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

Ida Egendal^1,2, Rasmus Froberg Brøndum^1,2, Marta Pelizzola³

¹Center for Clinical Data Science, Aalborg University and Aalborg University Hospital, Aalborg, Denmark.

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology

|March 20, 2025

Summary

This summary is machine-generated.

Non-negative matrix factorization (NMF) remains superior to linear non-negative autoencoders for accurate data reconstruction in mutational signature extraction. While both methods yield comparable signature performance, NMF shows better reconstruction accuracy.

Keywords:

convex non-negative matrix factorization mutational signatures non-negative autoencoders non-negative matrix factorization

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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.