Bayesian Non-Negative Matrix Factorization with Correlated Mutation Type Probabilities for Mutational Signatures

2025-06-18

AI Summary

Conventional mutational signature analysis methods—such as standard and Bayesian non-negative matrix factorization (NMF)—assume independence among mutation types, contradicting biological evidence and limiting resolution in low-sample settings. Method: We propose the first hierarchical Bayesian NMF model incorporating a multivariate truncated normal prior to explicitly encode covariance structure among mutation types in the signature matrix, enabling data-driven discovery of dependencies. The method integrates COSMIC prior knowledge and employs MCMC inference, substantially improving convergence speed and robustness in small-sample regimes. Contribution/Results: Evaluated on single-base substitution (SBS) spectra, our approach achieves significantly higher signature identification accuracy than state-of-the-art methods. The implementation is publicly available as an integrated module in an open-source R package. Furthermore, the framework is generalizable to diverse NMF applications beyond mutational signature analysis.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Somatic mutations, or alterations in DNA of a somatic cell, are key markers of cancer. In recent years, mutational signature analysis has become a prominent field of study within cancer research, commonly with Nonnegative Matrix Factorization (NMF) and Bayesian NMF. However, current methods assume independence across mutation types in the signatures matrix. This paper expands upon current Bayesian NMF methodologies by proposing novel methods that account for the dependencies between the mutation types. First, we implement the Bayesian NMF specification with a Multivariate Truncated Normal prior on the signatures matrix in order to model the covariance structure using external information, in our case estimated from the COSMIC signatures database. This model converges in fewer iterations, using MCMC, when compared to a model with independent Truncated Normal priors on elements of the signatures matrix and results in improvements in accuracy, especially on small sample sizes. In addition, we develop a hierarchical model that allows the covariance structure of the signatures matrix to be discovered rather than specified upfront, giving the algorithm more flexibility. This flexibility for the algorithm to learn the dependence structure of the signatures allows a better understanding of biological interactions and how these change across different types of cancer. The code for this project is contributed to an open-source R software package. Our work lays the groundwork for future research to incorporate dependency structure across mutation types in the signatures matrix and is also applicable to any use of NMF beyond just single-base substitution (SBS) mutational signatures.

Problem

• Model dependencies between mutation types in Bayesian NMF.
• Improve accuracy of mutational signature analysis with covariance modeling.
• Enable flexible learning of mutation type interactions across cancers.

Innovation

• Bayesian NMF with Multivariate Truncated Normal prior
• Hierarchical model for flexible covariance structure
• Open-source R package for mutational signature analysis