A Bayesian Boolean Matrix Factorization with Application to Copy Number Analysis in Cancer

A new Bayesian Boolean Matrix Factorization (BBMF) method has been proposed to analyze copy number alterations in cancer, offering a principled way to identify coordinated chromosomal changes that may drive tumor evolution. [1] The model, detailed in a paper submitted to the arXiv preprint server on June 16, 2026, addresses key limitations of existing Boolean Matrix Factorization (BooMF) techniques. Most current BooMF methods are heuristic and greedy, making them sensitive to initialization, prone to local optima, and lacking principled model selection or uncertainty quantification. [1] The BBMF approach instead uses a fully conjugate generative model with sparsity-inducing priors, enforcing Boolean constraints while yielding interpretable latent factors with coherent uncertainty quantification. [2] The model admits Gibbs sampling with closed-form full conditionals, avoiding the need for numerical approximations. [3] Standard factorization methods based on real-valued arithmetic often fail to respect the discrete structure of binary data or yield interpretable decompositions. [4] BooMF addresses this by decomposing a binary matrix into two lower-rank binary matrices using logical AND and OR operations, representing the data as a Boolean disjunction of interpretable patterns. [5] The authors argue that because cancer evolution can involve widespread, near-simultaneous chromosome-number changes—such as whole-genome duplication followed by brief genomic instability and strong selection—Boolean factorizations capture these patterns more naturally than additive models. [3] In simulation experiments, the researchers compared BBMF with the widely used Asso and GreConD+ boolean factorization algorithms. Across factorization ranks and data-generating mechanisms, BBMF more reliably recovered the true latent factors, seen in strongly diagonally dominant similarity matrices and factor patterns closely matching ground truth. [4] It was also competitive with or superior to alternatives in reconstruction accuracy and standard classification metrics. [5] The method was applied to arm-level copy-number alteration data in multiple myeloma, where binary entries indicate the presence or absence of chromosomal-arm amplifications. The model identified a small number of interpretable bicliques linking subsets of patients to recurrently co-altered chromosomal arms, providing a compact, biologically meaningful summary of tumor heterogeneity. [2] The paper was submitted by Adolphus Wagala and is available on arXiv, an open-access repository of electronic preprints that, as of November 2024, receives about 24,000 articles per month. [1] [9]