  We present several algorithms designed to learn a pattern of correspondence
between two data sets in situations where it is desirable to match elements
that exhibit a relationship belonging to a known parametric model. In the
motivating case study, the challenge is to better understand micro-RNA
regulation in the striatum of Huntington's disease model mice. The algorithms
unfold in two stages. First, an optimal transport plan P and an optimal affine
transformation are learned, using the Sinkhorn-Knopp algorithm and a mini-batch
gradient descent. Second, P is exploited to derive either several co-clusters
or several sets of matched elements. A simulation study illustrates how the
algorithms work and perform. The real data application further illustrates
their applicability and interest.
