On the Relation Between Linear Autoencoders and Non-Negative Matrix Factorization for Mutational Signature Extraction

Area of Science:

• Computational biology
• Genomics
• Machine learning

Background:

• Non-negative matrix factorization (NMF) is widely used for dimensionality reduction.
• Autoencoders are increasingly proposed as alternatives to NMF.
• The relationship between NMF and non-negative autoencoders requires detailed investigation.

Purpose of the Study:

• To investigate the relationship between autoencoders and NMF.
• To compare the performance of NMF and a non-negative linear autoencoder (AE-NMF) in mutational signature extraction.

Main Methods:

• Defined a non-negative linear autoencoder (AE-NMF) mathematically equivalent to convex NMF.
• Compared NMF and AE-NMF using simulated and real cancer genomics data for mutational signature extraction.

Main Results:

• NMF achieved more accurate data reconstructions than AE-NMF.
• Signatures extracted by both NMF and AE-NMF demonstrated comparable consistency and external validation performance.
• AE-NMF did not outperform NMF in mutational signature extraction.

Conclusions:

• Linear non-negative autoencoders do not offer an advantage over NMF for mutational signature extraction.
• NMF remains a robust tool for this application.
• Further research is needed to understand the theoretical implications of replacing NMF with autoencoders.