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Algorithms and statistical analysis for linear structured weighted total least squares problem

Geodesy and Geodynamics 2024年第2期15卷 177-188页

作者： Jian Xie Tianwei Qiu Cui Zhou Dongfang Lin Sichun Long School of Earth Science and Spatial Information Engineering Hunan University of Science and TechnologyXiangtan 411201China College of Science Central South University of Forestry and TechnologyChangsha 410018China National-Local Joint Engineering Laboratory of Geo-spatial Information Technology Hunan University of Science and TechnologyXiangtan 411201China

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.

关键词： Linear structured weighted total least squares Errors-in-variables Errors-in-observations Functional modelmodification Stochastic model modification Accuracyevaluation

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PSR-squares:基于程序空间约简器的SQL逆向合成系统

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通信学报 2023年第11期44卷 249-259页

作者：窦全胜张顺潘浩王荟贤唐焕玲山东工商学院信息与电子工程学院山东烟台264005 喀什大学计算机科学与技术学院新疆喀什844006

针对squares程序空间增长过快,导致程序合成效率偏低的问题,在squares的基础上,增加了以深度神经网络为核心的程序空间约简器,将给定的示例表示成二维张量,作为深度神经网络的输入,网络的输出是关于目标SQL语句合成规则的相关性标记向... 详细信息

针对squares程序空间增长过快,导致程序合成效率偏低的问题,在squares的基础上,增加了以深度神经网络为核心的程序空间约简器,将给定的示例表示成二维张量,作为深度神经网络的输入,网络的输出是关于目标SQL语句合成规则的相关性标记向量。约简器根据神经网络的输出结果,采用末N位淘汰策略,删除与目标SQL语句相关性弱的合成规则,以减少候选SQL语句的生成和验证,提升系统合成效率。对约简器中深度神经网络的结构设计、训练样本集的生成方法和网络训练过程进行了详细描述。同时将PSR-squares与当前有代表性SQL逆向合成系统进行实验对比,实验结果表明,PSR-squares的综合性能不同程度地优于其他合成系统,平均合成时间由squares的251 s降低至130 s,目标程序合成成功率由80%提升至89%。

关键词：程序合成 SQL逆向合成 squares 程序空间约简器领域特定语言

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Least squares twin support vector machine with asymmetric squared loss

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The Journal of China Universities of Posts and Telecommunications 2023年第1期30卷 1-16页

作者： Wu Qing Li Feiyan Zhang Hengchang Fan Jiulun Gao Xiaofeng School of Automation Xi'an University of Posts and TelecommunicationsXi'an 710121China School of Telecommunication and Information Engineering Xi'an University of Posts and TelecommunicationsXi'an 710121China

For classification problems,the traditional least squares twin support vector machine(LSTSVM)generates two nonparallel hyperplanes directly by solving two systems of linear equations instead of a pair of quadratic programming problems(QPPs),which makes LSTSVM much faster than the original TSVM.But the standard LSTSVM adopting quadratic loss measured by the minimal distance is sensitive to noise and unstable to re-sampling.To overcome this problem,the expectile distance is taken into consideration to measure the margin between classes and LSTSVM with asymmetric squared loss(aLSTSVM)is proposed.Compared to the original LSTSVM with the quadratic loss,the proposed aLSTSVM not only has comparable computational accuracy,but also performs good properties such as noise insensitivity,scatter minimization and re-sampling stability.Numerical experiments on synthetic datasets,normally distributed clustered(NDC)datasets and University of California,Irvine(UCI)datasets with different noises confirm the great performance and validity of our proposed algorithm.

关键词： classification least squares twin support vector machine asymmetric loss noise insensitivity

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Real-time object tracking via least squares transformation in spatial and Fourier domains for unmanned aerial vehicles

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Chinese Journal of Aeronautics 2019年第7期32卷 1716-1726页

作者： Xiaoyuan YANG Ridong ZHU Jingkai WANG Zhengze LI School of Mathematics and Systems Science Beihang University

This paper addresses the problem of real-time object tracking for unmanned aerial vehicles. We consider the task of object tracking as a classification problem. Training a good classifier always needs a huge number of samples, which is always time-consuming and not suitable for realtime applications. In this paper, we transform the large-scale least-squares problem in the spatial domain to a series of small-scale least-squares problems with constraints in the Fourier domain using the correlation filter technique. Then, this problem is efficiently solved by two stages. In the first stage, a fast method based on recursive least squares is used to solve the correlation filter problem without constraints in the Fourier domain. In the second stage, a weight matrix is constructed to prune the solution attained in the first stage to approach the constraints in the spatial domain. Then, the pruned classifier is used for tracking. To evaluate proposed tracker’s performance, comprehensive experiments are conducted on challenging aerial sequences in the UAV123 dataset. Experimental results demonstrate that proposed approach achieves a state-ofthe-art tracking performance in aerial sequences and operates at a mean speed of beyond 40 frames/s. For further analysis of proposed tracker’s robustness, extensive experiments are also performed on recent benchmarks OTB50, OTB100, and VOT2016.

