Usage

To use pyDiffMap in a project:

import pyDiffMap

To initialize a diffusion map object:

mydmap = diffusion_map.DiffusionMap.from_sklearn(n_evecs = 1, epsilon = 1.0, alpha = 0.5, k=64)

where n_evecs is the number of eigenvectors that are computed, epsilon is a scale parameter used to rescale distances between data points, alpha is a normalization parameter (typically between 0.0 and 1.0) that influences the effect of the sampling density, and k is the number of nearest neighbors considered when the kernel is computed. A larger k means increased accuracy but larger computation time. The from_sklearn command is used because we are constructing using the scikit-learn nearest neighbor framework. For additional optional arguments, see documentation.

We can also employ automatic epsilon detection due to an algorithm by Berry, Harlim and Giannakis:

mydmap = dm.DiffusionMap.from_sklearn(n_evecs = 1, alpha = 0.5, epsilon = 'bgh', k=64)

To fit to a dataset X (array-like, shape (n_query, n_features)):

mydmap.fit(X)

The diffusion map coordinates can also be accessed directly via:

dmap = mydmap.fit_transform(X)

This returns an array dmap with shape (n_query, n_evecs). E.g. dmap[:,0] is the first diffusion coordinate evaluated on the data X.

In order to compute diffusion coordinates at the out of sample location(s) Y:

dmap_Y = mydmap.transform(Y)