Abstract: To solve the problem that the iterative method for Linear Projection-Based Non-negative Matrix Factorization(LPBNMF)is complex,a method,called Linear Projective Non-negative Matrix Factorization(LP-NMF),was proposed．In LP-NMF,from projection and linear transformation angle,an objective function of Frobenius norm is considered．The Taylor series expansion is used．An iterative algorithm for basis matrix and linear transformation matrix is derived strictly and a proof of algorithm convergence is provided．Experimental results show that the algorithm is convergent,and relative to Non-negative Matrix Factorization(NMF)and so on,the orthogonality and the sparseness of the basis matrix are better,in face recognition,there is higher recognition accuracy．The method for LP-NMF is effective.

Key words: Projective non-negative matrix factorization,Linear transformation,Face recognition