Regularized Optimal Transport for Dynamic Semi-supervised Learning

TL;DR

This paper introduces a novel semi-supervised learning method using regularized optimal transport on bipartite graphs to improve label propagation, achieving state-of-the-art results on multiple benchmarks.

Contribution

It proposes a new graph-based semi-supervised learning approach leveraging optimal transport for label propagation with certainty scoring and out-of-sample extension.

Findings

Outperforms existing label propagation algorithms on 12 benchmarks.

Ensures prediction certainty using Shannon's entropy.

Provides an efficient extension for out-of-sample data.

Abstract

Semi-supervised learning provides an effective paradigm for leveraging unlabeled data to improve a model's performance. Among the many strategies proposed, graph-based methods have shown excellent properties, in particular since they allow to solve directly the transductive tasks according to Vapnik's principle and they can be extended efficiently for inductive tasks. In this paper, we propose a novel approach for the transductive semi-supervised learning, using a complete bipartite edge-weighted graph. The proposed approach uses the regularized optimal transport between empirical measures defined on labelled and unlabelled data points in order to obtain an affinity matrix from the optimal transport plan. This matrix is further used to propagate labels through the vertices of the graph in an incremental process ensuring the certainty of the predictions by incorporating a certainty score based on Shannon's entropy. We also analyze the convergence of our approach and we derive an efficient way to extend it for out-of-sample data. Experimental analysis was used to compare the proposed approach with other label propagation algorithms on 12 benchmark datasets, for which we surpass state-of-the-art results. We release our code.