A note on the universal approximation capability of support vector machines

The approximation capability of support vector machines (SVMs) is investigated. We show the universal approximation capability of SVMs with various kernels, including Gaussian, several dot product, or polynomial kernels, based on the universal approximation capability of their standard feedforward neural network counterparts. Moreover, it is shown that an SVM with polynomial kernel of degree p - 1 which is trained on a training set of size p can approximate the p training points up to any accuracy.