posted 2009-10-26T09:42:49Z
chigirev and bialek show how to apply the information bottleneck in a geometric setting: title: "Optimal manifold representation of data: An information theoretic perspective" abstract: "We introduce an information theoretic method for nonparametric, nonlinear dimensionality reduction, based on the infinite cluster limit of rate distortion theory. By constraining the information available to manifold coordinates, a natural probabilistic map emerges that assigns original data to corresponding points on a lower dimensional manifold. With only the information-distortion trade off as a parameter, our method determines the shape of the manifold, its dimensionality, the probabilistic map and the prior that provide optimal description of the data."