正交非负CP分解的图像表示和识别

摘要

An orthogonal non-negative CANDECOMP/PARAFAC factorization algorithm (ONNCP) is proposed. With the orthogonal constrain, the low-dimensional presentations of samples are kept non-negative in ONNCP. The relationship between NNCP and NMF is analyzed theoretically. The solution process and the convergence of the algorithm are discussed. The experiments indicate that, compared with other non-negative factorization algorithms, ONNCP can reduce the redundancy of the base images and enhance the sparseness of the base images due to its orthogonality. It also ensures the low-dimensional feature is non-negative. The algorithm can achieve better recognition rate in facial expression recognition and will convergence a fixed point. Furthermore, the algorithm can be generalized to any order tensor.%提出了一种正交非负CP分解算法.将图像库视为三阶张量,进行非负分解,并对非负因子增加了正交约束,保证了图像低维表示的非负性.实验结果表明,较之其他非负分解算法,正交非负CP算法通过增加基图像的正交约束,减少了基图像的冗余性,进一步提高了基图像的稀疏性,同时保证了低维特征的非负性；将其用于人脸表情识别,该算法具有较高的识别率,在有限次迭代次数内能够达到收敛,并且该算法可以推广到任意阶张量.