Label Propagation Through Optimal Transport

TL;DR

This paper introduces Optimal Transport Propagation (OTP), a semi-supervised learning method that uses optimal transport to propagate labels with high certainty, outperforming existing methods in accuracy.

Contribution

The paper proposes a novel label propagation method based on optimal transport, with a certainty control mechanism and convergence analysis, advancing semi-supervised learning techniques.

Findings

OTP outperforms state-of-the-art methods in experiments.

The approach ensures high prediction certitude through entropy-based control.

Convergence of the algorithm is theoretically analyzed.

Abstract

In this paper, we tackle the transductive semi-supervised learning problem that aims to obtain label predictions for the given unlabeled data points according to Vapnik's principle. Our proposed approach is based on optimal transport, a mathematical theory that has been successfully used to address various machine learning problems, and is starting to attract renewed interest in semi-supervised learning community. The proposed approach, Optimal Transport Propagation (OTP), performs in an incremental process, label propagation through the edges of a complete bipartite edge-weighted graph, whose affinity matrix is constructed from the optimal transport plan between empirical measures defined on labeled and unlabeled data. OTP ensures a high degree of predictions certitude by controlling the propagation process using a certainty score based on Shannon's entropy. We also provide a convergence analysis of our algorithm. Experiments task show the superiority of the proposed approach over the state-of-the-art. We make our code publicly available.