In this paper, a novel framework for semi-supervised learning based on graphs is introduced. We present an innovative approach for concurrently estimating label inference and performing a linear transformation. This specific linear transformation is directed towards achieving a discriminant subspace, which effectively reduces the dimensionality of the data. To enhance the semisupervised learning process, our framework places a strong emphasis on leveraging the inherent data structure and incorporating the information provided by soft labels from the available unlabeled samples. The method we propose ultimately results in an improved discriminative linear transformation. The effectiveness of our approach is verified through a series of experiments conducted on real image datasets. These experiments not only confirm the efficacy of our proposed method but also demonstrate its superior performance when compared to semi-supervised methods that simultaneously incorporate integration and label inference.