Semi-supervised Learning with Regularized Laplacian

We study a semi-supervised learning method based on the similarity graph and RegularizedLaplacian. We give convenient optimization formulation of the Regularized Laplacian method and establishits various properties. In particular, we show that the kernel of the methodcan be interpreted in terms of discrete and continuous time random walks and possesses several importantproperties of proximity measures. Both optimization and linear algebra methods can be used for efficientcomputation of the classification functions. We demonstrate on numerical examples that theRegularized Laplacian method is competitive with respect to the other state of the art semi-supervisedlearning methods.