megaman: Manifold Learning with Millions of points

Manifold Learning (ML) is a class of algorithms seeking a low-dimensional nonlinear representation of high-dimensional data. Thus ML algorithms are, at least in theory, most applicable to high-dimensional data and sample sizes to enable accurate estimation of the manifold. Despite this, most existing manifold learning implementations are not particularly scalable. Here we present a Python package that implements a variety of manifold learning algorithms in a modular and scalable fashion, using fast approximate neighbors searches and fast sparse eigendecompositions. The package incorporates theoretical advances in manifold learning, such as the unbiased Laplacian estimator introduced by Coifman and Lafon (2006) and the estimation of the embedding distortion by the Riemannian metric method introduced by Perraul-Joncas and Meila (2013). In benchmarks, even on a single-core desktop computer, our code embeds millions of data points in minutes, and takes just 200 minutes to embed the main sample of galaxy spectra from the Sloan Digital Sky Survey -- consisting of 0.6 million samples in 3750-dimensions -- a task which has not previously been possible.