Discriminative and robust least squares regression for semi-supervised image classification

Due to the ability to leverage information from both unlabeled and labeled data, semi-supervised classification has found extensive applications in various practical scenarios. However, there are two major drawbacks: (1) Traditional graph construction leads to high algorithmic complexity, which limits efficiency. (2) The decision boundary might be blurred by boundary points in common cases. To cope with these issues, inspired by classical Least Squares Regression (LSR), we present a novel semi-supervised classification algorithm termed as Discriminative and Robust LSR (DRLSR) for semi-supervised image classification. First of all, a manifold regularization term is designed and introduced to an LSR-based semi-supervised method to preserve local manifold structures and smooth structures of the subspace, which strengthens the discrimination ability. Meanwhile, preservation of local manifold structures also contributes to restrain decision boundaries from being blurred by boundary points, which strengthens robustness of the algorithm. After that, an efficient alternative optimization method is applied to our algorithm. Evidence of the effectiveness of DRLSR are compelled by extensive experimental results.