A genetic algorithm for solving the inverse problem of support vector machines

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.

[1]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[2]  Lalit M. Patnaik,et al.  Genetic algorithms: a survey , 1994, Computer.

[3]  Vladimir Vapnik,et al.  An overview of statistical learning theory , 1999, IEEE Trans. Neural Networks.

[4]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[5]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[6]  Nello Cristianini,et al.  On the generalization of soft margin algorithms , 2002, IEEE Trans. Inf. Theory.

[7]  Yoav Freund,et al.  Boosting the margin: A new explanation for the effectiveness of voting methods , 1997, ICML.