  In this work, we introduce a highly efficient algorithm to address the
nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix
factorization (NMF) with an additional underapproximation constraint. NMU
results are interesting as, compared to traditional NMF, they present
additional sparsity and part-based behavior, explaining unique data features.
To show these features in practice, we first present an application to the
analysis of climate data. We then present an NMU-based algorithm to robustly
fit multiple parametric models to a dataset. The proposed approach delivers
state-of-the-art results for the estimation of multiple fundamental matrices
and homographies, outperforming other alternatives in the literature and
exemplifying the use of efficient NMU computations.
