基于Hermite插值的SVM研究

在传统SVM的分类求解算法中,由于严格凸的无约束最优化问题中单变量函数x+是不可微的,不能使用通常的最优化的算法进行求解。三次Hermite插值多项式光滑的支持向量机模型采用的是一种多项式光滑技术,用三次Hermite插值多项式代替单变量函数x+,将原来不可微的模型变为可微的模型,并且给出了三次Hermite插值多项式光滑化单变量函数x+的推导过程。使用UCI机器学习数据集中的数据,通过实验验证了该模型的有效性。

SVM research based on Hermite interpolation

In traditional SVM solution algorithms,objective function is a strictly convex unconstrained optimization problem,but is not differentiable due to x ,which precludes the use of most used optimization algorithms.Polynomial smooth techniques are applied to SVM model and replace x by a very accurate smooth approximation that is Hermite Interpolation polynomial,thus the undifferential model is converted into a differential model.The deduction procedure of Hermite Interpolation polynomial smoothing x is extended.Experiments with UCI datasets show the validity of the model.