ABSTRACT
This chapter covers various methods for nonlinear dimensionality reduction, where the nonlinear aspect refers to the mapping between the highdimensional space and the low-dimensional space. We start off by discussing a method that has been around for many years called multidimensional scaling. We follow this with several recently developed nonlinear dimensionality reduction techniques called locally linear embedding, isometric feature mapping, and Hessian eigenmaps. We conclude by discussing two related methods from the machine learning community called self-organizing maps and generative topographic maps.
