Incremental Training of Support Vector Machines Using Truncated Hypercones

We discuss incremental training of support vector machines in which we approximate the regions, where support vector candidates exist, by truncated hypercones. We generate the truncated surface with the center being the center of unbounded support vectors and with the radius being the maximum distance from the center to support vectors. We determine the hypercone surface so that it includes a datum, which is far away from the separating hyperplane. Then to cope with non-separable cases, we shift the truncated hypercone along the rotating axis in parallel in the opposite direction of the separating hyperplane. We delete the data that are in the truncated hypercone and keep the remaining data as support vector candidates. In computer experiments, we show that we can delete many data without deteriorating the generalization ability.