中文摘要：

从支持向量域SVD（Support Vector Domain）出发，根据Takens延时相空间重构思想，利用支持向量机非线性映射，建立了混沌时间序列和混沌非线性相轨迹运动的SVD预测模型．采用数据集作为支持对象元素，机器自学习缩小模型泛化误差的上界，利用最小二乘支持向量域（SVD），预测了Henon／Lorenz／Rossler三种混沌时间序列．预测结果表明，三种预测模型将集合映射到一个更高维特征空间，通过嵌入维数，实现了序列预测。误差随嵌入维数变化趋于恒定，与支持向量机（SVM）相比，SVD所需支持向量少，收敛速度快，鲁棒性强，核函数选择容易灵活，且存在自适应方法．网格点数提高了10—20倍，序列预测在小样本、非线性、未知概率密度条件下，预测和实际值取得了一致．

英文摘要：

Starting from the support vector domain model, the paper establishes SVD predictive models of chaos time series as well as chaos phase trace of non-linear map, based on Takens phase space delay reconstructing theory. We adopted the method of data set as support object elements. Machine self-learning reduces error upper limit of the generalized model. The three chaos time series, Henon/Lorenz/Rossler are predicted by least square. The prediction result indicates that the predictive model makes the set to be mapped into an eigen space of higher dimensions, and the series is predicted by embed dimensions. The predictive error changes with the increase of embed dimension to a constant. Compared with SVM, the SVD requires smaller support vector, and has faster convergence rate. It has robustness characteristics with adaptive flexible kernel function choice. The predicted net points are ten to twenty times more than SVM. Under the conditions of small sample, non-linear, and unknown probability density, the predicted series is in concordance with the series＇ true value.