Diffusion Maps meet Nystr\"om

ABSTRACT Diffusion maps are an emerging data-driven technique for nonlinear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. Thus, long time-series data presents a significant challenge for fast and efficient embedding. We propose integrating the Nystr om method with diffusion maps in order to ease the computational demand. We achieve a speedup of roughly two to four times when approximating the dominant diffusion map components. Index Terms-- Dimension Reduction, Nystr om method 1. MOTIV A TION In the era of'big data', dimension reduction is critical for data science.