In a biometric recognition task, the manifold of data is the result of the interactions between the sub-manifold of dynamic factors of subjects and the sub-manifold of static factors of subjects. Therefore, instead of directly constructing the graph Laplacian of samples, we firstly divide each subject data into a static part (subject-invariant part) and a dynamic part (intra-subject variations) and then jointly learn their graph Laplacians to yield a new graph Laplcian. We use this new graph Laplacian to replace the original graph Laplacian of Locality Preserving Projections (LPP) to present a new supervised dimensionality reduction algorithm. We name this algorithm Globality-Locality Preserving Projections (GLPP). Moreover, we also extend GLPP into a 2D version for dimensionality reduction of 2D data. Compared to LPP, the subspace learned by GLPP more precisely preserves the manifold structures of the data and is more robust to the noisy samples. We apply it to face recognition and gait recognition. Extensive results demonstrate the superiority of GLPP in comparison with the state-of-the-art algorithms.