关键词： Correlation filter Discrete Fourier transform Least squares Object tracking Unmanned aerial vehicle

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LKLR: A Local Tangent Space-Alignment Kernel Least-squares Regression Algorithm

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Tsinghua Science and Technology 2019年第4期24卷 389-399页

作者： Chao Tan Genlin Ji the School of Computer Science and Engineering Southeast University the School of Computer Science and Technology Nanjing Normal University the School of Computer Science and Technology Nanjing Normal University

In the fields of machine learning and data mining, label learning is a nascent area of research, and within this paradigm, there is much room for improving multi-label manifold learning algorithms for high-dimensional data. Thus far, researchers have experimented with mapping relationships from the feature space to the traditional logical label space(using neighbors in the label space, for example, to predict logical label vectors from the feature space's manifold structure). Here we combine the feature manifold's and label space's local topological structures to reconstruct the label manifold. To achieve this, we use a nonlinear manifold learning algorithm to transform the local topological structure from the feature space to the label space. Our algorithm adopts a regularized leastsquares kernel method to realize the reconstruction process, employing an optimization function to find the best solution. Extensive experiments show that our algorithm significantly improves multi-label manifold learning in terms of learning accuracy and time complexity.

关键词： multi-label manifold learning local topological structure regularized least squares kernel method

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Real-Time Patient-Specific ECG Arrhythmia Detection by Quantum Genetic Algorithm of Least squares Twin SVM

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Journal of Beijing Institute of Technology 2020年第1期29卷 29-37页

作者： Duan Li Ruizheng Shi Ni Yao Fubao Zhu Ke Wang School of Computer and Communication Engineering Zhengzhou University of Light IndustryZhengzhou 450001China Department of Cardiology Xiangya HospitalCentral South UniversityChangsha 410008China

The automatic detection of cardiac arrhythmias through remote monitoring is still a challenging task since electrocardiograms(ECGs)are easily contaminated by physiological artifacts and external noises,and these morphological characteristics show significant variations for different patients.A fast patient-specific arrhythmia diagnosis classifier scheme is proposed,in which a wavelet adaptive threshold denoising is combined with quantum genetic algorithm(QAG)based on least squares twin support vector machine(LSTSVM).The wavelet adaptive threshold denoising is employed for noise reduction,and then morphological features combined with the timing interval features are extracted to evaluate the classifier.For each patient,an individual and fast classifier will be trained by common and patient-specific training data.Following the recommendations of the Association for the Advancements of Medical Instrumentation(AAMI),experimental results over the MIT-BIH arrhythmia benchmark database demonstrated that our proposed method achieved the average detection accuracy of 98.22%,99.65%and 99.41%for the abnormal,ventricular ectopic beats(VEBs)and supra-VEBs(SVEBs),respectively.Besides the detection accuracy,sensitivity and specificity,our proposed method consumes the less CPU running time compared with the other representative state of the art methods.It can be ported to Android based embedded system,henceforth suitable for a wearable device.

关键词： wearable ECG monitoring systems patient-specific arrhythmia classification quantum genetic algorithm least squares twin SVM

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A multivariate partial least squares approach to joint association analysis for multiple correlated traits

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The Crop Journal 2016年第1期4卷 21-29页

作者： Yang Xu Wenming Hu Zefeng Yang Chenwu Xu Jiangsu Key Laboratory of Crop Genetics and Physiology Co-Innovation Center for Modern Production Technology of Grain CropsKey Laboratory of Plant Functional Genomics of the Ministry of Education Yangzhou University

Many complex traits are highly correlated rather than independent. By taking the correlation structure of multiple traits into account, joint association analyses can achieve both higher statistical power and more accurate estimation. To develop a statistical approach to joint association analysis that includes allele detection and genetic effect estimation, we combined multivariate partial least squares regression with variable selection strategies and selected the optimal model using the Bayesian Information Criterion(BIC). We then performed extensive simulations under varying heritabilities and sample sizes to compare the performance achieved using our method with those obtained by single-trait multilocus methods. Joint association analysis has measurable advantages over single-trait methods, as it exhibits superior gene detection power, especially for pleiotropic genes. Sample size, heritability,polymorphic information content(PIC), and magnitude of gene effects influence the statistical power, accuracy and precision of effect estimation by the joint association analysis.

