使用自动微分的分类算法

The Classified Algorithm With Automatic Differentiation

解决支持向量机中的分类算法需要计算多变量函数的有关偏导数问题,通常使用的计算方法符号微分和差分近似．对于中大规模问题来说,使用符号微分方法,成本昂贵,有时甚至不可行,在计算导数的方向梯度时,利用差分方法虽然可以降低计算成本,但得到的是近似值,而且确定恰当的差分区间也很困难．本文将自动微分技术与分类算法相结合,以较低的成本精确计算了中大规模问题函数的导数,建立并研究了使用自动微分的分类算法．并用数值试验验证了这一算法的有效性．

Evaluation relevant to the partial derivatives of the multivariable functions is often done in the classified method of the support vectors machines, usually by means of the symbolic differentiation or the divided difference. But for the middle and large scale problems, the computation cost by symbolic differentiation is very expensive. When the direction derivative is evaluated, the computation cost by divided difference can be reduced, but it is only one kind of approximate computation. Moreover, it is very difficult to confirm the divided difference interval rightly. The article combines the automatic differentiation with the classified algorithm and researches the classified algorithm with the automatic differentiation, by which the derivatives of the function can be evaluated both exactly and economically. At last, new algorithm is implemented by basic numerical experiments.