Current methods of feature selection based on a self-representation framework use all the features of the original data in their representation framework. This issue carries over redundant and noisy features into the representation space, thereby diminishing the quality and effectiveness of the results. This work proposes a novel representation learning method, dubbed GRSSLFS (Graph Regularized Self-Representation and Sparse Subspace Learning), that mitigates the drawbacks of using all features. GRSSLFS employs an approach for constructing a basis for the feature space, which includes those features with the highest variance. The objective function of GRSSLFS is then developed based on a self-representation framework that combines subspace learning and matrix factorization of the basis matrix. Moreover, these basis features are incorporated into a manifold learning term to preserve the geometrical structure of the underlying data. We provide an evaluation of effectiveness and performance of GRSSLFS on several widely used benchmark datasets. The results show that GRSSLFS achieves a high level of performance compared to several classic and state-of-the-art feature selection methods.