Scalable Manifold Learning for Big Data with Apache Spark

Non-linear spectral dimensionality reduction methods, such as Isomap, remain important technique for learning manifolds. However, due to computational complexity, exact manifold learning using Isomap is currently impossible from large-scale data. In this paper, we propose a distributed memory framework implementing end-to-end exact Isomap under Apache Spark model. We show how each critical step of the Isomap algorithm can be efficiently realized using basic Spark model, without the need to provision data in the secondary storage. We show how the entire method can be implemented using PySpark, offloading compute intensive linear algebra routines to BLAS. Through experimental results, we demonstrate excellent scalability of our method, and we show that it can process datasets orders of magnitude larger than what is currently possible, using a 25-node parallel cluster.