scanpy.metrics.morans_i

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

Calculate Moran’s I Global Autocorrelation Statistic.

Moran’s I is a global autocorrelation statistic for some measure on a graph. It is commonly used in spatial data analysis to assess autocorrelation on a 2D grid. It is closely related to Geary’s C, but not identical. More info can be found here.

\[I = \frac{ N \sum_{i, j} w_{i, j} z_{i} z_{j} }{ S_{0} \sum_{i} z_{i}^{2} }\]

Parameters:

adata : AnnData
vals : Union[ndarray, spmatrix, None] (default: None): Values to calculate Moran’s I 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 Morans I for each components of a dimensionality reduction:

import scanpy as sc, numpy as np

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

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

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