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.

翻译：在此工作中,我们使用竞争性系统空间隔离理论解决基于图形的半监督学习问题。 首先,我们通过直接模拟相应的竞争性系统来定义一个离散对应的图表。 这个模型没有我们所期望的独特解决方案。 然而,我们建议了一些解决方案的梯度预测和正规化方法。 然后,我们侧重于一个与最近关于反应扩散系统空间隔离的数字结果略有不同的模型。 在这种情况下,我们显示模型有一个独特的解决方案,并以此为基础提出了新的分类算法。 最后,我们提出了数字实验,表明该方法效率高、低标签率与其他半监督的学习算法可比。