The PRIMPing Routine -- Tiling through Proximal Alternating Linearized Minimization

TL;DR

This paper introduces a novel Boolean matrix factorization algorithm based on proximal alternating linearized minimization that minimizes description length, demonstrating robustness and interpretability in noisy data scenarios.

Contribution

The paper presents a new optimization-based Boolean matrix factorization method that minimizes description length, improving robustness and interpretability over existing algorithms.

Findings

Outperforms existing algorithms in noisy data conditions

Identifies interpretable patterns in synthetic and image data

Demonstrates flexibility with various cost measures

Abstract

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.