diffusion_maps.rst

Diffusion Maps

Diffusion Maps is a non-linear dimensionality reduction method that uses eigenfunctions of Markov matrices to diffusion maps for efficient representations of complex geometric structures. The diffusion kernel :math: k must satisfy the following properties:

1. math

   k is symmetric :math: {bf k}(x, y) = {bf k}(y, x)

2. math

   k is positivity preserving :math: {bf k}(x, y) ≥ 0

For more information see Coifman-Lafon2006Diffusionmaps.

Example

We create CDenseFeatures (RealFeatures, here 64 bit float values).

diffusionmaps.sg:create_features

We create a CDiffusionMaps instance, and set its parameters.

diffusionmaps.sg:set_parameters

Then we apply diffusion maps, which gives us distance embeddings.

diffusionmaps.sg:apply_convert

We can also extract the estimated feature_matrix.

diffusionmaps.sg:extract

References

Diffusion_map

../../references.bib