Semi-Supervised Dimensionality Reduction by Linear Compression and Stretching

Dimensionality reduction is a fundamental and important research topic in the field of machine learning. This paper focuses on a dimensionality reduction technique that exploits semi-supervising information in the form of pairwise constraints; specifically, these constraints specify whether two instances belong to the same class or not. We propose two dual linear methods to accomplish dimensionality reduction under that setting. These two methods overcome the difficulty of maximizing between-class difference and minimizing within-class difference at the same time, by transforming the original data into a new space in such a way that the bi-objective problem is (almost) equivalently reduced to a single objective problem. Empirical evaluations on a broad range of public datasets show that the two proposed methods are superior to several existing methods for semi-supervised dimensionality reduction.