# The PRIMPing Routine -- Tiling through Proximal Alternating Linearized Minimization

arXiv: https://arxiv.org/abs/1906.09722 · HTML: https://mlsanity.com/paper/1906.09722/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2019.

## Built on by (most cited first, 5 of 5)

- [Efficiently Factorizing Boolean Matrices using Proximal Gradient Descent](https://mlsanity.com/paper/2307.07615/) (2023)
- [Boolean and mathbbFp-Matrix Factorization: From Theory to Practice](https://mlsanity.com/paper/2207.11917/) (2022)
- [Visualizing Overlapping Biclusterings and Boolean Matrix Factorizations](https://mlsanity.com/paper/2307.07396/) (2023)
- [Federated Binary Matrix Factorization using Proximal Optimization](https://mlsanity.com/paper/2407.01776/) (2024)
- [Algorithms for Boolean Matrix Factorization using Integer Programming and Heuristics](https://mlsanity.com/paper/2512.03807/) (2025)

## Abstract (arXiv)

Mining and exploring databases should provide users with knowledge and new insights. Tiles of data strive to unveil true underlying structure and distinguish valuable information from various kinds of noise. We propose a novel Boolean matrix factorization algorithm to solve the tiling problem, based on recent results from optimization theory. In contrast to existing work, the new algorithm minimizes the description length of the resulting factorization. This approach is well known for model selection and data compression, but not for finding suitable factorizations via numerical optimization. We demonstrate the superior robustness of the new approach in the presence of several kinds of noise and types of underlying structure. Moreover, our general framework can work with any cost measure having a suitable real-valued relaxation. Thereby, no convexity assumptions have to be met. The experimental results on synthetic data and image data show that the new method identifies interpretable patterns which explain the data almost always better than the competing algorithms.