Nonlinear Dimensionality Reduction with Diffusion Maps in Practice

TL;DR

This paper reviews the practical application of Diffusion Maps for nonlinear dimensionality reduction, highlighting preprocessing, parameter tuning, and component relevance issues, and introduces a new method for identifying key components.

Contribution

It provides a practical review of Diffusion Maps, discusses common pitfalls, and introduces a technique for selecting the most relevant components.

Findings

First components are not always the most relevant.

Preprocessing and parameter choices significantly affect results.

A new method helps identify the most relevant components.

Abstract

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.