有良好拟合能力,相比现有方法提高了预测准确率,可实现精矿品位的准确在线预测,为浮选过程的智能调控提供实时可靠的精矿品位反馈信息.展开更多
为研究不同养殖方式下宁都黄鸡肌肉关键挥发性风味物质,将试验鸡随机分为笼养组和平养组,饲喂同一日粮。试验鸡达上市日龄时对鸡肉进行感官品尝评价和挥发性风味物质检测,并采用正交偏最小二乘-判别分析(orthogonal partial least squar...为研究不同养殖方式下宁都黄鸡肌肉关键挥发性风味物质,将试验鸡随机分为笼养组和平养组,饲喂同一日粮。试验鸡达上市日龄时对鸡肉进行感官品尝评价和挥发性风味物质检测,并采用正交偏最小二乘-判别分析(orthogonal partial least squares-discriminant analysis,OPLS-DA)方法筛选与不同养殖方式相关的差异性风味物质。结果表明:平养组和笼养组共有的挥发性风味物质27种,主要为酚类、醇类和烃类。挥发性风味物质中,己醛、1-辛烯-3-醇、E-2-壬烯醛、正己醇、壬醛、2,3-戊二酮、癸醛、2,3-辛二酮、E-2-辛烯醛为具有显著性差异的挥发性风味物质。综上,这一研究可为地方鸡肉品质基于风味物质的评价提供科学依据。展开更多
Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsi...Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.展开更多
This study used near-infrared(NIR)spectroscopy to predict mechanical properties of wood.NIR spectra were collected in wavelengths 900–1700 nm,and spectra averaged by radial and tangential surface spectra were used to...This study used near-infrared(NIR)spectroscopy to predict mechanical properties of wood.NIR spectra were collected in wavelengths 900–1700 nm,and spectra averaged by radial and tangential surface spectra were used to establish a partial least square(PLS)model based on correlation local embedding(CLE).Mongolian oak(Quercus mongolica Fisch.ex Ledeb.)was used to test the eff ectiveness of the model.The cross-validation method was used to verify the robustness of the CLE–PLS model.Ninety samples were tested as the calibration set and forty-fi ve as the validation set.The results show that the prediction coeffi cient of determination(R2 p)is 0.80 for MOR,and 0.78 for MOE.The ratio of performance to deviation is 2.23 for MOR and 2.15 for MOE.展开更多
In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived ...In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.展开更多
文摘This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.
文摘One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.
文摘In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.
基金Supported by the National Natural Science Foundation of China(50576033)the Aeronautical Science Foundation of China(04C52019)~~
文摘In order to realize direct thrust control instead of conventional sensors-based control for aero-engine, a thrust estimator with high accuracy is designed by using the boosting technique to improve the performance of least squares support vector regression （LSSVR）. There exist two distinct features compared with the conven- tional boosting technique： （1） Sampling without replacement is used to avoid numerical instability for modeling LSSVR. （2） To realize the sparseness of LSSVR and reduce the computational complexity, only a subset of the training samples is used to construct LSSVR. Thus, this boosting method for LSSVR is called the boosting sparse LSSVR （BSLSSVR）. Finally, simulation results show that BSLSSVR-based thrust estimator can satisfy the requirement of direct thrust control, i.e. , maximum absolute value of relative error of thrust estimation is not more than 5‰.
文摘针对浮选过程变量滞后、耦合特征及建模样本数量少所导致精矿品位难以准确预测的问题,提出了一种基于改进麻雀搜索算法(Improved Sparrow Search Algorithm,ISSA)优化混核最小二乘支持向量机(Hybrid Kernel Least Squares Support Vector Machine,HKLSSVM)的浮选过程精矿品位预测方法.首先采集浮选现场载流X荧光品位分析仪数据作为建模变量并进行预处理,建立基于最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)的预测模型,以此构建新型混合核函数,将输入空间映射至高维特征空间,再引入改进麻雀搜索算法对模型参数进行优化,提出基于ISSA-HKLSSVM方法实现精矿品位预测,最后开发基于LabVIEW的浮选精矿品位预测系统对本文提出方法实际验证.实验结果表明,本文提出方法对于浮选过程小样本建模具有良好拟合能力,相比现有方法提高了预测准确率,可实现精矿品位的准确在线预测,为浮选过程的智能调控提供实时可靠的精矿品位反馈信息.
文摘为研究不同养殖方式下宁都黄鸡肌肉关键挥发性风味物质,将试验鸡随机分为笼养组和平养组,饲喂同一日粮。试验鸡达上市日龄时对鸡肉进行感官品尝评价和挥发性风味物质检测,并采用正交偏最小二乘-判别分析(orthogonal partial least squares-discriminant analysis,OPLS-DA)方法筛选与不同养殖方式相关的差异性风味物质。结果表明:平养组和笼养组共有的挥发性风味物质27种,主要为酚类、醇类和烃类。挥发性风味物质中,己醛、1-辛烯-3-醇、E-2-壬烯醛、正己醇、壬醛、2,3-戊二酮、癸醛、2,3-辛二酮、E-2-辛烯醛为具有显著性差异的挥发性风味物质。综上,这一研究可为地方鸡肉品质基于风味物质的评价提供科学依据。
基金supported by the National Natural Science Foundation of China(6177202062202433+4 种基金621723716227242262036010)the Natural Science Foundation of Henan Province(22100002)the Postdoctoral Research Grant in Henan Province(202103111)。
文摘Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.
基金financially supported by the China State Forestry Administration“948”projects(2015-4-52)Fundamental Research Funds for the Central Universities(2572017DB05)Heilongjiang Natural Science Foundation(C2017005)。
文摘This study used near-infrared(NIR)spectroscopy to predict mechanical properties of wood.NIR spectra were collected in wavelengths 900–1700 nm,and spectra averaged by radial and tangential surface spectra were used to establish a partial least square(PLS)model based on correlation local embedding(CLE).Mongolian oak(Quercus mongolica Fisch.ex Ledeb.)was used to test the eff ectiveness of the model.The cross-validation method was used to verify the robustness of the CLE–PLS model.Ninety samples were tested as the calibration set and forty-fi ve as the validation set.The results show that the prediction coeffi cient of determination(R2 p)is 0.80 for MOR,and 0.78 for MOE.The ratio of performance to deviation is 2.23 for MOR and 2.15 for MOE.
文摘In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.
