本文的核心工作：提出加入正交约束的3-factor NMF方法及其解法、正确性、收敛性证明和加入正交约束的好处
加入正交约束的好处：
（1）解的唯一性：降低了矩阵分解的自由度
（2）聚类解释，及证明
ref: 关于trace（矩阵的迹）和求导之间的关系。ref： http://www.cnblogs.com/crackpotisback/p/5545708.html （链接点在于tr(a) = a， 其中a为常数）
| 文献题目 | 去谷歌学术搜索 | ||||||||||
| Orthogonal Nonnegative Matrix Tri-factorizations for Clustering | |||||||||||
| 文献作者 | Chris Ding | ||||||||||
| 文献发表年限 | 2006 | ||||||||||
| 文献关键字 | |||||||||||
| 3-factor NMF; semi-NMF; 带有正交约束的NMF求解方法；证明NMF等同于k-means； Nonnegative, non-negative; trace, 矩阵的迹trace；矩阵分解自由度； the degree of freedom | |||||||||||
| 摘要描述 | |||||||||||
| Currently, most research on nonnegative matrix factorization (NMF) focus on 2-factor X = FG T factorization. We provide a systematic analysis of 3-factor X = FSG T NMF. While unconstrained 3-factor NMF is equivalent to unconstrained 2-factor NMF, constrained 3- factor NMF brings new features to constrained 2-factor NMF. We study the orthogonality constraint because it leads to rigorous clus- tering interpretation. We provide new rules for updating F, S, G and prove the convergence of these algorithms. Experiments on 5 datasets and a real world case study are performed to show the capability of bi-orthogonal 3-factor NMF on simultaneously clus- tering rows and columns of the input data matrix. We provide a new approach of evaluating the quality of clustering on words us- ing class aggregate distribution and multi-peak distribution. We also provide an overview of various NMF extensions and examine their relationships. | |||||||||||
