The nonnegative matrix factorization (NMF) has been widely used because it can accomplish both feature representation learning and dimension reduction. However, there are two critical and challenging issues affecting the performance of NMF models. One is the selection of matrix factorization rank, while most of the existing methods are based on experiments or experience. For tackling this issue, an adaptive and stable NMF model is constructed based on an adaptive factorization rank selection (AFRS) strategy, which skillfully and simply integrates a row constraint similar to the generalized elastic net. The other is the sensitivity to the initial value of the iteration, which seriously affects the result of matrix factorization. This issue is alleviated by complementing NMF and deep learning each other and avoiding complex network structure. The proposed NMF model is called deep AFRS-NMF model for short, and the corresponding optimization solution, convergence and stability are analyzed. Moreover, the statistical consistency is discussed between the rank obtained by the proposed model and the ideal rank. The performance of the proposed deep AFRS-NMF model is demonstrated by applying in genetic data-based tumor recognition. Experiments show that the factorization rank obtained by the deep AFRS-NMF model is stable and superior to classical and state-of-the-art methods.

非负矩阵分解（NMF）因其可以同时完成特征表示学习和降维而被广泛使用。但是，有两个关键且具有挑战性的问题会影响 NMF 模型的性能。一种是矩阵分解秩的选择，而现有的方法大多基于实验或经验。为了解决这个问题，基于自适应分解秩选择（AFRS）策略构建了一个自适应且稳定的 NMF 模型，该策略巧妙且简单地集成了类似于广义弹性网络的行约束。另一个是对迭代初值的敏感性，严重影响矩阵分解的结果。通过将 NMF 和深度学习相辅相成，避免复杂的网络结构，可以缓解这个问题。所提出的NMF模型简称为深度AFRS-NMF模型，分析了相应的优化解、收敛性和稳定性。此外，讨论了所提出模型获得的秩与理想秩之间的统计一致性。通过应用于基于遗传数据的肿瘤识别，证明了所提出的深度 AFRS-NMF 模型的性能。实验表明，深度AFRS-NMF模型得到的分解秩是稳定的，优于经典和最先进的方法。通过应用于基于遗传数据的肿瘤识别，证明了所提出的深度 AFRS-NMF 模型的性能。实验表明，深度AFRS-NMF模型得到的分解秩是稳定的，优于经典和最先进的方法。通过应用于基于遗传数据的肿瘤识别，证明了所提出的深度 AFRS-NMF 模型的性能。实验表明，深度AFRS-NMF模型得到的分解秩是稳定的，优于经典和最先进的方法。