libpysal.weights.Kernel¶

class
libpysal.weights.
Kernel
(data, bandwidth=None, fixed=True, k=2, function='triangular', eps=1.0000001, ids=None, diagonal=False, distance_metric='euclidean', radius=None, **kwargs)[source]¶ Spatial weights based on kernel functions.
 Parameters
 data
array
(n,k) or KDTree where KDtree.data is array (n,k) n observations on k characteristics used to measure distances between the n objects
 bandwidth
float
or arraylike (optional) the bandwidth \(h_i\) for the kernel.
 fixed
binary
If true then \(h_i=h \forall i\). If false then bandwidth is adaptive across observations.
 k
int
the number of nearest neighbors to use for determining bandwidth. For fixed bandwidth, \(h_i=max(dknn) \forall i\) where \(dknn\) is a vector of knearest neighbor distances (the distance to the kth nearest neighbor for each observation). For adaptive bandwidths, \(h_i=dknn_i\)
 diagonalbool
If true, set diagonal weights = 1.0, if false (default), diagonals weights are set to value according to kernel function.
 function{‘triangular’,’uniform’,’quadratic’,’quartic’,’gaussian’}
kernel function defined as follows with
\[z_{i,j} = d_{i,j}/h_i\]triangular
\[K(z) = (1  z) \ if z \le 1\]uniform
\[K(z) = 1/2 \ if z \le 1\]quadratic
\[K(z) = (3/4)(1z^2) \ if z \le 1\]quartic
\[K(z) = (15/16)(1z^2)^2 \ if z \le 1\]gaussian
\[K(z) = (2\pi)^{(1/2)} exp(z^2 / 2)\] eps
float
adjustment to ensure knn distance range is closed on the knnth observations
 data
Examples
>>> from libpysal.weights import Kernel >>> points=[(10, 10), (20, 10), (40, 10), (15, 20), (30, 20), (30, 30)] >>> kw=Kernel(points) >>> kw.weights[0] [1.0, 0.500000049999995, 0.4409830615267465] >>> kw.neighbors[0] [0, 1, 3] >>> kw.bandwidth array([[20.000002], [20.000002], [20.000002], [20.000002], [20.000002], [20.000002]]) >>> kw15=Kernel(points,bandwidth=15.0) >>> kw15[0] {0: 1.0, 1: 0.33333333333333337, 3: 0.2546440075000701} >>> kw15.neighbors[0] [0, 1, 3] >>> kw15.bandwidth array([[15.], [15.], [15.], [15.], [15.], [15.]])
Adaptive bandwidths user specified
>>> bw=[25.0,15.0,25.0,16.0,14.5,25.0] >>> kwa=Kernel(points,bandwidth=bw) >>> kwa.weights[0] [1.0, 0.6, 0.552786404500042, 0.10557280900008403] >>> kwa.neighbors[0] [0, 1, 3, 4] >>> kwa.bandwidth array([[25. ], [15. ], [25. ], [16. ], [14.5], [25. ]])
Endogenous adaptive bandwidths
>>> kwea=Kernel(points,fixed=False) >>> kwea.weights[0] [1.0, 0.10557289844279438, 9.99999900663795e08] >>> kwea.neighbors[0] [0, 1, 3] >>> kwea.bandwidth array([[11.18034101], [11.18034101], [20.000002 ], [11.18034101], [14.14213704], [18.02775818]])
Endogenous adaptive bandwidths with Gaussian kernel
>>> kweag=Kernel(points,fixed=False,function='gaussian') >>> kweag.weights[0] [0.3989422804014327, 0.2674190291577696, 0.2419707487162134] >>> kweag.bandwidth array([[11.18034101], [11.18034101], [20.000002 ], [11.18034101], [14.14213704], [18.02775818]])
Diagonals to 1.0
