小样本数据的支持向量机回归模型参数及预测区间研究

Research on Parameters and Forecasting Interval of Support Vector Regression Model to Small Sample

支持向量机是由统计学习理论发展起来的机器学习算法,它从结构风险最小化的角度保证了模型的最大泛化能力。文中运用支持向量机进行小样本数据回归分析研究。首先利用推广性的界理论指导支持向量机回归模型参数的选取,以保证模型具有最大的推广能力;其次,运用基于正态分布和基于t分布的两种区间预测方法进行了预测值的区间估计;最后,利用模拟序列和真实的航空发动机油样光谱分析数据作为实验数据,建立了支持向量机回归分析模型,并与最小二乘法进行了比较。结果表明,所提出的支持向量机模型参数选取和区间估计方法适用于小样本数据的回归分析,具有较高的预测精度。

Support vector machine is a new machine learning method based on statistic learning theory （SLT）, it can assure the most generalization on the foundation of structural risk minimization. The small sample data modeled with support vector regression （SVR） is described. Firstly, model parameters are. chosen according to the bound theory of generalization performance in order to assure the most generalization of regression model; then, the two forecasting interval methods are applied, one is based on normal distribution, the other is based on t distribution ; in the end, the SVR model is established by using simulated data and true aero - engine spectrometric oil analysis data, and it is compared with least square method. The result indicated that the parameter selection and interval estimation method of SVR regression model has high accuracy to regression analysis of small sample data.