支持向量机函数拟合在分形插值中的应用

Application of support vector machines function regression in fractal interpolation

为消除分形插值曲线的断裂和周期现象 ,论文提出在分形插值的后期使用基于统计学习理论 ( SL T)的支持向量机 ( SVM)函数拟合方法。统计学习理论 ( SL T)着重研究在小样本情况下的统计规律及学习方法性质。支持向量机是建立在 SL T理论框架上新的通用学习算法。用该方法对随机生成的分形模型进行拟合实验 ,达到很好的效果。所以 ,在分形插值后期使用 SVM函数拟合 ,不但可以消除插值曲线的不确定性 ,还可以保留分形曲线显示细节变化的优点。

Rupture of fractal curves is controled using support vector machine function regression in the later period of fractal interpolation. The method uses Statistical Learning Theory (SLT) which mainly considers the statistic properties of small samples, especially the properties of the learning procedure in such cases. SLT provides a new framework for the general learning problem and a powerful new learning method called support vector machine which can solve small sample learning problems better. The method not only eliminates the rupture of fractal curve in sample calculations, but also has the advantage of fractal interpolation, which can display details.