Semi-supervised Learning with Explicit Relationship Regularization

TL;DR

This paper introduces a novel explicit relationship regularization method for semi-supervised learning, leveraging the structure of target space relationships to improve classification and embedding tasks.

Contribution

It proposes explicitly regularizing relationships between function evaluations, enhancing semi-supervised learning performance over existing implicit methods.

Findings

Significant improvement in semi-supervised classification accuracy.

Enhanced spectral data embedding quality.

Effective in constrained clustering and dimensionality reduction.

Abstract

In many learning tasks, the structure of the target space of a function holds rich information about the relationships between evaluations of functions on different data points. Existing approaches attempt to exploit this relationship information implicitly by enforcing smoothness on function evaluations only. However, what happens if we explicitly regularize the relationships between function evaluations? Inspired by homophily, we regularize based on a smooth relationship function, either defined from the data or with labels. In experiments, we demonstrate that this significantly improves the performance of state-of-the-art algorithms in semi-supervised classification and in spectral data embedding for constrained clustering and dimensionality reduction.