Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have primarily centered their evaluation on the least squares error, which may not be the most appropriate metric for assessing the quality of approximations on diverse datasets. For instance, when dealing with data types such as audio signals and documents, it is widely acknowledged that $\beta$-divergences offer a more suitable alternative. In this paper, we develop new models and algorithms for deep NMF using some $\beta$-divergences, with a focus on the Kullback-Leibler divergence. Subsequently, we apply these techniques to the extraction of facial features, the identification of topics within document collections, and the identification of materials within hyperspectral images.

翻译：深度非负矩阵分解（Deep NMF）近年作为一种从不同尺度提取多层特征的有效技术而兴起。然而，所有现有的深度NMF模型和算法主要基于最小二乘误差进行评估，这一指标对于衡量不同数据集上近似质量的适用性可能并非最优。例如，在处理音频信号和文档等数据类型时，普遍认为β散度（β-divergences）是更合适的替代指标。本文针对部分β散度（重点聚焦于Kullback-Leibler散度）提出了深度NMF的新模型与算法。随后，我们将这些技术应用于人脸特征提取、文档集合主题识别以及高光谱图像中的物质识别。