scanpy.metrics.gearys_c

scanpy.metrics.gearys_c(adata, *, vals=None, use_graph=None, layer=None, obsm=None, obsp=None, use_raw=False)

Calculate Geary’s C, as used by VISION.

Geary’s C is a measure of autocorrelation for some measure on a graph. This can be to whether measures are correlated between neighboring cells. Lower values indicate greater correlation.

\[C = \frac{ (N - 1)\sum_{i,j} w_{i,j} (x_i - x_j)^2 }{ 2W \sum_i (x_i - \bar{x})^2 }\]

Parameters:

adata : AnnData
vals : Union[ndarray, spmatrix, None] (default: None): Values to calculate Geary’s C for. If this is two dimensional, should be of shape (n_features, n_cells). Otherwise should be of shape (n_cells,). This matrix can be selected from elements of the anndata object by using key word arguments: layer, obsm, obsp, or use_raw.
use_graph : Optional[str] (default: None): Key to use for graph in anndata object. If not provided, default neighbors connectivities will be used instead.
layer : Optional[str] (default: None): Key for adata.layers to choose vals.
obsm : Optional[str] (default: None): Key for adata.obsm to choose vals.
obsp : Optional[str] (default: None): Key for adata.obsp to choose vals.
use_raw : bool (default: False): Whether to use adata.raw.X for vals.

This function can also be called on the graph and values directly. In this case the signature looks like:

Parameters:

g: The graph
vals: The values

See the examples for more info.

Return type:

Union[ndarray, float]

Returns:

: If vals is two dimensional, returns a 1 dimensional ndarray array. Returns a scalar if vals is 1d.

Examples

Calculate Gearys C for each components of a dimensionality reduction:

import scanpy as sc, numpy as np

pbmc = sc.datasets.pbmc68k_processed()
pc_c = sc.metrics.gearys_c(pbmc, obsm="X_pca")

It’s equivalent to call the function directly on the underlying arrays:

alt = sc.metrics.gearys_c(pbmc.obsp["connectivities"], pbmc.obsm["X_pca"].T)
np.testing.assert_array_equal(pc_c, alt)