线性矩阵方程的中心对称解

在矩阵的向量函数和Kronecker积的基础上定义了矩阵的部分向量函数,利用Moore-Penrose的有关知识给出了矩阵方程的中心对称解的结构和性质.     

对偶基矢量组在张量分析中的作用与意义

在数学上将客观定律用量的分量形式表达为对坐标系具有不变性的方程，是张量分析所要解决的核心问题，为此，需从单一一的基矢量组发展为对偶的两个基矢量组，文中给地偶基几何意义解释的新证明，进一步阐明了“同变”与“逆变”的含义，说明“同变”较为现在广泛使用的     

Variable Selection for Kernel Classification

In this article, a variable selection procedure, called surrogate selection, is proposed which can be applied when a support vector machine or kernel Fisher discriminant analysis is used in a binary classification problem. Surrogate selection applies the lasso after substituting the kernel discriminant scores for the binary group labels, as well as values for the input variable observations. Empirical results are reported, showing that surrogate selection performs well.     

类复向量在空间连杆机构运动分析上的应用

利用类复向量理论,对任意空间连杆机构进行运动分析,由于类复向量的旋转具有坐标变换的功能,以及利用其性质消去某些中间运动变量可以取代等同条件或约束方程,从而使计算过程明显简化。     

Bayesian Additive Machine: classification with a semiparametric discriminant function

In this paper, we propose a new Bayesian inference approach for classification based on the traditional hinge loss used for classical support vector machines, which we call the Bayesian Additive Machine (BAM). Unlike existing approaches, the new model has a semiparametric discriminant function where some feature effects are nonlinear and others are linear. This separation of features is achieved automatically during model fitting without user pre-specification. Following the literature on sparse regression of high-dimensional models, we can also identify the irrelevant features. By introducing spike-and-slab priors using two sets of indicator variables, these multiple goals are achieved simultaneously and automatically, without any parameter tuning such as cross-validation. An efficient partially collapsed Markov chain Monte Carlo algorithm is developed for posterior exploration based on a data augmentation scheme for the hinge loss. Our simulations and three real data examples demonstrate that the new approach is a strong competitor to some approaches that were proposed recently for dealing with challenging classification examples with high dimensionality.     

A quadratic programming approach to the construction of simultaneous confidence intervals

Richmond (1982) uses a linear programming approach to the construction of simultaneous confidence intervals for a set of linear estimable parametric functions of the normal mean vector. We present a quadratic programming approach which constructs narrower confidence intervals than the linear programming approach given by Richmond (1982).     

基于支持向量机回归模型的重庆市房地产金融风险预警研究

以房地产金融风险单项指标的评价标准为依据,利用基于支持向量机（SVM）的回归分析模型对重庆市房地产的金融风险状况进行预警分析研究。通过研究评价指标变量与模型输出数值之间的关系,分析房地产金融风险状况与各评价指标变量的非线性关系,预测出各年度的金融风险状况及金融风险的走势,从而为有针对性地降低金融风险水平制定相应的宏观调控政策提供理论参考。     

中俄相互投资的母国贸易效应比较

基于2003—2017年中俄双边投资与贸易额,借助协整检验、误差修正模型(ECM)和向量自回归模型(VAR)等方法,分析中国与俄罗斯相互投资分别对母国贸易的影响。研究结果表明:长期来看,中国对俄罗斯投资与双边贸易呈互补效应,而俄罗斯对中国投资却与双边贸易呈现替代效应;短期来看,中俄相互投资对双边贸易均不具有动态关系。中国对俄罗斯低科技含量制成品、高科技含量制成品的出口及初级制成品、资源性制成品和中等科技含量制成品的进口均与其投资之间存在着长期均衡关系;俄罗斯对中国初级制成品的出口、低科技含量制成品和中等科技含量制成品的进出口以及资源性制成品和高科技含量制成品的进口与俄罗斯在中国的投资存在着长期均衡关系。     

基于最小二乘支持向量机的岩石可钻性研究

岩石可钻性的确定直接影响钻头选型和钻速预测，国内外各主要油田虽对地层岩性的测定相当重视，但适合于油气井钻井条件的岩石可钻性问题仍未彻底解决。针对目前国内在钻头选型方面存在的困难和问题，提出了利用LS-SVM最小二乘支持向量机求取岩石可钻性的实用方法。该方法以测井资料为参数，利用LS-SVM支持向量机技术建立岩石可钻性的数学模型。该模型在SC油田DU4井中的应用中取得了较好效果。