Multiclass Diffuse Interface Models for Semi-Supervised Learning on Graphs

TL;DR

This paper introduces a novel multiclass diffuse interface model for semi-supervised learning on graphs, leveraging a variational approach with a periodic potential to improve class boundary sharpness and symmetry.

Contribution

The authors develop a new graph-based variational algorithm using a diffuse interface model with a symmetric smoothness measure, enhancing multiclass classification performance.

Findings

Competitive with state-of-the-art graph algorithms

Allows sharp class transitions

Preserves symmetry among class labels

Abstract

We present a graph-based variational algorithm for multiclass classification of high-dimensional data, motivated by total variation techniques. The energy functional is based on a diffuse interface model with a periodic potential. We augment the model by introducing an alternative measure of smoothness that preserves symmetry among the class labels. Through this modification of the standard Laplacian, we construct an efficient multiclass method that allows for sharp transitions between classes. The experimental results demonstrate that our approach is competitive with the state of the art among other graph-based algorithms.