As an effective feature representation method, non-negative matrix factorization (NMF) cannot utilize the label information sufficiently, which makes it not be suitable for the classification task. In this paper, we propose a joint feature representation and classification framework named adaptive graph semi-supervised nonnegative matrix factorization (AGSSNMF). Firstly, to enhance the discriminative ability of feature representation and accomplish the classification task, a regression model with nonnegative matrix factorization (called as RNMF) is proposed, which exploits the relation between the label information and feature representation. Secondly, to overcome the drawback of insufficient labels, an adaptive graph-based label propagation (refereed as AGLP) model is established, which adopts a local constraint to reflect the local structure of data. Then, we integrate RNMF and AGLP into a unified framework for feature representation and classification. Finally, an iterative optimization algorithm is used to solve the objective function. Extensive experiments show that the proposed framework has excellent performance compared with some well-known methods.

作为一种有效的特征表示方法，非负矩阵分解（NMF）无法充分利用标签信息，因此不适合分类任务。在本文中，我们提出了一个联合特征表示和分类框架，称为自适应图半监督非负矩阵分解（AGSSNMF）。首先，为了增强特征表示的判别能力并完成分类任务，提出了一种具有非负矩阵分解的回归模型（RNMF），该模型利用了标签信息与特征表示之间的关系。其次，为了克服标签不足的缺点，建立了基于图的自适应标签传播（称为AGLP）模型，它采用局部约束来反映数据的局部结构。然后，我们将RNMF和AGLP集成到用于特征表示和分类的统一框架中。最后，使用迭代优化算法求解目标函数。大量的实验表明，与一些众所周知的方法相比，该框架具有出色的性能。