  Learning approaches rely on hyperparameters that impact the algorithm's
performance and affect the knowledge extraction process from data. Recently,
Nonnegative Matrix Factorization (NMF) has attracted a growing interest as a
learning algorithm. This technique captures the latent information embedded in
large datasets while preserving feature properties. NMF can be formalized as a
penalized optimization task in which tuning the penalty hyperparameters is an
open issue. The current literature does not provide any general framework
addressing this task. This study proposes to express the penalty
hyperparameters problem in NMF in terms of a bi-level optimization. We design a
novel algorithm, named Alternating Bi-level (AltBi), which incorporates the
hyperparameters tuning procedure into the updates of NMF factors. Results of
the existence and convergence of numerical solutions, under appropriate
assumptions, are studied, and numerical experiments are provided.
