The Target Polish: A New Approach to Outlier-Resistant Non-Negative Matrix and Tensor Factorization

P. Fogel, C. Geissler, and G. Luta. arXiv, July 16th 2025.

Relative error (using the non-corrupted data) as a function of the update iteration.

This paper presents Target Polish, a robust and highly efficient framework for non-negative matrix and tensor factorization, designed to meet the demands of real-world, noisy data environments.

Unlike traditional weighted NMF methods—which are robust to outliers but computationally slow due to multiplicative update rules—Target Polish introduces a novel, adaptive smoothing technique based on weighted medians. This allows it to remain fully compatible with the Fast-HALS algorithm, known for its speed and scalability, and preserves its additive update mechanism.

From a business application standpoint, this approach is particularly well-suited for:

• Credit scoring and fraud detection, where financial or behavioral datasets often contain anomalies or irregular reporting;

• Customer segmentation in marketing or retail analytics, where structured and unstructured noise in transaction data can degrade clustering performance;

• Medical diagnostics and imaging, where data robustness is essential due to acquisition artifacts or measurement errors;

• Supply chain and logistics optimization, where incomplete or noisy tracking data can hinder forecasting models.

Empirical benchmarks on image datasets with both structured (block) and unstructured (salt) noise show that Target Polish matches or exceeds the accuracy of leading robust NMF techniques while reducing computation time by up to an order of magnitude.

This makes it an ideal solution for companies seeking scalable, interpretable, and resilient matrix factorization techniques in high-volume or time-constrained operational settings.

Free Download: https://arxiv.org/abs/2507.10484