Module diffusion_maps 

Diffusion Maps for nonlinear dimensionality reduction Diffusion Maps for Nonlinear Dimensionality Reduction

Diffusion Maps (Coifman & Lafon, 2006) embed data points based on the connectivity of the underlying manifold, using a diffusion process on a graph constructed from the data.

Algorithm

1. Construct an anisotropic kernel from the data
2. Normalize to form a Markov chain transition matrix
3. Eigendecompose the transition matrix
4. Embed using eigenvectors scaled by eigenvalues^t (diffusion time)

Features

• Anisotropic diffusion kernel (alpha parameter controls density normalization)
• Multi-scale analysis via diffusion time parameter
• Automatic dimensionality selection via spectral gap analysis
• Out-of-sample extension via Nystrom approximation

Structs

DiffusionMaps

Diffusion Maps for nonlinear dimensionality reduction