文中给出了几种非负矩阵求法，包括乘子步长法，和标准的有界优化问题求法，例如利用函数：
max(0,\theta-\alpha*\gradient)
另外，知乎上一篇文章https://zhuanlan.zhihu.com/p/22043930 对这几种方法做了一个简单但很通俗的描述，值得学习，尤其是他关于分解矩阵的投影概念。
对NMF更详细的描述： https://blog.csdn.net/winone361/article/details/54962836
| 文献题目 | 去谷歌学术搜索 | ||||||||||
| Projected Gradient Methods for Nonnegative Matrix Factorization | |||||||||||
| 文献作者 | Chih-Jen Lin | ||||||||||
| 文献发表年限 | 2007 | ||||||||||
| 文献关键字 | |||||||||||
| 非负矩阵求法；NMF解释; VQ (vector quantization->K-means) | |||||||||||
| 摘要描述 | |||||||||||
| Nonnegative matrix factorization (NMF) can be formulated as a mini- mization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided. | |||||||||||
