Diffusion Maps

Preface

A high dimensional biological measurement can follow a smooth path even when that path is curved and hard to see. A cell moving through a developmental process changes thousands of measured genes at once, although the process may have only one or two main directions of change. The straight line distance between two measurements can cut through regions where no observations occur and may not reflect their separation along the observed process.

Diffusion maps are a nonlinear dimensionality reduction method for this setting. The method builds a graph from local relationships and studies how a random walk moves through it. Observations are close in the resulting coordinates when random walks starting from them spread through the graph in similar ways.

Start with Understanding diffusion maps.