Abstract Many previous graph-based methods perform dimensionality reduction on a pre-defifined graph. However, due to the noise and redundant information in the original data, the pre-defifined graph has no clear structure and may not be appropriate for the subsequent task. To overcome the drawbacks, in this paper, we propose a novel approach called linear manifold regularization with adaptive graph (LMRAG) for semi-supervised dimensionality reduction. LMRAG directly incorporates the graph construction into the objective function, thus the projection matrix and the adaptive graph can be simultaneously optimized. Due to the structure constraint, the learned graph is sparse and has clear structure. Extensive experiments on several benchmark datasets demonstrate the effectiveness of the proposed method