Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization
This addresses the problem of classifying high-dimensional data with limited labeled examples for researchers in graph-based machine learning, but it is incremental as it extends an existing binary method to multiclass.
The paper tackles multiclass semi-supervised learning on graphs by generalizing a binary diffuse interface model to multiple classes, achieving competitive performance with state-of-the-art methods on synthetic data and benchmarks like COIL and MNIST.
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.