In order to develop linear local tangent space alignment to supervised learning algorithm

an algorithm called orthogonal discriminant linear local tangent space alignment is proposed.The algorithm makes use of class information of the data samples to compute the interclass scatter matrix.Then we modify the objective function of the original algorithm

constructing the new optimization problem.Moreover

on this basis

the algorithm orthogonalizes the subspace to obtain the orthogonal one.The effectiveness of the algorithm has been verified on two standard face databases.With local tangent space representing for local geometrical structure of the manifold of the data samples，the algorithm fuses discriminant information and orthogonal technique to preserve the local geometrical structure and discriminant structure

and the algorithm improves the recognition performance.