Graphical methods for dimensionality reduction on manifolds

The goal of statistical methods for dimensionality reduction is to detect and discover low dimensional structures in high dimensional data. Here, we discuss a recently proposed method, known as Maximum Entropy Unfolding (MEU), for learning faithful low dimensional representations of high dimensional data. This method represents a new perspective on spectral dimensionality reduction and, joined with the theory of Gaussian Markov random fields, provides a unifying probabilistic approach to spectral dimensionality reduction techniques. Parameter estimation as well as approaches to learning the structure of the GMRF are discussed.