Solving SVM inverse problems based on clustering

Support vector machine (SVM) theory was originally developed on the basis of a linearly separable binary classification problem. The inverse problem of SVM is how to split a given dataset into two clusters such that the margin between the two clusters attains maximum. Due to the computational complexity, it is difficult to give an exact and feasible solution to the inverse problem. This paper makes an attempt to reduce the complexity of the inverse problem by clustering. It is demonstrated that the maximum margin between the two clusters is equivalent to the distance between the two closest points in convex hulls in the linearly separable case. For the inseparable case, the maximum margin between the two sets is equivalent to the distance between the two closest points in the reduced convex hulls.