Least Squares One-Class Support Tensor Machine

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.

An Analysis of Liberia’s Vulnerability to Climate Change in the Context of Least Developed Countries (LDCs): A Review

Climate change is an alarming global challenge, particularly affecting the least developed countries (LDCs) including Liberia. These countries, located in regions prone to unpredictable temperature and precipitation changes, are facing significant challenges, particularly in climate-sensitive sectors such as mining and agriculture. LDCs need more resilience to adverse climate shocks but have limited capacity for adaptation compared to other developed and developing nations. This paper examines Liberia’s susceptibility to climate change as a least developed country, focusing on its exposure, sensitivity, and adaptive capacity. It provides an overview of LDCs and outlines the global distribution of carbon dioxide emissions. The paper also evaluates specific challenges that amplify Liberia’s vulnerability and constrain sustainable adaptation, providing insight into climate change’s existing and potential effects. The paper emphasizes the urgency of addressing climate impacts on Liberia and calls for concerted local and international efforts for effective and sustainable mitigation efforts. It provides recommendations for policy decisions and calls for further research on climate change mitigation and adaptation.

Comparative Study of Probabilistic and Least-Squares Methods for Developing Predictive Models

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.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

Two-Stage Procrustes Rotation with Sparse Target Matrix and Least Squares Criterion with Regularization and Generalized Weighting

In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using two types of approximation: 1) approximate the zeros in the target by the non-zeros in the loadings, and 2) approximate the non-zeros in the target by the non-zeros in the loadings. The central issue of Procrustes rotation considered in the article is that it equally treats the two types of approximation, while the former is more important for simplifying the loading matrix. Furthermore, a well-known issue of Simplimax is the computational inefficiency in estimating the sparse target matrix, which yields a considerable number of local minima. The research proposes a new rotation procedure that consists of the following two stages. The first stage estimates sparse target matrix with lesser computational cost by regularization technique. In the second stage, a loading matrix is rotated to the target, emphasizing on the approximation of non-zeros to zeros in the target by least squares criterion with generalized weighing that is newly proposed by the study. The simulation study and real data examples revealed that the proposed method surely simplifies loading matrices.

Revisiting Akaike’s Final Prediction Error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

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.

基于LEAST的高速网络大流检测算法

针对大流漏检率过高，占用SRAM过大问题，提出了基于最少（LEAST）改进型大流检测算法。主要思想：利用LEAST淘汰机制将小流丢弃使得大流能够被保护，采用窗口-储备策略解决检测大流的公平性问题。通过相关组织所提供的实际互联网数据进行了实验比较，结果显示：与现有算法相比，新算法具有更高的测量准确性，平均大流漏检率降低至0％～0．13％。

Least-Squares及Galerkin谱元方法求解环形区域内的泊松方程

为研究基于Least-Squares变分及Galerkin变分两种形式的谱元方法的求解特性,推导了极坐标系中采用两种变分方法求解环形区域内Poisson方程时对应的弱解形式,采用Chebyshev多项式构造插值基函数进行空间离散,得到两种谱元方法对应的代数方程组,由此分析了系数矩阵结构的特点。数值计算结果显示:Least-Squares谱元方法为实现方程的降阶而引入新的求解变量,使得代数方程组形式更为复杂,但边界条件的处理比Galerkin谱元方法更为简单;两种谱元方法均能求解极坐标系中的Poisson方程且能获得高精度的数值解,二者绝对误差分布基本一致;固定单元内的插值阶数时,增加单元数可减小数值误差,且表现出代数精度的特点,误差降低速度较慢,而固定单元数时,在一定范围内数值误差随插值阶数的增加而减小的速度更快,表现出谱精度的特点;单元内插值阶数较高时,代数方程组系数矩阵的条件数急剧增多,方程组呈现病态,数值误差增大,这一特点限制了单元内插值阶数的取值。研究内容对深入了解两种谱元方法在极坐标系中求解Poisson方程时的特点、进一步采用相关分裂算法求解实际流动问题具有参考价值。

Properties of the total least squares estimation

Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.

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.

