From a statistical standpoint, manifold learning converges at a non-parametric rate of n to the negative power 1/(alpha x dimension + beta). Thus, accurate manifold learning typically requires large amounts of data. Unfortunately, from a computational standpoint, it is commonly believed that manifold learning algorithms "have poor scaling properties".
In this talk, we will discuss the question of scalability for manifold learning algorithms such as non-linear dimension reduction and semi-supervised learning via Gaussian Processes. We also present a python package that makes the former practical for data sets in the millions.
|