An approach to the learning curves of an incremental support vector machines

Support victor machines (SVMs) are known to result in a quadratic programming problem, that requires a large computational complexity. To overcome this problem, the authors proposed two incremental SVMs from the geometrical point of view in the previous study, both have a linear complexity with respect to the number of examples on average. One method was shown to produce the same solution as an SVM in batch mode, but the other,which stores the set of support vectors, was known to have a larger generalization error. In this study, we derive the learning curves of the latter method, assuming that the probability the set of support vectors is updated is proportional to the current margin and so is the decrease of the margin in the update, too. In the derivation, we employ the disc approximation which is to be justified yet, but the result agrees well with computer simulations.