Consistent Semi-Supervised Graph Regularization for High Dimensional Data

TL;DR

This paper introduces a new semi-supervised graph regularization method with centering to improve high-dimensional data learning, supported by theoretical analysis and empirical validation.

Contribution

It proposes a novel centering-based regularization approach that addresses the inconsistency problem in high-dimensional semi-supervised learning.

Findings

The new method outperforms traditional Laplacian regularization in high dimensions.

Theoretical analysis explains the origin of the inconsistency issue.

Empirical results demonstrate improved learning efficiency with the proposed approach.

Abstract

Semi-supervised Laplacian regularization, a standard graph-based approach for learning from both labelled and unlabelled data, was recently demonstrated to have an insignificant high dimensional learning efficiency with respect to unlabelled data (Mai and Couillet 2018), causing it to be outperformed by its unsupervised counterpart, spectral clustering, given sufficient unlabelled data. Following a detailed discussion on the origin of this inconsistency problem, a novel regularization approach involving centering operation is proposed as solution, supported by both theoretical analysis and empirical results.