  In this work we introduce a comprehensive algorithmic pipeline for multiple
parametric model estimation. The proposed approach analyzes the information
produced by a random sampling algorithm (e.g., RANSAC) from a machine
learning/optimization perspective, using a \textit{parameterless} biclustering
algorithm based on L1 nonnegative matrix factorization (L1-NMF). The proposed
framework exploits consistent patterns that naturally arise during the RANSAC
execution, while explicitly avoiding spurious inconsistencies. Contrarily to
the main trends in the literature, the proposed technique does not impose
non-intersecting parametric models. A new accelerated algorithm to compute
L1-NMFs allows to handle medium-sized problems faster while also extending the
usability of the algorithm to much larger datasets. This accelerated algorithm
has applications in any other context where an L1-NMF is needed, beyond the
biclustering approach to parameter estimation here addressed. We accompany the
algorithmic presentation with theoretical foundations and numerous and diverse
examples.
