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.
