Factorized Diffusion Map Approximation

Abstract

Diffusion maps are among the most powerful Machine Learning tools to analyze and work with complex high-dimensional datasets. Unfortunately, the estimation of these maps from a finite sample is known to suffer from the curse of dimensionality. Motivated by other machine learning models for which the existence of structure in the underlying distribution of data can reduce the complexity of estimation, we study and show how the factorization of the underlying distribution into independent subspaces can help us to estimate diffusion maps more accurately. Building upon this result, we propose and develop an algorithm that can automatically factorize a high dimensional data space in order to minimize the error of estimation of its diffusion map, even in the case when the underlying distribution is not decomposable. Experiments on both the synthetic and real-world datasets demonstrate improved estimation performance of our method over the standard diffusion-map framework.