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）近期作为一种从不同尺度提取多层次特征的有效技术而兴起。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，而该指标可能并非衡量不同数据集逼近质量的最适指标。例如，在处理音频信号和文档等数据类型时，学界普遍认为$\beta$-散度是更优的替代方案。本文针对部分$\beta$-散度（重点聚焦于Kullback-Leibler散度），提出新的深度NMF模型与算法，进而将这些技术应用于面部特征提取、文档集合主题识别，以及高光谱图像中物质成分识别任务。