Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization

TL;DR

This paper introduces a graph-based variational algorithm for multiclass semi-supervised learning that minimizes an energy functional to achieve sharp class boundaries while incorporating prior data information.

Contribution

It generalizes binary diffuse interface models to multiclass classification on graphs using a Ginzburg-Landau functional minimization approach.

Findings

Competitive performance on synthetic, COIL, and MNIST datasets.

Effectively incorporates prior information in semi-supervised setting.

Sharp class transitions achieved with energy minimization.

Abstract

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification function with sharp transitions between classes, while preserving symmetry among the class labels. The third term is a data fidelity term, allowing us to incorporate prior information into the model in a semi-supervised framework. The performance of the algorithm on synthetic data, as well as on the COIL and MNIST benchmark datasets, is competitive with state-of-the-art graph-based multiclass segmentation methods.