# Bayesian Boolean Matrix Factorisation Source: [Bayesian Boolean Matrix Factorisation]() Collection index: [llms.txt]() Data updated: 2026-06-05T05:01:16.371Z Authors: Tammo Rukat, Chris C. Holmes, Michalis K. Titsias, Christopher Yau Published: 2017-02-20T20:31:39.000Z ## Abstract Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic generative model for Boolean matrix factorisation and derive a Metropolised Gibbs sampler that facilitates efficient parallel posterior inference. On real world and simulated data, our method outperforms all currently existing approaches for Boolean matrix factorisation and completion. This is the first method to provide full posterior inference for Boolean Matrix factorisation which is relevant in applications, e.g. for controlling false positive rates in collaborative filtering and, crucially, improves the interpretability of the inferred patterns. The proposed algorithm scales to large datasets as we demonstrate by analysing single cell gene expression data in 1.3 million mouse brain cells across 11 thousand genes on commodity hardware. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Collaborative Filtering on MovieLens 100k](): Collaborative Filtering; MovieLens 100k; Reconstruction Accuracy: 70.1. ## Original sources and implementation [Original paper]() [PDF]()