Semi-supervised Gaussian random field transduction and induction

This paper proposes a semi-supervised inductive algorithm adopting a Gaussian random field(GRF)and Gaussian process.We introduce the prior based on graph regularization.This regularization term measures the p-smoothness over the graph.A new conditional probability called the extended Bernoulli model(EBM)is also proposed.EBM generalizes the logistic regression to the semi-supervised case,and especially,it can naturally represent the margin.In the training phase,a novel solution is given to the discrete regularization framework defined on the graphs.For the new test data,we present the prediction formulation,and explain how the margin model affects the classification boundary.A hyper-parameter estimation method is also developed.Experimental results show that our method is competitive with the existing semi-supervised inductive and transductive methods.