An Introduction to Nonlinear Dimensionality Reduction by Maximum Variance Unfolding

Many problems in AI are simplified by clever representations of sensory or symbolic input. How to discover such representations automatically, from large amounts of unlabeled data, remains a fundamental challenge. The goal of statistical methods for dimensionality reduction is to detect and discover low dimensional structure in high dimensional data. In this paper, we review a recently proposed algorithm maximum variance unfolding - for learning faithful low dimensional representations of high dimensional data. The algorithm relies on modern tools in convex optimization that are proving increasingly useful in many areas of machine learning.