  In this work we address graph based semi-supervised learning using the theory
of the spatial segregation of competitive systems. First, we define a discrete
counterpart over connected graphs by using direct analogue of the corresponding
competitive system. This model turns out doesn't have a unique solution as we
expected. Nevertheless, we suggest gradient projected and regularization
methods to reach some of the solutions. Then we focus on a slightly different
model motivated from the recent numerical results on the spatial segregation of
reaction-diffusion systems. In this case we show that the model has a unique
solution and propose a novel classification algorithm based on it. Finally, we
present numerical experiments showing the method is efficient and comparable to
other semi-supervised learning algorithms at high and low label rates.
