论文标题
Zellner惩罚的非负矩阵分解
Nonnegative Matrix Factorization with Zellner Penalty
论文作者
论文摘要
非负矩阵分解（NMF）是一种相对较新的无监督学习算法，将非负数据矩阵分解为基于零件的，较低的尺寸，线性的线性表示。 NMF在图像处理，文本挖掘，推荐系统和许多其他领域中都有应用。自成立以来，NMF算法已由众多作者修改和探索。一种这样的修改涉及将辅助约束添加到分解的目标函数中。这些辅助约束的目的是对目标函数施加特定于任务的惩罚或限制。尽管已经研究了许多辅助约束，但没有人使用与数据相关的惩罚。在本文中，我们提出了使用数据依赖性辅助约束的Zellner非负矩阵分解（ZNMF）。我们使用剑桥ORL数据库评估ZnMF算法的面部识别性能和其他几种众所周知的约束NMF算法。
Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image processing, text mining, recommendation systems and a variety of other fields. Since its inception, the NMF algorithm has been modified and explored by numerous authors. One such modification involves the addition of auxiliary constraints to the objective function of the factorization. The purpose of these auxiliary constraints is to impose task-specific penalties or restrictions on the objective function. Though many auxiliary constraints have been studied, none have made use of data-dependent penalties. In this paper, we propose Zellner nonnegative matrix factorization (ZNMF), which uses data-dependent auxiliary constraints. We assess the facial recognition performance of the ZNMF algorithm and several other well-known constrained NMF algorithms using the Cambridge ORL database.
