基于信息几何的混沌支持向量机预测

复杂环境中存在大量的混沌现象,难以用传统的预测方法进行准确预测.针对这一问题,本文利用信息几何理论、支持向量机理论与重构相空间理论,提出混沌支持向量机CSVM,对含有混沌现象的时间序列进行预测;针对混沌环境下核函数难于构造,从信息几何角度,提出在混沌环境下,如何方便准确得进行构造核函数;最后将CSVM应用于Henon混沌系统实验.实验结果表明,误差随嵌入维数变化和延迟时间变化趋于恒定;与BP、RBF和SVM相比,CSVM具有所需支持向量少,收敛速度快,准确性高等特点.

Prediction with Chaos SVM Based on Information Geometry

There are many chaos phenomenons in complex environment, so it is difficult to predict by the traditional methods. Chaos support vector machine was given to predict time-series with chaos phenomenon to overcome the disadvantages of the traditional methods in this paper based on information geometry, SVM theory and chaos theory. Especially, a new kernel function was introduced into the chaos support vector machine from the perspective of information geometry and thus it is easy to design the kernel function. Finally, the method was applied to Henon chaos system compared with the BP, RBF and SVM. The prediction results indicate that the predictive error changes with the increase of embed dimension and delay time to a constant. And the results also show that the chaos support vector machine is more precise although it requires smaller support vector, and has faster convergence rate, compared with BP,RBF and SVM.