The inverse problem of support vector machines and its solution

Support vector machine (SVM) is novel type learning machine, based on statistical learning theory, which tasks involving classification, regression or novelty detection. This paper investigates an inverse problem of support vector machines (SVMs). The inverse problem is how to split a given dataset into two clusters such that the margin between the two clusters attains the maximum. Here the margin is defined according to the separating hyper-plane generated by support vectors. It is difficult to give an exact solution to this problem. In this paper, we design a genetic algorithm to solve this problem. Numerical simulations show the feasibility and effectiveness of this algorithm. This study on the inverse problem of SVMs is motivated by designing a heuristic algorithm for generating decision trees with high generalization capability.