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 $\beta$-divergences. 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）近年来已成为一种在不同尺度上提取多层次特征的重要技术。然而，现有所有深度NMF模型与算法的评估主要集中于最小二乘误差，而这一指标可能并非衡量不同数据集近似质量的最优指标。例如，在处理音频信号和文档等数据类型时，普遍认为$\beta$-散度是更合适的替代方案。本文中，我们基于$\beta$-散度开发了用于深度NMF的新模型与算法。随后，我们将这些技术应用于面部特征提取、文档集合的主题识别以及高光谱图像中材料的识别。