Semi-supervised learning(SSL)

as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data

has been attracting increasing attention in machine learning community.Of various SSL methods

graph based approaches have attracted more extensive research due to their elegant mathematical formulation and good performance.However

there may exist several nontrivial concerns such as such as model parameters sensitiveness and insufficient discriminative information in data space

etc

in existing graph based SSL approaches.To these ends

in this paper

we propose a robust Sparse Feature Space embedding Regularization(SFSR)SSL framework.The main idea of the proposed SFSR includes three folds:(1)linearly embedding input data into its feature spaces(2)sparsely reconstructing input data using its feature space embedding projection images;and(3)preserving the same sparse representation relationship among labels of data as that among data in some label space spanned linearly by input data

thus constructing a novel sparse nearest feature space embedding regularizer

coined as SFSR.The comprehensive experimental results on several real-world benchmark databases are presented to demonstrate the significantly robust effectiveness of our proposed method.