The aim of this study is to provide a foundation to understand the
relationship between non-negative matrix factorization (NMF) and non-negative
autoencoders enabling proper interpretation and understanding of
autoencoder-based alternatives to NMF. Since its introduction, NMF has been a
popular tool for extracting interpretable, low-dimensional representations of
high-dimensional data. However, recently, several studies have proposed to
replace NMF with autoencoders. This increasing popularity of autoencoders
warrants an investigation on whether this replacement is in general valid and
reasonable. Moreover, the exact relationship between non-negative autoencoders
and NMF has not been thoroughly explored. Thus, a main aim of this study is to
investigate in detail the relationship between non-negative autoencoders and
NMF. We find that the connection between the two models can be established
through convex NMF, which is a restricted case of NMF. In particular, convex
NMF is a special case of an autoencoder. The performance of NMF and
autoencoders is compared within the context of extraction of mutational
signatures from cancer genomics data. We find that the reconstructions based on
NMF are more accurate compared to autoencoders, while the signatures extracted
using both methods show comparable consistencies and values when externally
validated. These findings suggest that the non-negative autoencoders
investigated in this article do not provide an improvement of NMF in the field
of mutational signature extraction.

通过对非负矩阵因式分解 (NMF) 和非负自动编码器之间的关系进行详细探究，发现这两种模型之间的连接可以通过凸 NMF 建立，该模型是自动编码器的特例。在从癌症基因组数据中提取突变特征的背景下，将 NMF 和自动编码器的性能进行比较，结果显示 NMF 基于重构的准确性优于自动编码器，而使用两种方法提取的特征在外部验证时表现出可比性和一致性，这表明本文中研究的非负自动编码器在突变特征提取领域并没有改进 NMF 的效果。

自编码器与非负矩阵分解的关系及其在突变特征提取中的应用

On the Relation Between Autoencoders and Non-negative Matrix  Factorization, and Their Application for Mutational Signature Extraction

Unlike typical visual scene recognition domains, in which massive datasets
are accessible to deep neural networks, medical image interpretations are often
obstructed by the paucity of data. In this paper, we investigate the
effectiveness of data-based few-shot learning in medical imaging by exploring
different data attribute representations in a low-dimensional space. We
introduce different types of non-negative matrix factorization (NMF) in
few-shot learning, addressing the data scarcity issue in medical image
classification. Extensive empirical studies are conducted in terms of
validating the effectiveness of NMF, especially its supervised variants (e.g.,
discriminative NMF, and supervised and constrained NMF with sparseness), and
the comparison with principal component analysis (PCA), i.e., the collaborative
representation-based dimensionality reduction technique derived from
eigenvectors. With 14 different datasets covering 11 distinct illness
categories, thorough experimental results and comparison with related
techniques demonstrate that NMF is a competitive alternative to PCA for
few-shot learning in medical imaging, and the supervised NMF algorithms are
more discriminative in the subspace with greater effectiveness. Furthermore, we
show that the part-based representation of NMF, especially its supervised
variants, is dramatically impactful in detecting lesion areas in medical
imaging with limited samples.

利用少样本学习，探讨在医学图像中通过数据属性表达在低维空间的非负矩阵因式分解 (NMF) 的有效性，实验证明 NMF 是医学图像中少样本学习的一种竞争性替代方案，尤其是用于检测限制样本医学图像中异常区域的有监督 NMF 算法的效果更具区分度。