The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this...The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this solution is affected by time and memory constraints when dealing with large datasets.In this paper,we present a least squares version for TSVR in the primal space,termed primal least squares TSVR (PLSTSVR).By introducing the least squares method,the inequality constraints of TSVR are transformed into equality constraints.Furthermore,we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space;thus,we need only to solve two systems of linear equations instead of two QPPs.Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time.We further investigate its validity in predicting the opening price of stock.展开更多
针对目前光滑孪生支持向量回归机(smooth twin support vector regression,STSVR)中采用的Sigmoid光滑函数逼近精度不高,从而导致算法泛化能力不够理想的问题,引入一种具有更强逼近能力的光滑(chen-harker-kanzow-smale,CHKS)函数,采用C...针对目前光滑孪生支持向量回归机(smooth twin support vector regression,STSVR)中采用的Sigmoid光滑函数逼近精度不高,从而导致算法泛化能力不够理想的问题,引入一种具有更强逼近能力的光滑(chen-harker-kanzow-smale,CHKS)函数,采用CHKS函数逼近孪生支持向量回归机的不可微项,并用Newton-Armijo算法求解相应的模型,提出了光滑CHKS孪生支持向量回归机(smooth CHKS twin support vector regression,SCTSVR).不仅从理论上证明了SCTSVR具有严格凸,能满足任意阶光滑和全局收敛的性能,而且在人工数据集和UCI数据集上的实验表明了SCTSVR比STSVR具有更好的回归性能.展开更多
孪生支持向量回归机(Twin Support Vector Regression,TSVR or TWSVR)是一种基于统计学习理论的回归算法,它以结构风险最小化原理为理论基础,通过适当地选择函数子集及该子集中的判别函数,使学习机的实际风险达到最小,保证了在有限训练...孪生支持向量回归机(Twin Support Vector Regression,TSVR or TWSVR)是一种基于统计学习理论的回归算法,它以结构风险最小化原理为理论基础,通过适当地选择函数子集及该子集中的判别函数,使学习机的实际风险达到最小,保证了在有限训练样本上得到的小误差分类器对独立测试集的测试误差仍然较小.孪生支持向量回归机通过将线性不可分样本映射到高维特征空间,使得映射后的样本在该高维特征空间内线性可分,保证了其具有较好的泛化性能.孪生支持向量回归机的算法思想基于孪生支持向量机(Twin Support Vector Machine,TWSVM),几何意义是使所有样本点尽可能地处于两条回归超平面的上(下)不敏感边界之间,最终的回归结果由两个超平面的回归值取平均得到.孪生支持向量回归机需求解两个规模较小的二次规划问题(Quadratic Programming Problems,QPPs)便可得到两条具有较小拟合误差的回归超平面,训练时间和拟合精度都高于传统的支持向量回归机(Support Vector Regression,SVR),且其QPPs的对偶问题存在全局最优解,避免了容易陷入局部最优的问题,故孪生支持向量回归机已成为机器学习的热门领域之一.但孪生支持向量回归机作为机器学习领域的一个较新的理论,其数学模型与算法思想都尚不成熟,在泛化性能、求解速度、矩阵稀疏性、参数选取、对偶问题等方面仍存在进一步改进的空间.本文首先给出了两种孪生支持向量回归机的数学模型与几何意义,然后将孪生支持向量回归机的几个常见的改进策略归纳如下.(1)加权孪生支持向量回归机由于孪生支持向量回归机中每个训练样本受到的惩罚是相同的,但每个样本对超平面的影响不同,尤其是噪声和离群值会使算法性能降低,并且在不同位置的训练样本应给予不同的处罚更为合理,因此考虑在孪生支持向量回归机的每个QPP中引入一个�展开更多
孪生支持向量回归机(Twin Support Vector Regression,TSVR)的数学模型是求解一对约束优化问题,如何将约束优化问题转化为无约束优化问题进行求解是一个难题.在TSVR约束优化模型的基础上,依据最优化理论提出TSVR的无约束优化问题.然而,...孪生支持向量回归机(Twin Support Vector Regression,TSVR)的数学模型是求解一对约束优化问题,如何将约束优化问题转化为无约束优化问题进行求解是一个难题.在TSVR约束优化模型的基础上,依据最优化理论提出TSVR的无约束优化问题.然而,无约束优化问题的目标函数有可能不可微,为解决这个问题,引入极大熵函数,确保优化问题都是可微的.标准的极大熵函数法有可能发生数值溢出,所以对极大熵函数法进行了改进,提出自适应调节极大熵函数法来逼近TSVR的不可微项,并提出基于自适应调节极大熵函数法的TSVR学习算法.实验结果表明,和其他回归方法相比,所提算法不仅能够提高回归精度,而且效率得到了较大的提高.展开更多
In order to improve the end-point hit rate of basic oxygen furnace steelmaking,a novel dynamic control model was proposed based on an improved twin support vector regression algorithm.The controlled objects were the e...In order to improve the end-point hit rate of basic oxygen furnace steelmaking,a novel dynamic control model was proposed based on an improved twin support vector regression algorithm.The controlled objects were the end-point carbon content and temperature.The proposed control model was established by using the low carbon steel samples collected from a steel plant,which consists of two prediction models,a preprocess model,two regulation units,a controller and a basic oxygen furnace.The test results of 100 heats show that the prediction models can achieve a double hit rate of 90%within the error bound of 0.005 wt.%C and 15℃.The preprocess model was used to predict an initial end-blow oxygen volume.However,the double hit rate of the carbon con tent and temperature only achieves 65%.Then,the oxygen volume and coolant additi ons were adjusted by the regulation units to improve the hit rate.Finally,the double hit rate after the regulation is reached up to 90%.The results indicate that the proposed dynamic control model is efficient to guide the real production for low carbon steel,and the modeling method is also suitable for the applications of other steel grades.展开更多
基金supported by the National Basic Research Program (973) of China(No.2013CB329502)the National Natural Science Foundation of China(No.61379101)the Fundamental Research Funds for the Central Universities,China(No.2012LWB39)
文摘The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this solution is affected by time and memory constraints when dealing with large datasets.In this paper,we present a least squares version for TSVR in the primal space,termed primal least squares TSVR (PLSTSVR).By introducing the least squares method,the inequality constraints of TSVR are transformed into equality constraints.Furthermore,we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space;thus,we need only to solve two systems of linear equations instead of two QPPs.Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time.We further investigate its validity in predicting the opening price of stock.
