The standard implementation of traditional projection algorithms takes all the t raining samples as the input data,which scales badly with the dataset size and m akes computations for large samples application infeasible.We introduce a block optimization and batch alignment strategy to propose a novel locally discriminan t projection (LDP) algorithm for solving this problem.The advantages of the prop osed algorithm are:Firstly,it preserves the intra class structure of the manifol d and maximizes margins between the data of different classes;Secondly,the final projection matrix of the proposed algorithm has the orthogonality property;Thir dly,there is no small sample size problem in this algorithm;Finally,LDP can be e asily extended to the incremental LDP (ILDP) for learning the locally discrimina nt subspace with the newly inserted data by employing the singular value decompo sition updating algorithm.The experimental data by employing the singular value decomposition updating algoirthm.The experimental results on COIL image database ,USPS hand written digit database on ExYaleB face database demonstrate that ILDP has higher recognition rate compared with the classical ILDA,LSDA and MMP algor ithms.Especially in the USPS database,ILDP reaches recognition rate of 90% while the others are all below 85%.Meanwhile,ILDP bears less computational cost,which needs only less than 0.5s for training USPS database.