spacenet.pcf.cross_weighted_pair_correlation_function

spacenet.pcf.cross_weighted_pair_correlation_function(spatial_network, labels_for_objects_A, labels_for_objects_B, object_indices_A=None, object_indices_B=None, spatial_kernel_bandwidth=10, spatial_kernel_n=2, r_min=0, r_max=100, r_step=10, marker_kernel_bandwidth_A=0.2, marker_kernel_n_A=1, marker_min_A=0, marker_max_A=1, marker_step_A=0.1, marker_kernel_bandwidth_B=0.2, marker_kernel_n_B=1, marker_min_B=0, marker_max_B=1, marker_step_B=0.1, edge_weight_name='Distance', return_confidence_interval=False, low_memory=False, verbose=True, n_jobs=1)

Compute the cross weighted pair correlation function between two populations of objects (A and B) on a spatial network, where the contributions of each object to the pair correlation function are weighted by a kernel function based on their marker levels. Polynomial kernels are used to weight contributions based on marker levels, and the pair correlation function is computed across a range of distances (r) and target marker values for both populations. The function can also compute confidence intervals using spatial bootstrapping.

Parameters:

spatial_networknetworkx.Graph

The spatial network on which to compute the pair correlation function. Edges should have a weight attribute corresponding to the distance between nodes.

labels_for_objects_Anp.array

An array of continuous marker values for the objects in population A. The length of this array should match the number of nodes in the network, and the values should correspond to the marker levels for each node.

labels_for_objects_Bnp.array

An array of continuous marker values for the objects in population B. The length of this array should match the number of nodes in the network, and the values should correspond to the marker levels for each node.

object_indices_Aarray-like, optional

The indices of the nodes in population A. If None, all nodes in the network will be considered as part of population A. Default is None.

object_indices_Barray-like, optional

The indices of the nodes in population B. If None, all nodes in the network will be considered as part of population B. Default is None.

spatial_kernel_bandwidthfloat, optional

The bandwidth parameter for the spatial kernel function. This controls the smoothness of the pair correlation function. Default is 10.

spatial_kernel_nint, optional

The exponent parameter for the spatial kernel function. This controls the shape of the kernel. Default is 2 (which corresponds to a Gaussian-like kernel).

r_minfloat, optional

The minimum distance to consider when computing the pair correlation function. Default is 0.

r_maxfloat, optional

The maximum distance to consider when computing the pair correlation function. Default is 100.

r_stepfloat, optional

The step size for the distance bins when computing the pair correlation function. Default is 10.

marker_kernel_bandwidth_Afloat, optional

The bandwidth parameter for the marker kernel function for population A. This controls the smoothness of the weighting based on marker levels. Default is 0.2.

marker_kernel_n_Aint, optional

The exponent parameter for the marker kernel function for population A. This controls the shape of the kernel for marker weighting. Default is 1 (which corresponds to a triangular kernel).

marker_min_Afloat, optional

The minimum marker value to consider for population A when computing the marker kernel. Default is 0.

marker_max_Afloat, optional

The maximum marker value to consider for population A when computing the marker kernel. Default is 1.

marker_step_Afloat, optional

The step size for the marker values when computing the marker kernel for population A. Default is 0.1.

marker_kernel_bandwidth_Bfloat, optional

The bandwidth parameter for the marker kernel function for population B. This controls the smoothness of the weighting based on marker levels for population B. Default is 0.2.

marker_kernel_n_Bint, optional

The exponent parameter for the marker kernel function for population B. This controls the shape of the kernel for marker weighting for population B. Default is 1 (which corresponds to a triangular kernel).

marker_min_Bfloat, optional

The minimum marker value to consider for population B when computing the marker kernel. Default is 0.

marker_max_Bfloat, optional

The maximum marker value to consider for population B when computing the marker kernel. Default is 1.

marker_step_Bfloat, optional

The step size for the marker values when computing the marker kernel for population B. Default is 0.1.

edge_weight_namestr, optional

The name of the edge attribute in the network that corresponds to the distance between nodes. Default is ‘Distance’.

return_confidence_intervalbool, optional

Whether to compute and return 95% confidence intervals for the pair correlation function using spatial bootstrapping. Default is False.

low_memorybool, optional

Whether to use a low-memory implementation of Dijkstra’s algorithm that computes distances in batches. This can be useful for large networks that do not fit in memory. Default is False.

verbosebool, optional

Whether to print progress messages during computation. Default is True.

Returns:

tau_Anumpy.ndarray

The target marker values for label A at which the pair correlation function was computed.

tau_Bnumpy.ndarray

The target marker values for label B at which the pair correlation function was computed.

radiinumpy.ndarray

The radii at which the pair correlation function was computed.

gnumpy.ndarray

The values of the pair correlation function at the corresponding target marker values and radii. This will be a 3D array with dimensions corresponding to (number of target marker values for A, number of target marker values for B, number of radii).

confidence_intervalnumpy.ndarray (if return_confidence_interval is True)

If return_confidence_interval is True, this will be a numpy array (2, number of target marker values for A, number of target marker values for B, number of radii) containing the confidence intervals for the pair correlation function at each combination of target marker values and radius. The CI[0,:,:,:] corresponds to the lower bounds of the confidence intervals, and CI[1,:,:,:] corresponds to the upper bounds. If return_confidence_interval is False, this will not be returned.

Notes

For details, see the reference paper…