【摘要】 统计学习理论是研究有限样本情况下机器学习规律的理论。支持向量机是基于统计学习理论的一种新型的机器学习方法,可以解决样本空间中的高度非线性分类和回归等问题。建立了两种模型,模型Ⅰ将黄河干流兰州站的径流时间序列作为输入,模型Ⅱ将径流时间序列和太阳黑子作为输入,两种模型都应用支持向量机对次年的年径流进行预测。结果表明,SVM模型泛化能力强,具有较满意的预测效果。它较好地解决了小样本、过学习、高维数、局部最小等问题,同时模型Ⅱ的预测效果优于模型Ⅰ的,说明径流除了与径流时间序列本身有关外,与太阳黑子活动等有较密切的关系。虽然两者间的物理关系尚需进一步研究,但是支持向量机反映出两者间的非线性关系。更多还原

【Abstract】 Statistical learning theory is suitable for calculating the statistics of small-sample data.As a new machine learning method based on this theory,the support vector machine(SVM) can solve the problems of nonlinear classification and regression in sample space.This paper develops two SVM models,one takes the runoff of Lanzhou station on Yellow River as its input,and the other takes the same runoff and the sunspot effect as its inputs.Both models are applied to the prediction of the annual runoff of next year.The results show that SVM possesses stronger generalization ability and higher prediction accuracy,and it is a useful tool to overcome the problems of small-sample,over-fitting learning,high-dimension and local minimum trapping.An improvement of prediction results by the second model over the first one indicates that the runoff is closely related to the sunspot activity.Though the physical meaning of this relation is not clear yet,the nonlinear relationship can be modeled by the SVM model.更多还原