Divergence based graph estimation for manifold learning

Manifold learning algorithms rely on a neighbourhood graph to provide an estimate of the data´s local topology. Unfortunately, current methods for estimating local topology assume local Euclidean geometry and locally uniform data density, which often leads to poor embeddings of the data. We address these shortcomings by proposing a framework that combines local learning with parametric density estimation for local topology estimation. Given a data set D ⊂ χ, we first estimate a new metric space (X; d_X) that characterizes the varying sample density of χ in X, and then use (X; d_X) as a new (pilot) input space for manifold learning. The proposed framework results in significantly improved embeddings, which we demonstrated objectively by assessing clustering accuracy.