Deep Unfolding for Non-Negative Matrix Factorization with Application to Mutational Signature Analysis

Area of Science:

• Computational biology
• Machine learning
• Genomics

Background:

• Non-negative matrix factorization (NMF) is a key dimensionality reduction technique gaining traction in biological research.
• Standard NMF algorithms often yield locally optimal solutions, limiting unique decomposition.
• NMF optimization techniques can inform deep learning architectures by unrolling iterative processes.

Purpose of the Study:

• To develop unfolded deep networks for non-negative matrix factorization (NMF) and its regularized variants.
• To apply these methods in both supervised and unsupervised learning settings for biological data analysis.
• To improve the accuracy of reconstructing mutational signatures and their exposures from mutation data.

Main Methods:

• Development of unfolded deep neural networks tailored for NMF.
• Implementation of regularized NMF variants within the deep network framework.
• Application to simulated and real-world mutation datasets for signature and exposure reconstruction.

Main Results:

• Demonstrated increased accuracy of the unfolded deep network approach compared to standard NMF formulations.
• Successfully reconstructed underlying mutational signatures and their exposures using the developed method.
• Validated the approach on both simulated and empirical biological mutation data.

Conclusions:

• Unfolded deep networks offer a more accurate and robust method for NMF in biological applications.
• The developed technique advances the analysis of mutation data, improving the understanding of mutational processes.
• This work provides a foundation for integrating NMF principles into advanced deep learning models for genomics.