Ridge regression is an important method in supervised learning. It is wide used in multi-class classification and recognition. An important step in ridge regression is to define a special multivariate label matrix, which is used to encode multi-class samples. By regarding the ridge regression as a supervised learning method based on graph, methods for constructing multivariate label matrix were extended. On the basis of ridge regression, a new method named sparse smooth ridge regression was proposed by considering the global dimension smoothness and the sparseness of the projection matrix. Experiments on several public datasets show that the proposed method performs better than a series of state-of-the-art supervised linear algorithms. Furthermore, experiments show that the proposed label matrix construction methods do not reduce the performance of the original ridge regression. Besides, it can further improve the performance of the proposed sparse smooth ridge regression.