Sparse Manifold Clustering and Embedding (SMCE) can adaptively select nearby points that lie in the same manifold based on sparse representation. However, there is no explicit project matrix in SMCE, and the unsupervised nature restricts its discriminating capability. Supervised Sparse Manifold Embedding (SSME) was proposed for dimensionality reduction of hyperspectral data. At first, the SSME method finds the sparse coefficients in affine subspace by solving a sparse optimization problem. It constructs the similarity weight matrix using the sparse coefficients, and naturally incorporates the label information into the weights. Then, it tries to extract discriminative features by increasing the compactness between homogeneous data in a low-dimensional embedding space. The experiments show that the SSME method not only inherits the merits of the sparsity property but also improves the severability of data points from different classes.