  Various Non-negative Matrix factorization (NMF) based methods add new terms
to the cost function to adapt the model to specific tasks, such as clustering,
or to preserve some structural properties in the reduced space (e.g., local
invariance). The added term is mainly weighted by a hyper-parameter to control
the balance of the overall formula to guide the optimization process towards
the objective. The result is a parameterized NMF method. However, NMF method
adopts unsupervised approaches to estimate the factorizing matrices. Thus, the
ability to perform prediction (e.g. classification) using the new obtained
features is not guaranteed. The objective of this work is to design an
evolutionary framework to learn the hyper-parameter of the parameterized NMF
and estimate the factorizing matrices in a supervised way to be more suitable
for classification problems. Moreover, we claim that applying NMF-based
algorithms separately to different class-pairs instead of applying it once to
the whole dataset improves the effectiveness of the matrix factorization
process. This results in training multiple parameterized NMF algorithms with
different balancing parameter values. A cross-validation combination learning
framework is adopted and a Genetic Algorithm is used to identify the optimal
set of hyper-parameter values. The experiments we conducted on both real and
synthetic datasets demonstrated the effectiveness of the proposed approach.
