College of Computer Science, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China.
IEEE Trans Pattern Anal Mach Intell. 2012 Jul;34(7):1299-311. doi: 10.1109/TPAMI.2011.217. Epub 2011 Nov 8.
Nonnegative matrix factorization (NMF) is a popular technique for finding parts-based, linear representations of nonnegative data. It has been successfully applied in a wide range of applications such as pattern recognition, information retrieval, and computer vision. However, NMF is essentially an unsupervised method and cannot make use of label information. In this paper, we propose a novel semi-supervised matrix decomposition method, called Constrained Nonnegative Matrix Factorization (CNMF), which incorporates the label information as additional constraints. Specifically, we show how explicitly combining label information improves the discriminating power of the resulting matrix decomposition. We explore the proposed CNMF method with two cost function formulations and provide the corresponding update solutions for the optimization problems. Empirical experiments demonstrate the effectiveness of our novel algorithm in comparison to the state-of-the-art approaches through a set of evaluations based on real-world applications.
非负矩阵分解 (NMF) 是一种流行的技术，用于寻找基于部分的非负数据的线性表示。它已成功应用于模式识别、信息检索和计算机视觉等广泛的应用中。然而，NMF 本质上是一种无监督方法，不能利用标签信息。在本文中，我们提出了一种新的半监督矩阵分解方法，称为约束非负矩阵分解 (CNMF)，它将标签信息作为附加约束。具体来说，我们展示了如何显式地结合标签信息来提高矩阵分解的判别能力。我们探讨了所提出的 CNMF 方法的两种代价函数公式，并提供了优化问题的相应更新解决方案。通过基于真实应用的一系列评估，实验结果表明我们的新算法与最先进的方法相比是有效的。
