A bottom-up method for simplifying support vector solutions.

The high generalization ability of support vector machines (SVMs) has been shown in many practical applications, however, they are considerably slower in test phase than other learning approaches due to the possibly big number of support vectors comprised in their solution. In this letter, we describe a method to reduce such number of support vectors. The reduction process iteratively selects two nearest support vectors belonging to the same class and replaces them by a newly constructed one. Through the analysis of relation between vectors in input and feature spaces, we present the construction of the new vectors that requires to find the unique maximum point of a one-variable function on (0,1), not to minimize a function of many variables with local minima in previous reduced set methods. Experimental results on real life dataset show that the proposed method is effective in reducing number of support vectors and preserving machine's generalization performance.