There have been several recently presented works on finding information-geometric embeddings using the properties of statistical manifolds. These methods have generally focused on embedding probability density functions into an open Euclidean space. In this paper we propose adding an additional constraint by embedding onto the surface of the sphere in an unsupervised manner. This additional constraint is shown to have superior performance for both manifold reconstruction and visualization when the true underlying statistical manifold is that of a low-dimensional sphere. We call the proposed method Spherical Laplacian Information Maps (SLIM), and we illustrate its utilization as a proof-of-concept on both real and synthetic data.
Kevin M. Carter, Raviv Raich, and Alfred O. Hero III, “Spherical laplacian information maps (SLIM) for dimensionality reduction,” in Proc. of 2009 IEEE Workshop on Statistical Signal Processing. Sept, 2009. (.pdf).