二维投影非负矩阵分解算法及其在人脸识别中的应用

建立在最小化非负矩阵分解损失函数上的人脸识别算法需同时计算基矩阵和系数矩阵, 导致求解这类问题十分耗时. 本文把非负属性引入二维主成分分析(2-dimensional principal component analysis, 2DPCA)中, 提出了一种新的二维投影非负矩阵分解(2-dimensional projective non-negative matrix factorization, 2DPNMF)人脸识别算法. 该算法在保持人脸图像的局部结构情况下, 突破了最小化非负矩阵分解损失函数的约束, 仅需计算投影矩阵(基矩阵), 从而降低了计算复杂度. 本文从理论上证明了所提出算法的收敛性, 同时, 使用了YALE、FERET和AR三个人脸库进行实验, 结果表明2DPNMF不仅识别率高, 而且速度优于非负矩阵分解和二维主成分分析.

2-dimensional Projective Non-negative Matrix Factorization and Its Application to Face Recognition

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.