回归型加权支持向量机方法及其应用

Weighted support vector machines for regression and its application

针对各样本重要性的差异,提出了给各个样本的惩罚系数和误差要求赋予不同权重的加权支持向量机方法.给出了对偶最优化问题的描述及其SMO训练算法.在近红外光谱汽油辛烷值测定实验中,训练样本的重要性通过测试样本与该样本的空间距离来表征.实验表明采用加权支持向量机方法提高了汽油辛烷值的测量精度,从而说明了该方法可以提高回归估计函数的泛化能力.

In the standard support vector machines for regression, the required error of regression estimation and the penalty for violation of the required error are equally considered for every training sample, which is unsuitable in case there exists significant difference among the training samples. In the proposed weighted support vector machines, each training sample had different approximation error requirement and different penalty. The dual quadratic optimization of weighted support vector machines for regression and its sequential minimal optimization (SMO) algorithms were given. The experiments on the measurement of gasoline octane numbers by near-infrared spectroscopy, where the importance of each training sample was characterized by the geometrical distance from the test sample, show that the measurement accuracy is improved with the proposed weighted support vector machines.