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
Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research exten...Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research extends existing work in the literature.展开更多
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.
文摘Necessary and sufficient conditions are derived for some matrix equations that have a common least-squares solution.A general expression is provided when certain resolvable conditions are satisfied.This research extends existing work in the literature.
文摘针对铝酸钠溶液浓度在线检测仪表稳定性差、具有放射性、维护保养成本高等不足及人工检测严重滞后的问题,结合蒸发过程工艺机理分析,选取影响铝酸钠溶液浓度的参数为辅助变量,采用加权损失函数的最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)实现了铝酸钠溶液浓度的鲁棒软测量。并采用斯密特正交化方法约简核矩阵,降低计算复杂度。工业过程数据仿真结果表明,建立的软测量模型能够连续在线检测铝酸钠溶液浓度,并获得了比标准LSSVM、加权LSSVM及多核LSSVM更高的预测精度,完全满足工业要求。
