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

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.