本文针对两种不同用途的支撑矢量机,分类支撑矢量机和回归支撑矢量机,分别证明了它们的一些几何性质,从这些性质出发讨论了这两种支撑矢量机对新增样本的推广能力,新增样本对支撑矢量,非支撑矢量的影响以及新增样本本身的一些特点,得到了一些非常有价值的结论.从这些结论可以看出支撑矢量机对新增样本具有良好的推广能力,即对新增样本的良好的包容性和适应性,并且支撑矢量机是一种可积累的学习模型.

Some geometry of Support Vector Machines for classification and regression is described and proven.And then the generalization performance of SVMs on newly-added samples is discussed.Through the analysis of the property of newly-added samples and the effect of them on support vectors and non-support vectors,some valuable results are presented.These enable us to conclude that SVM has a good compatibility,adaptability and generalization performance for newly-added samples and is a hereditable learning model.