Nonlinear Dimensionality Reduction with Diffusion Maps in Practice
This is an incremental review for practitioners in fields like biology and engineering using Diffusion Maps.
The paper addresses the lack of comprehensive discussion on data preprocessing, parameter settings, and component selection in Diffusion Maps, a nonlinear dimensionality reduction technique, by providing a practice-oriented review and illustrating pitfalls, with results showing that the first components are not always the most relevant.
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology, engineering, and social sciences. But data preprocessing, parameter settings and component selection have a significant influence on the resulting manifold, something which has not been comprehensively discussed in the literature so far. We provide a practice oriented review of the Diffusion Map technique, illustrate pitfalls and showcase a recently introduced technique for identifying the most relevant components. Our results show that the first components are not necessarily the most relevant ones.