Department of Computer Science and Engineering, University of Texas at Arlington, Nedderman Hall, Room 307, 416 YatesStreet, Arlington, TX 76019, USA.
IEEE Trans Pattern Anal Mach Intell. 2010 Jan;32(1):45-55. doi: 10.1109/TPAMI.2008.277.
We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X=FG(T), we focus on algorithms in which G is restricted to containing nonnegative entries, but allowing the data matrix X to have mixed signs, thus extending the applicable range of NMF methods. We also consider algorithms in which the basis vectors of F are constrained to be convex combinations of the data points. This is used for a kernel extension of NMF. We provide algorithms for computing these new factorizations and we provide supporting theoretical analysis. We also analyze the relationships between our algorithms and clustering algorithms, and consider the implications for sparseness of solutions. Finally, we present experimental results that explore the properties of these new methods.
我们提出了几种非负矩阵分解（NMF）主题的新变体。考虑到 X=FG(T) 的分解形式，我们专注于 G 限制为包含非负元素但允许数据矩阵 X 具有混合符号的算法，从而扩展了 NMF 方法的适用范围。我们还考虑了 F 的基向量被约束为数据点的凸组合的算法。这用于 NMF 的核扩展。我们提供了用于计算这些新分解的算法，并提供了支持性的理论分析。我们还分析了我们的算法与聚类算法之间的关系，并考虑了对解稀疏性的影响。最后，我们提出了实验结果，探索了这些新方法的性质。
