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

TL;DR

The paper presents 'Target Polish,' a novel robust NMF framework that combines outlier resistance with fast convergence by integrating a median-based data polishing step compatible with the Fast-HALS algorithm, leading to improved efficiency and accuracy.

Contribution

It introduces 'Target Polish,' a new outlier-resistant NMF method that maintains computational efficiency by integrating median-based data polishing with Fast-HALS.

Findings

Matches or exceeds state-of-the-art robustness in noisy image datasets.

Reduces computational time by an order of magnitude.

Effective against structured and unstructured noise.

Abstract

This paper introduces the "Target Polish," a robust and computationally efficient framework for Non-Negative Matrix Factorization (NMF). Although conventional weighted NMF approaches are resistant to outliers, they converge slowly due to the use of multiplicative updates to minimize the objective criterion. In contrast, the Target Polish approach remains compatible with the Fast-HALS algorithm, which is renowned for its speed, by adaptively "polishing" the data with a weighted median-based transformation. This innovation provides outlier resistance while maintaining the highly efficient additive update structure of Fast-HALS. Empirical evaluations using image datasets corrupted with structured (block) and unstructured (salt) noise demonstrate that the Target Polish approach matches or exceeds the accuracy of state-of-the-art robust NMF methods while reducing computational time by an order of magnitude in the studied scenarios.