Standard support vector machines （SVMs） train- ing algorithms have O（l3） computational and O（l2） space complexities, where l is the training set size. It is thus com- /putationally infeasible on very large data ...Standard support vector machines （SVMs） train- ing algorithms have O（l3） computational and O（l2） space complexities, where l is the training set size. It is thus com- /putationally infeasible on very large data sets.To alleviate the Computational burden in SVM training, we propose an algo- rithm to train SVMs on a bound vectors set that is extracted based on Fisher projection. For linear separate problems, we use linear Fisher discriminant to compute the projection line, while for non-linear separate problems, we use kernel Fisher discriminant to compute the projection line. For each case, we select a certain ratio samples whose projections are adja- cent to those of the other class as bound vectors. Theoretical analysis shows that the proposed algorithm is with low com- putational and space complexities.Extensive experiments on several classification benchmarks demonstrate the effective- ness of our approach.展开更多
There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions...There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.展开更多
基金This work was sponsored by the National Natural Sci- ence Foundation of China （Grant Nos. 61370083, 61073043, 61073041 and 61370086）, the National Research Foundation for the Doctoral Program of Higher Education of China （20112304110011 and 20122304110012）, the Natural Science Foundation of Heilongjiang Province （F200901）, and the Harbin Outstanding Academic Leader Foundation of Heilongjiang Province of China （2011RFXXG015）.
文摘Standard support vector machines （SVMs） train- ing algorithms have O（l3） computational and O（l2） space complexities, where l is the training set size. It is thus com- /putationally infeasible on very large data sets.To alleviate the Computational burden in SVM training, we propose an algo- rithm to train SVMs on a bound vectors set that is extracted based on Fisher projection. For linear separate problems, we use linear Fisher discriminant to compute the projection line, while for non-linear separate problems, we use kernel Fisher discriminant to compute the projection line. For each case, we select a certain ratio samples whose projections are adja- cent to those of the other class as bound vectors. Theoretical analysis shows that the proposed algorithm is with low com- putational and space complexities.Extensive experiments on several classification benchmarks demonstrate the effective- ness of our approach.
基金Supported by the National Natural Science Foundation of China(11361001)Natural Science Foundation of Ningxia(NZ14101)
文摘There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.
