关键词: 支持向量机, 多分类, 闭凸包

Abstract: According to the maximal margin linear classifier and the contraction of closed convex hull，2-classification linearly non-separable problem can be transformed to linearly separable problem by using proposed contraction methods of closed convex hull.Multi-classification problem can be solved by contracting closed convex，and multi-classification algorithm based on the contraction of closed convex hull is presented.The geometric meaning of optimization problem is obvious.The shortcomings of complicated objective function in multi-classification are overcame，nonlinear separable multi-classification problem can be solved using kernel method.

Key words: Support Vector Machine（SVM）, multi-classification, closed convex hull