ON THE ACCURACY OF THE LEAST SQUARES AND THE TOTAL LEAST SQUARES METHODS

Consider solving an overdetermined system of linear algebraic equations by both the least squares method (LS) and the total least squares method (TLS). Extensive published computational evidence shows that when the original system is consistent. one often obtains more accurate solutions by using the TLS method rather than the LS method. These numerical observations contrast with existing analytic perturbation theories for the LS and TLS methods which show that the upper bounds for the LS solution are always smaller than the corresponding upper bounds for the TLS solutions. In this paper we derive a new upper bound for the TLS solution and indicate when the TLS method can be more accurate than the LS method.Many applied problems in signal processing lead to overdetermined systems of linear equations where the matrix and right hand side are determined by the experimental observations (usually in the form of a lime series). It often happens that as the number of columns of the matrix becomes larger, the

Outliers, inliers and the generalized least trinuned squares estimator in system identification

The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity 0( N In N) for large N, where N is the number of measurements. We also show that though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers. Keywords Least squares - Least trimmed squares - Outliers - System identification - Parameter estimation - Robust parameter estimation This work was supported in part by NSF ECS — 9710297 and ECS — 0098181.

Perturbation Analysis for the Matrix-Scaled Total Least Squares Problem

In this paper, we extend matrix scaled total least squares (MSTLS) problem with a single right-hand side to the case of multiple right-hand sides. Firstly, under some mild conditions, this paper gives an explicit expression of the minimum norm solution of MSTLS problem with multiple right-hand sides. Then, we present the Kronecker-product-based formulae for the normwise, mixed and componentwise condition numbers of the MSTLS problem. For easy estimation, we also exhibit Kronecker-product-free upper bounds for these condition numbers. All these results can reduce to those of the total least squares (TLS) problem which were given by Zheng et al. Finally, two numerical experiments are performed to illustrate our results.

偏最小二乘(PartialLeast Square)方法的拟合指标及其在满意度研究中的应用

本文在对顾客满意度模型及PLS方法进行简单介绍的基础上,对PLS的拟合指标,包括共同因子、多元相关平方和冗余,进行了讨论。

Regularized least-squares migration of simultaneous-source seismic data with adaptive singular spectrum analysis

Simultaneous-source acquisition has been recog- nized as an economic and efficient acquisition method, but the direct imaging of the simultaneous-source data produces migration artifacts because of the interference of adjacent sources. To overcome this problem, we propose the regularized least-squares reverse time migration method （RLSRTM） using the singular spectrum analysis technique that imposes sparseness constraints on the inverted model. Additionally, the difference spectrum theory of singular values is presented so that RLSRTM can be implemented adaptively to eliminate the migration artifacts. With numerical tests on a fiat layer model and a Marmousi model, we validate the superior imaging quality, efficiency and convergence of RLSRTM compared with LSRTM when dealing with simultaneoussource data, incomplete data and noisy data.

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.

Least Squares Evaluations for Form and Profile Errors of Ellipse Using Coordinate Data

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.

Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model

In this paper, an improved weighted least squares （WLS）, together with autoregressive （AR） model, is proposed to improve prediction accuracy of earth rotation parameters（ERP）. Four weighting schemes are developed and the optimal power e for determination of the weight elements is studied. The results show that the improved WLS-AR model can improve the ERP prediction accuracy effectively, and for different prediction intervals of ERP, different weight scheme should be chosen.

Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings （RBs） during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB （GZN 110） under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least- square estimation （SNLSE）, is introduced to identify the model parameters. It is shown that the proposed simplified Bouc- Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.

Practical constrained least-square algorithm for moving source location using TDOA and FDOA measurements

By utilizing the time difference of arrival （TDOA） and frequency difference of arrival （FDOA） measurements of signals received at a number of receivers, a constrained least-square （CLS） algorithm for estimating the position and velocity of a moving source is proposed. By utilizing the Lagrange multipliers technique, the known relation between the intermediate variables and the source location coordinates could be exploited to constrain the solution. And without requiring apriori knowledge of TDOA and FDOA measurement noises, the proposed algorithm can satisfy the demand of practical applications. Additionally, on basis of con- volute and polynomial rooting operations, the Lagrange multipliers can be obtained efficiently and robustly allowing real-time imple- mentation and global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least square （WLS） approach especially for higher measurement noise level.