  The efficiency of graph-based semi-supervised algorithms depends on the graph
of instances on which they are applied. The instances are often in a vectorial
form before a graph linking them is built. The construction of the graph relies
on a metric over the vectorial space that help define the weight of the
connection between entities. The classic choice for this metric is usually a
distance measure or a similarity measure based on the euclidean norm. We claim
that in some cases the euclidean norm on the initial vectorial space might not
be the more appropriate to solve the task efficiently. We propose an algorithm
that aims at learning the most appropriate vectorial representation for
building a graph on which the task at hand is solved efficiently.