文摘针对目前光滑孪生支持向量回归机(smooth twin support vector regression,STSVR)中采用的Sigmoid光滑函数逼近精度不高,从而导致算法泛化能力不够理想的问题,引入一种具有更强逼近能力的光滑(chen-harker-kanzow-smale,CHKS)函数,采用CHKS函数逼近孪生支持向量回归机的不可微项,并用Newton-Armijo算法求解相应的模型,提出了光滑CHKS孪生支持向量回归机(smooth CHKS twin support vector regression,SCTSVR).不仅从理论上证明了SCTSVR具有严格凸,能满足任意阶光滑和全局收敛的性能,而且在人工数据集和UCI数据集上的实验表明了SCTSVR比STSVR具有更好的回归性能.
文摘孪生支持向量回归机(Twin Support Vector Regression,TSVR or TWSVR)是一种基于统计学习理论的回归算法,它以结构风险最小化原理为理论基础,通过适当地选择函数子集及该子集中的判别函数,使学习机的实际风险达到最小,保证了在有限训练样本上得到的小误差分类器对独立测试集的测试误差仍然较小.孪生支持向量回归机通过将线性不可分样本映射到高维特征空间,使得映射后的样本在该高维特征空间内线性可分,保证了其具有较好的泛化性能.孪生支持向量回归机的算法思想基于孪生支持向量机(Twin Support Vector Machine,TWSVM),几何意义是使所有样本点尽可能地处于两条回归超平面的上(下)不敏感边界之间,最终的回归结果由两个超平面的回归值取平均得到.孪生支持向量回归机需求解两个规模较小的二次规划问题(Quadratic Programming Problems,QPPs)便可得到两条具有较小拟合误差的回归超平面,训练时间和拟合精度都高于传统的支持向量回归机(Support Vector Regression,SVR),且其QPPs的对偶问题存在全局最优解,避免了容易陷入局部最优的问题,故孪生支持向量回归机已成为机器学习的热门领域之一.但孪生支持向量回归机作为机器学习领域的一个较新的理论,其数学模型与算法思想都尚不成熟,在泛化性能、求解速度、矩阵稀疏性、参数选取、对偶问题等方面仍存在进一步改进的空间.本文首先给出了两种孪生支持向量回归机的数学模型与几何意义,然后将孪生支持向量回归机的几个常见的改进策略归纳如下.(1)加权孪生支持向量回归机由于孪生支持向量回归机中每个训练样本受到的惩罚是相同的,但每个样本对超平面的影响不同,尤其是噪声和离群值会使算法性能降低,并且在不同位置的训练样本应给予不同的处罚更为合理,因此考虑在孪生支持向量回归机的每个QPP中引入一个�
文摘孪生支持向量回归机(Twin Support Vector Regression,TSVR)的数学模型是求解一对约束优化问题,如何将约束优化问题转化为无约束优化问题进行求解是一个难题.在TSVR约束优化模型的基础上,依据最优化理论提出TSVR的无约束优化问题.然而,无约束优化问题的目标函数有可能不可微,为解决这个问题,引入极大熵函数,确保优化问题都是可微的.标准的极大熵函数法有可能发生数值溢出,所以对极大熵函数法进行了改进,提出自适应调节极大熵函数法来逼近TSVR的不可微项,并提出基于自适应调节极大熵函数法的TSVR学习算法.实验结果表明,和其他回归方法相比,所提算法不仅能够提高回归精度,而且效率得到了较大的提高.
基金This work was supported by Liaoning Province PhD Start-up Fund(No.201601291)Liaoning Province Ministry of Education Scientific Study Project(No.2O17LNQN11).
文摘In order to improve the end-point hit rate of basic oxygen furnace steelmaking,a novel dynamic control model was proposed based on an improved twin support vector regression algorithm.The controlled objects were the end-point carbon content and temperature.The proposed control model was established by using the low carbon steel samples collected from a steel plant,which consists of two prediction models,a preprocess model,two regulation units,a controller and a basic oxygen furnace.The test results of 100 heats show that the prediction models can achieve a double hit rate of 90%within the error bound of 0.005 wt.%C and 15℃.The preprocess model was used to predict an initial end-blow oxygen volume.However,the double hit rate of the carbon con tent and temperature only achieves 65%.Then,the oxygen volume and coolant additi ons were adjusted by the regulation units to improve the hit rate.Finally,the double hit rate after the regulation is reached up to 90%.The results indicate that the proposed dynamic control model is efficient to guide the real production for low carbon steel,and the modeling method is also suitable for the applications of other steel grades.