关键词： Association analysis Multiple correlated traits Supersaturated model Multilocus Multivariate partial least squares

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Local geoid height approximation and interpolation using moving least squares approach

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Geodesy and Geodynamics 2020年第2期11卷 120-126页

作者： M.Kiani School of Surveying and Geospatial Data Engineering University of TehranTehranIran

In this paper an introduction of the moving least squares approach is presented in the context of data approximation and interpolation problems in Geodesy.An application of this method is presented for geoid height approximation and interpolation using different polynomial basis functions for the approximant and interpolant,respectively,in a regular grid of geoid height data in the region 16.0417°≤φ≤47.9583°and 36.0417°≤λ≤69.9582°,with increment 0.0833°in both latitudal and longitudal directions.The results of approximation and interpolation are then compared with the geoid height data from GPS-Levelling approach.Using the standard deviation of the difference of the results,it is shown that the planar interpolant,with reciprocal of distance as weight function,is the best choice in this local approximation and interpolation problem.

关键词： Approximation and interpolation points GPS-Levelling Moving Least squares Geoid height Grid points

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Seasonal Least squares Support Vector Machine with Fruit Fly Optimization Algorithm in Electricity Consumption Forecasting

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Journal of Donghua University(English Edition) 2019年第1期36卷 67-76页

作者：王子龙夏晨霞 College of Economics and Management Nanjing University of Aeronautics and Astronautics

Electricity is the guarantee of economic development and daily life. Thus, accurate monthly electricity consumption forecasting can provide reliable guidance for power construction planning. In this paper, a hybrid model in combination of least squares support vector machine(LSSVM) model with fruit fly optimization algorithm(FOA) and the seasonal index adjustment is constructed to predict monthly electricity consumption. The monthly electricity consumption demonstrates a nonlinear characteristic and seasonal tendency. The LSSVM has a good fit for nonlinear data, so it has been widely applied to handling nonlinear time series prediction. However, there is no unified selection method for key parameters and no unified method to deal with the effect of seasonal tendency. Therefore, the FOA was hybridized with the LSSVM and the seasonal index adjustment to solve this problem. In order to evaluate the forecasting performance of hybrid model, two samples of monthly electricity consumption of China and the United States were employed, besides several different models were applied to forecast the two empirical time series. The results of the two samples all show that, for seasonal data, the adjusted model with seasonal indexes has better forecasting performance. The forecasting performance is better than the models without seasonal indexes. The fruit fly optimized LSSVM model outperforms other alternative models. In other words, the proposed hybrid model is a feasible method for the electricity consumption forecasting.

关键词： forecasting fruit fly optimization algorithm(FOA) least squares support vector machine(LSSVM) seasonal index

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基于激光诱导击穿光谱的合金钢组分偏最小二乘法定量分析

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光谱学与光谱分析 2014年第2期34卷 542-547页

作者：丛智博孙兰香辛勇李洋齐立峰杨志家中国科学院沈阳自动化研究所工业控制网络与系统研究室辽宁沈阳110016

在炼钢中合金浓度的检测和控制对产品质量影响很大,激光诱导击穿光谱(laser induced breakdown spectroscopy,LIBS)技术具有快速、非接触、无需制样等特点,非常适合应用于合金成分的在线分析。但是由于合金中的C,S,P元素的成分含量都很... 详细信息

在炼钢中合金浓度的检测和控制对产品质量影响很大,激光诱导击穿光谱(laser induced breakdown spectroscopy,LIBS)技术具有快速、非接触、无需制样等特点,非常适合应用于合金成分的在线分析。但是由于合金中的C,S,P元素的成分含量都很低,其原子发射谱线极易淹没在复杂的铁元素特征谱线之中,造成这些重要元素在线定量分析困难。以合金钢标准光谱样品为研究对象,获取激光诱导击穿光谱数据,采用定标曲线法(calibration curve,CC)和偏最小二乘法(partial least squares,PLS),对合金钢样品的主量和微量元素进行定量分析。比较两种方法的定标结果得出:对于主量元素,PLS方法的定量分析水平优于传统的CC法;更重要的是对于微量元素,由于特征谱线极弱,CC法无法得出定量结果,而PLS法仍然具有良好的定量分析能力。同时,将PLS法回归模型特征谱线处的回归系数与原始有背景干扰的光谱强度数据进行比较,阐述了LIBS数据定量分析中PLS方法的优势。结果表明,在激光诱导击穿光谱合金成分分析中,PLS方法适合用于C等微量元素的定量分析。

关键词：激光诱导击穿光谱偏最小二乘法微量元素定量分析 Laser-induced breakdown spectroscopy (LIBS) Partial least squares method (PLS)

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