Semi-supervised Learning with Regularized Laplacian

TL;DR

This paper introduces a semi-supervised learning approach using the Regularized Laplacian on similarity graphs, providing a new optimization framework and demonstrating competitive performance through numerical experiments.

Contribution

It offers a new optimization formulation for the Regularized Laplacian method and analyzes its properties, linking it to random walk interpretations.

Findings

The method can be efficiently computed using optimization and linear algebra.

It performs competitively compared to state-of-the-art semi-supervised methods.

The kernel relates to random walk proximity measures.

Abstract

We study a semi-supervised learning method based on the similarity graph and RegularizedLaplacian. We give convenient optimization formulation of the Regularized Laplacian method and establishits various properties. In particular, we show that the kernel of the methodcan be interpreted in terms of discrete and continuous time random walks and possesses several importantproperties of proximity measures. Both optimization and linear algebra methods can be used for efficientcomputation of the classification functions. We demonstrate on numerical examples that theRegularized Laplacian method is competitive with respect to the other state of the art semi-supervisedlearning methods.