Discriminative Orthogonal Nonnegative matrix factorization with flexibility for data representation
Discriminative Orthogonal Nonnegative matrix factorization with flexibility for data representation
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DOI：
10.1016/j.eswa.2013.08.026
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发表时间：
2014-03
期刊：
影响因子：
--
通讯作者：
Ping Li;Jiajun Bu;Yi Yang;R. Ji;Chun Chen;Deng Cai
中科院分区：
文献类型：
--
作者：
Ping Li;Jiajun Bu;Yi Yang;R. Ji;Chun Chen;Deng Cai
在人脸分析、文档聚类和协作过滤等多学科应用中，学习信息量大的数据表示是至关重要的。作为一种非常有用的工具，非负矩阵分解(NMF)经常被用来学习结构良好的数据表示。虽然以前的一些NMF变体研究了数据的几何结构，但现有的工作往往忽略了数据的类间散布和总散布所揭示的判别信息。为了解决这一问题，我们提出了一种新的方法--判别正交非负矩阵分解(DON)，它通过流形判别学习同时保持局部流形结构和全局判别信息。特别是，为了学习数据表示的判别结构，我们引入了缩放指示矩阵，它自然地满足正交性条件。因此，我们对目标函数施加了正交性约束。然而，过多的约束将导致非常稀疏的数据表示，这在现实中是意想不到的。因此，我们进一步使这种正交性变得灵活。此外，我们还给出了优化框架以及更新规则的收敛证明。对几种最先进的方法进行了广泛的比较，证明了该方法的有效性。
Learning an informative data representation is of vital importance in multidisciplinary applications, e.g., face analysis, document clustering and collaborative filtering. As a very useful tool, Nonnegative matrix factorization (NMF) is often employed to learn a well-structured data representation. While the geometrical structure of the data has been studied in some previous NMF variants, the existing works typically neglect the discriminant information revealed by the between-class scatter and the total scatter of the data. To address this issue, we present a novel approach namedDiscriminative Orthogonal Nonnegative matrix factorization(DON), which preserves both the local manifold structure and the global discriminant information simultaneously through manifold discriminant learning. In particular, to learn the discriminant structure for the data representation, we introduce the scaled indicator matrix, which naturally satisfies the orthogonality condition. Thus, we impose the orthogonality constraints on the objective function. However, too heavy constraints will lead to a very sparse data representation that is unexpected in reality. So we further make this orthogonality flexible. In addition, we provide the optimization framework with the convergence proof of the updating rules. Extensive comparisons over several state-of-the-art approaches demonstrate the efficacy of the proposed method.