论文标题
深层矩阵因化的一致且灵活的框架
A consistent and flexible framework for deep matrix factorizations
论文作者
论文摘要
深矩阵因素化（深MF）是最新的无监督数据挖掘技术，其灵感来自受约束的低级别近似值。他们旨在提取高维数据集中功能的复杂层次结构。文献中提出的大多数损失功能是为了评估深MF模型的质量和潜在的优化框架，因为在不同层上使用了不同的损失。在本文中，我们引入了深层MF的两个有意义的损失功能，并提出了一个通用框架来解决相应的优化问题。我们通过整合各种约束和正规化（例如稀疏性，非负和最小体积）来说明这种方法的有效性。这些模型成功地应用于合成和真实数据，即高光谱抗面部特征。
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss functions proposed in the literature to evaluate the quality of deep MF models and the underlying optimization frameworks are not consistent because different losses are used at different layers. In this paper, we introduce two meaningful loss functions for deep MF and present a generic framework to solve the corresponding optimization problems. We illustrate the effectiveness of this approach through the integration of various constraints and regularizations, such as sparsity, nonnegativity and minimum-volume. The models are successfully applied on both synthetic and real data, namely for hyperspectral unmixing and extraction of facial features.
