2-dimensional Projective Non-negative Matrix Factorization and Its Application to Face Recognition
二维投影非负矩阵分解算法及其在人脸识别中的应用

Face recognition algorithms through minimizing the loss function of non-negative matrix factorization must simultaneously calculate the base matrix and the coefficient matrix, which leads to the high computational complexity. This paper introduces the non-negative properties into 2-dimensional principal component analysis (2DPCA), and then proposes a novel 2-dimensional projective non-negative matrix factorization (2DPNMF) for face recognition. 2DPNMF preserves the local structure of face images but breaks through the restriction of minimizing the loss function of non-negative matrix factorization. Since 2DPNMF only needs calculating the projection matrix (base matrix), its computational complexity is greatly reduced. This paper theoretically proves the convergence of the proposed algorithm and uses YALE face database, FERET face database, and AR face database for the comparison experiments. Experimental results show that 2DPNMF has higher recognition performance as well as a much faster speed than NMF and 2DPCA.