Nonlinear Non-Negative Component Analysis Algorithms
Nonlinear Non-Negative Component Analysis Algorithms
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DOI：
10.1109/tip.2009.2038816
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发表时间：
2010-04
影响因子：
10.6
通讯作者：
S. Zafeiriou;M. Petrou
中科院分区：
文献类型：
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作者：
S. Zafeiriou;M. Petrou
本文提出了用于数据表示和识别的非线性非负分量分析的一般解决方案。将非负矩阵分解(NMF)算法与核理论相结合，在多项式特征空间中提出了一种新的NMF算法，提出了一种基于核的非线性非负分量分析方法，即投影梯度核非负矩阵分解(PGKNMF)方法。在该方法中，可以采用任意的正定核函数，同时保证过程的极限点是优化问题的一个固定点。此外，对于高斯径向基函数(RBF)核的特殊情况，我们提出了不动点算法。我们展示了所提出的方法在人脸和面部表情识别应用中的能力。
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.