Convergence theorem for kernel perceptron

The convergence of the kernel perceptron algorithm is examined. We first introduce the kernel perceptron algorithm which is an application of kernel methods to perceptron learning and also an extension of the algebraic perceptron algorithm to a general kernel function and a general learning coefficient. Although the naive perceptron is shown to converge, it is not clear whether the kernel perceptron algorithm converges or not. We prove that it converges when the learning coefficient is unity and derive the condition of the learning coefficient to converge for given examples.