Paul Fogel

Paul Fogel, Christophe Geissler, George Luta

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.

Paul Fogel

Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination of these profiles. The non-negativity constraint is imposed while estimating archetypal profiles, due to the non-negative nature of the observed signal. Apart from non negativity, a volume constraint can be applied on the Score matrix W to enhance the ability of learning parts of NMF. In this report, we describe a very simple algorithm, which in effect achieves volume minimization, although indirectly.