Geometric Manifold Learning

We present algorithms for analyzing massive and high dimensional data sets motivated by theorems from geometry and topology. Optimization criteria for computing data projections are discussed and skew radial basis functions (sRBFs) for constructing nonlinear mappings with sharp transitions are demonstrated. Examples related to modeling dynamical systems, including hurricane intensity and financial time series prediction, are presented. The article represents an overview of the authors' and collaborators' work in manifold learning.