Department of Electrical and Electronic Engineering, Imperial College London, London, UK.
IEEE Trans Image Process. 2010 Apr;19(4):1050-66. doi: 10.1109/TIP.2009.2038816. Epub 2009 Dec 18.
In this paper, general solutions for nonlinear non-negative component analysis for data representation and recognition are proposed. Motivated by a combination of the non-negative matrix factorization (NMF) algorithm and kernel theory, which has lead to a recently proposed NMF algorithm in a polynomial feature space, we propose a general framework where one can build a nonlinear non-negative component analysis method using kernels, the so-called projected gradient kernel non-negative matrix factorization (PGKNMF). In the proposed approach, arbitrary positive definite kernels can be adopted while at the same time it is ensured that the limit point of the procedure is a stationary point of the optimization problem. Moreover, we propose fixed point algorithms for the special case of Gaussian radial basis function (RBF) kernels. We demonstrate the power of the proposed methods in face and facial expression recognition applications.
本文提出了一种用于数据表示和识别的非线性非负成分分析的通用解。受非负矩阵分解（NMF）算法和核理论的组合的启发，这导致了最近在多项式特征空间中提出的 NMF 算法，我们提出了一个通用框架，其中可以使用核构建非线性非负成分分析方法，即所谓的投影梯度核非负矩阵分解（PGKNMF）。在提出的方法中，可以采用任意正定核，同时确保过程的极限点是优化问题的稳定点。此外，我们还针对高斯径向基函数（RBF）核的特例提出了定点算法。我们在人脸和面部表情识别应用中展示了所提出方法的强大功能。
