# From-Below Boolean Matrix Factorization Algorithm Based on MDL

## TL;DR

This paper introduces a new from-below Boolean matrix factorization algorithm based on formal concept analysis and the MDL principle, demonstrating superior performance over existing methods in various experiments.

## Contribution

The paper presents a novel from-below BMF algorithm that leverages formal concept analysis and MDL for improved factorization quality.

## Key findings

- Outperforms existing BMF algorithms in experiments
- Uses MDL for effective model order selection
- Achieves better results on standard data sets

## Abstract

During the past few years Boolean matrix factorization (BMF) has become an important direction in data analysis. The minimum description length principle (MDL) was successfully adapted in BMF for the model order selection. Nevertheless, a BMF algorithm performing good results from the standpoint of standard measures in BMF is missing. In this paper, we propose a novel from-below Boolean matrix factorization algorithm based on formal concept analysis. The algorithm utilizes the MDL principle as a criterion for the factor selection. On various experiments we show that the proposed algorithm outperforms---from different standpoints---existing state-of-the-art BMF algorithms.