Abstract: A novel dimensionality reduction method called Local Marginal Discriminant Analysis (LMDA) is proposed in this paper based on spectral graph theory and manifold learning. Based on Neighborhood Preserving Projections (NPP), the reconstruction distortion in the intra-class caused by linear projections is minimized, and at the same time the integrity of the Laplacian matrix of the intra-class graph is kept, and margin between inter-class and intra-class is also maximized by constructing a weighted compactness nearest-neighbor graphs and a counterpart penalty graph. Finally, the numerical experimental results compared to other methods show that LMDA outperforms NPP.