Method for Convergent Projective Non-negative Matrix Factorization

Abstract

In order to solve the problem of algorithm convergence in Projective Non-negative Matrix Factorization (P-NMF), a method, called Convergent Projective Non-negative Matrix Factorization (CP-NMF), is proposed. In CP-NMF, an objective function of Frobenius norm is defined. The Taylor series expansion and the Newton iteration formula of solving root are used. An iterative algorithm for basis matrix is derived, and a proof of algorithm convergence is provided. Experimental results show that the convergence speed of the algorithm is higher, however it is affected by the initial value of the basis matrix; relative to Non-negative Matrix Factorization (NMF), the orthogonality and the sparseness of the basis matrix are better, however the reconstructed results of data show that the basis matrix is still approximately orthogonal; in face recognition, there is higher recognition accuracy. The method for CP-NMF is effective.