For classifying images with various appearances, graph embedding based subspace learning has difficulty in taking a comprehensive consideration of both local geometrical structure and between-class discriminative information. In addition, when no sufficient training samples exist, using only the simple weight graph corresponding to labeled samples, the embedding subspace may not be accurately modeled. We present a semisupervised graph embedding algorithm by combining graph embedding and sparse representation. This algorithm can effectively learn a compact and semantic subspace by using a locally connected graph, which can model the geometrical structure and essential correlation of subclusters within a class and can fully utilize both labeled and unlabeled samples. Moreover, using -norm, the proposed algorithm can preserve the sparse representation property of images from the original space in the lower dimensional projected space. Our experiments demonstrate that the proposed algorithm has better performance than the alternatives reported in recent literature.