As one of the most effective feature learning methods, Nonnegative Matrix Factorization (NMF) has been widely used in many scientific fields, such as computer vision, data mining, and bioinformatics. However, NMF is an unsupervised method that cannot fully utilize the label information of data. Thus, its performance is limited in some recognition and classification problems. To remedy this shortcoming, this paper proposes a Semisupervised Discriminative NMF (SDNMF) method. First, we design a Soft-Labeled NMF (SLNMF) model by introducing a soft-label matrix-based regression term into the original NMF, so that the relationship between the soft-label matrix and low-dimensional features can be constructed to improve the discriminative ability of low-dimensional features. Second, to effectively estimate the soft-label matrix, a Label Propagation (LP) model is adopted to fully explore the spatial distribution relationship between the labeled and unlabeled samples. Third, an Adaptive Graph Learning (AGL) model is proposed to exploit the geometric relationship of samples well, which could enhance the performance of LP. Finally, the above three models (i.e., SLNMF, LP, and AGL) are integrated into a unified framework for effective feature learning, which can not only effectively explore the structural relationship matrix between data, but also predict the labels for unknown samples. Moreover, an iterative optimization algorithm is presented to solve our objective function. The convergence and computational complexity analysis of the proposed SDNMF method are also provided. Extensive experiments are conducted on several standard data sets. Compared with related methods, the experimental results verify that the proposed SDNMF method achieves better performance.

中文翻译：

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SDNMF：用于特征学习的半监督判别非负矩阵分解

作为最有效的特征学习方法之一，非负矩阵分解（NMF）已广泛应用于许多科学领域，如计算机视觉、数据挖掘和生物信息学。然而，NMF 是一种无监督的方法，不能充分利用数据的标签信息。因此，其性能在某些识别和分类问题上受到限制。为了弥补这一缺点，本文提出了一种半监督判别 NMF (SDNMF) 方法。首先，我们通过在原始 NMF 中引入基于软标签矩阵的回归项来设计软标签 NMF（SLNMF）模型，从而可以构建软标签矩阵与低维特征之间的关系，从而提高低维特征的判别能力。其次，为了有效地估计软标签矩阵，采用标签传播（LP）模型来充分探索标记和未标记样本之间的空间分布关系。第三，提出了一种自适应图学习（AGL）模型来很好地利用样本的几何关系，从而提高 LP 的性能。最后，将上述三种模型（即SLNMF、LP和AGL）集成到一个统一的框架中进行有效的特征学习，不仅可以有效地探索数据之间的结构关系矩阵，还可以预测未知样本的标签。此外，提出了一种迭代优化算法来求解我们的目标函数。还提供了所提出的 SDNMF 方法的收敛性和计算复杂性分析。在几个标准数据集上进行了广泛的实验。与相关方法相比，