Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques able to extract the information contained in large data sets in a relevant way. However, such low-rank approaches are unable to mine complex, interleaved features that underlie hierarchical semantics. Recently, deep matrix factorization (deep MF) was introduced to deal with the extraction of several layers of features and has been shown to reach outstanding performances on unsupervised tasks. Deep MF was motivated by the success of deep learning, as it is conceptually close to some neural networks paradigms. In this survey paper, we present the main models, algorithms, and applications of deep MF through a comprehensive literature review. We also discuss theoretical questions and perspectives of research as deep MF is likely to become an important paradigm in unsupervised learning in the next few years.

几十年来，约束低秩矩阵近似是一种强大的线性降维技术，能够以相关方式提取包含在大型数据集中的信息。然而，这种低等级的方法无法挖掘作为分层语义基础的复杂、交错的特征。最近，引入了深度矩阵分解（deep MF）来处理多层特征的提取，并已被证明在无监督任务上表现出色。深度 MF 的动机是深度学习的成功，因为它在概念上接近一些神经网络范式。在这篇调查论文中，我们通过全面的文献综述介绍了深度 MF 的主要模型、算法和应用。