brainspace.gradient.embedding.diffusion_mapping

brainspace.gradient.embedding.diffusion_mapping(adj, n_components=10, alpha=0.5, diffusion_time=0, random_state=None)[source]

Compute diffusion map of affinity matrix.

Parameters:
  • adj (ndarray or sparse matrix, shape = (n, n)) – Affinity matrix.
  • n_components (int or None, optional) – Number of eigenvectors. If None, selection of n_components is based on 95% drop-off in eigenvalues. When n_components is None, the maximum number of eigenvectors is restricted to n_components <= sqrt(n). Default is 10.
  • alpha (float, optional) – Anisotropic diffusion parameter, 0 <= alpha <= 1. Default is 0.5.
  • diffusion_time (int, optional) – Diffusion time or scale. If diffusion_time == 0 use multi-scale diffusion maps. Default is 0.
  • random_state (int or None, optional) – Random state. Default is None.
Returns:

  • v (ndarray, shape (n, n_components)) – Eigenvectors of the affinity matrix in same order.
  • w (ndarray, shape (n_components,)) – Eigenvalues of the affinity matrix in descending order.

References

  • Coifman, R.R.; S. Lafon. (2006). “Diffusion maps”. Applied and Computational Harmonic Analysis 21: 5-30. doi:10.1016/j.acha.2006.04.006
  • Joseph W.R., Peter E.F., Ann B.L., Chad M.S. Accurate parameter estimation for star formation history in galaxies using SDSS spectra.