摘要
针对多核最小二乘支持向量机(multiple kernel least squares support vector machine,MK-LSSVM)忽略了核函数的代价以及缺乏稀疏性的问题,提出了一种代价约束的稀疏多核最小二乘支持向量机方法.将MK-LSSVM的原始优化问题转化为二阶锥规划形式,引入核函数代价因子,约束复杂核函数的权重,以节约变量存储空间和计算时间,利用Schmidt正交化理论约简核矩阵,进一步减小计算量,并根据支持向量的数目以及活动核函数的类型评估多核学习的总代价.测试数据集仿真结果表明,相比传统的MK-LSSVM,该方法利用更少的支持向量和更简单的组合核函数达到了相同的精度要求,代价更小.采用该方法预测浮选回收率的代价值降低了27.56.
Considering the neglect of kernel function cost and lack of sparsity of multiple kernel least squares support vector machine（MK-LSSVM）,a cost-constraint based multiple kernel least squares vector machine with sparsity is proposed.The primal optimal problem of MK-LSSVM is converted into second-order cone programming,and then the weight of complex kernel function is restricted by introducing cost factors so as to save storage space and computing time of variable quantity.Furthermore,the kernel matrices are reduced by Schmidt orthogonalization theory to lower computational complexity.The total cost of multiple kernel learning can be evaluated according to the number of support vectors and active kernel functions.The simulation results on testing datasets show that the proposed method can achieve the same accuracy as MK-LSSVM by using less support vectors and simpler mixture kernel functions with cheaper consumption and better real-time performance.The cost vaule of froth flotation mineral recovery prediction used the proposed method reduces 27.56.
出处
《信息与控制》
CSCD
北大核心
2012年第5期617-621,共5页
Information and Control
基金
国家杰出青年科学基金资助项目(61025015)
国家自然科学基金重点资助项目(61134006)
关键词
代价约束
多核学习
最小二乘支持向量机
稀疏性
泡沫浮选
回收率
cost-constraint
multiple kernel learning
least squares support vector machine
sparsity
froth flotation
recovery
