The performance of semi-supervised Laplacian regularized regression with the least square loss

Abstract

The capacity convergence rate for a kind of kernel regularized semi-supervised Laplacian learning algorithm is bounded with the convex analysis approach. The algorithm is a graph-based regression whose structure shares the feature of both the kernel regularized regression and the kernel regularized Laplacian ranking. It is shown that the kernel reproducing the hypothesis space has contributions to the clustering ability of the algorithm. If the scale parameters in the Gaussian weights are chosen properly, then the learning rate can be controlled by the unlabeled samples and the algorithm converges with the increase of the number of the unlabeled samples. The results of this paper show that choosing suitable structure the semi-supervised learning approach can not only increase the learning rate, but also finish the learning process by increasing the number of unlabeled samples.