  Supervised classification and representation learning are two widely used
classes of methods to analyze multivariate images. Although complementary,
these methods have been scarcely considered jointly in a hierarchical modeling.
In this paper, a method coupling these two approaches is designed using a
matrix cofactorization formulation. Each task is modeled as a factorization
matrix problem and a term relating both coding matrices is then introduced to
drive an appropriate coupling. The link can be interpreted as a clustering
operation over a low-dimensional representation vectors. The attribution
vectors of the clustering are then used as features vectors for the
classification task, i.e., the coding vectors of the corresponding
factorization problem. A proximal gradient descent algorithm, ensuring
convergence to a critical point of the objective function, is then derived to
solve the resulting non-convex non-smooth optimization problem. An evaluation
of the proposed method is finally conducted both on synthetic and real data in
the specific context of hyperspectral image interpretation, unifying two
standard analysis techniques, namely unmixing and classification.
