scanpy.tl.diffmap

scanpy.tl.diffmap(adata, n_comps=15, neighbors_key=None, random_state=0, copy=False)

Diffusion Maps [Coifman05] [Haghverdi15] [Wolf18].

Diffusion maps [Coifman05] has been proposed for visualizing single-cell data by [Haghverdi15]. The tool uses the adapted Gaussian kernel suggested by [Haghverdi16] in the implementation of [Wolf18].

The width (“sigma”) of the connectivity kernel is implicitly determined by the number of neighbors used to compute the single-cell graph in neighbors(). To reproduce the original implementation using a Gaussian kernel, use method=='gauss' in neighbors(). To use an exponential kernel, use the default method=='umap'. Differences between these options shouldn’t usually be dramatic.

Parameters

adata : AnnData

Annotated data matrix.

n_comps : int (default: 15)

The number of dimensions of the representation.

neighbors_key : Optional[str] (default: None)

If not specified, diffmap looks .uns[‘neighbors’] for neighbors settings and .obsp[‘connectivities’], .obsp[‘distances’] for connectivities and distances respectively (default storage places for pp.neighbors). If specified, diffmap looks .uns[neighbors_key] for neighbors settings and .obsp[.uns[neighbors_key][‘connectivities_key’]], .obsp[.uns[neighbors_key][‘distances_key’]] for connectivities and distances respectively.

random_state : Union[None, int, RandomState] (default: 0)

A numpy random seed

copy : bool (default: False)

Return a copy instead of writing to adata.

Returns

Depending on copy, returns or updates adata with the following fields.

X_diffmapnumpy.ndarray (adata.obsm)

Diffusion map representation of data, which is the right eigen basis of the transition matrix with eigenvectors as columns.

diffmap_evalsnumpy.ndarray (adata.uns)

Array of size (number of eigen vectors). Eigenvalues of transition matrix.

Notes

The 0-th column in adata.obsm["X_diffmap"] is the steady-state solution, which is non-informative in diffusion maps. Therefore, the first diffusion component is at index 1, e.g. adata.obsm["X_diffmap"][:,1]