IEEE Trans Pattern Anal Mach Intell. 2011 Aug;33(8):1548-60. doi: 10.1109/TPAMI.2010.231. Epub 2010 Dec 23.
Matrix factorization techniques have been frequently applied in information retrieval, computer vision, and pattern recognition. Among them, Nonnegative Matrix Factorization (NMF) has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain. On the other hand, from the geometric perspective, the data is usually sampled from a low-dimensional manifold embedded in a high-dimensional ambient space. One then hopes to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In this paper, we propose a novel algorithm, called Graph Regularized Nonnegative Matrix Factorization (GNMF), for this purpose. In GNMF, an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization, which respects the graph structure. Our empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.
矩阵分解技术在信息检索、计算机视觉和模式识别等领域得到了广泛的应用。其中，非负矩阵分解（NMF）因其对自然发生的数据的心理和生理解释而受到关注，这些数据的表示可能基于人类大脑的部分。另一方面，从几何的角度来看，数据通常是从嵌入在高维环境空间中的低维流形中采样得到的。人们希望找到一种紧凑的表示形式，揭示隐藏的语义，同时尊重内在的几何结构。为此，在本文中，我们提出了一种新的算法，称为图正则化非负矩阵分解（GNMF）。在 GNMF 中，构建了一个关联图来编码几何信息，我们寻求一种尊重图结构的矩阵分解。我们的实证研究表明，与基于最先进算法的真实问题相比，所提出的算法取得了令人鼓舞的结果。
