Graph Based Semi-supervised Learning Using Spatial Segregation Theory

TL;DR

This paper introduces a novel graph-based semi-supervised learning method inspired by spatial segregation theory, demonstrating its effectiveness and uniqueness in certain models through numerical experiments.

Contribution

It develops a new classification algorithm based on spatial segregation theory with proven uniqueness and competitive performance.

Findings

The model with spatial segregation has a unique solution.

The proposed algorithm performs well at various label rates.

Numerical experiments show efficiency comparable to existing methods.

Abstract

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.