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 . In this paper, two kinds of support vector machines, classification support vector machines and regression support vector machines are respectively used to prove their geometric properties. Based on these properties, these two kinds of support vector machines are discussed to promote the new samples, The new sample has some very valuable conclusions about the influence of support vector and unsupported vector and the new sample itself. From these results, it can be seen that support vector machine has a good promotion ability for the new sample, that is, Good inclusion and adaptability to the new sample, and support vector machine is a kind of accumulative learning model.