This study introduces a groundbreaking structure for semi-supervised learning based on graphs. Our technique provides an all-encompassing strategy that simultaneously tackles the challenges of label prediction and linear transformation. Specifically, the linear transformation we advocate is designed to forge a distinguishing subspace, thereby significantly compressing the data’s dimensionality.In advancing semi-supervised learning techniques, our framework particularly focuses on effectively utilizing the intrinsic data configuration and the provisional labels related to the unlabeled examples in our possession. This distinctive methodology leads to a more sophisticated and discriminative form of linear transformation. Tests carried out on authentic image datasets clearly validate the efficiency of the method we advocate. These tests repeatedly show enhanced performance in contrast to semi-supervised strategies that address the fusion of data and label deduction in isolation.