A Unified Semi-Supervised Dimensionality Reduction Framework for Manifold Learning

TL;DR

This paper introduces a comprehensive semi-supervised framework for manifold learning that integrates labeled and unlabeled data, generalizes existing methods, and includes a novel kernelization approach for non-linear problems.

Contribution

It presents a unified framework that encompasses supervised and unsupervised manifold learning, explaining their relationships and enabling extensions for complex data structures.

Findings

Framework generalizes existing spectral methods

Enables use of both labeled and unlabeled data

Introduces 'KPCA trick' for non-linear problems

Abstract

We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived under our framework are able to employ both labeled and unlabeled examples and are able to handle complex problems where data form separate clusters of manifolds. Our framework offers simple views, explains relationships among existing frameworks and provides further extensions which can improve existing algorithms. Furthermore, a new semi-supervised kernelization framework called ``KPCA trick'' is proposed to handle non-linear problems.