>>> kq = Kernel(points,function='gaussian') >>> kq.weights {0: [0.3989422804014327, 0.35206533556593145, 0.3412334260702758], 1: [0.35206533556593145, 0.3989422804014327, 0.2419707487162134, 0.3412334260702758, 0.31069657591175387], 2: [0.2419707487162134, 0.3989422804014327, 0.31069657591175387], 3: [0.3412334260702758, 0.3412334260702758, 0.3989422804014327, 0.3011374490937829, 0.26575287272131043], 4: [0.31069657591175387, 0.31069657591175387, 0.3011374490937829, 0.3989422804014327, 0.35206533556593145], 5: [0.26575287272131043, 0.35206533556593145, 0.3989422804014327]} >>> kqd = Kernel(points, function='gaussian', diagonal=True) >>> kqd.weights {0: [1.0, 0.35206533556593145, 0.3412334260702758], 1: [0.35206533556593145, 1.0, 0.2419707487162134, 0.3412334260702758, 0.31069657591175387], 2: [0.2419707487162134, 1.0, 0.31069657591175387], 3: [0.3412334260702758, 0.3412334260702758, 1.0, 0.3011374490937829, 0.26575287272131043], 4: [0.31069657591175387, 0.31069657591175387, 0.3011374490937829, 1.0, 0.35206533556593145], 5: [0.26575287272131043, 0.35206533556593145, 1.0]}
 Attributes

__init__
(self, data, bandwidth=None, fixed=True, k=2, function='triangular', eps=1.0000001, ids=None, diagonal=False, distance_metric='euclidean', radius=None, **kwargs)[source]¶ Initialize self. See help(type(self)) for accurate signature.
Methods
__init__
(self, data[, bandwidth, fixed, k, …])Initialize self.
asymmetry
(self[, intrinsic])Asymmetry check.
from_WSP
(WSP[, silence_warnings])from_adjlist
(adjlist[, focal_col, …])Return an adjacency list representation of a weights object.
from_array
(array, \*\*kwargs)Construct a Kernel weights from an array.
from_dataframe
(df[, geom_col, ids])Make Kernel weights from a dataframe.
from_file
([path, format])Read a weights file into a W object.
from_networkx
(graph[, weight_col])Convert a
networkx
graph to a PySALW
object.from_shapefile
(filepath[, idVariable])Kernel based weights from shapefile
full
(self)Generate a full
numpy.ndarray
.get_transform
(self)Getter for transform property.
plot
(self, gdf[, indexed_on, ax, color, …])Plot spatial weights objects.
remap_ids
(self, new_ids)In place modification throughout
W
of id values fromw.id_order
tonew_ids
in all.set_shapefile
(self, shapefile[, idVariable, …])Adding metadata for writing headers of
.gal
and.gwt
files.set_transform
(self[, value])Transformations of weights.
symmetrize
(self[, inplace])Construct a symmetric KNN weight.
to_WSP
(self)Generate a
WSP
object.to_adjlist
(self[, remove_symmetric, …])Compute an adjacency list representation of a weights object.
to_file
(self[, path, format])Write a weights to a file.
to_networkx
(self)Convert a weights object to a
networkx
graph.Attributes
asymmetries
List of id pairs with asymmetric weights.
cardinalities
Number of neighbors for each observation.
component_labels
Store the graph component in which each observation falls.
diagW2
Diagonal of \(WW\).
diagWtW
Diagonal of \(W^{'}W\).
diagWtW_WW
Diagonal of \(W^{'}W + WW\).
histogram
Cardinality histogram as a dictionary where key is the id and value is the number of neighbors for that unit.
id2i
Dictionary where the key is an ID and the value is that ID’s index in
W.id_order
.id_order
Returns the ids for the observations in the order in which they would be encountered if iterating over the weights.
id_order_set
Returns
True
if user has setid_order
,False
if not.islands
List of ids without any neighbors.
max_neighbors
Largest number of neighbors.
mean_neighbors
Average number of neighbors.
min_neighbors
Minimum number of neighbors.
n
Number of units.
n_components
Store whether the adjacency matrix is fully connected.
neighbor_offsets
Given the current
id_order
,neighbor_offsets[id]
is the offsets of the id’s neighbors inid_order
.nonzero
Number of nonzero weights.
pct_nonzero
Percentage of nonzero weights.
s0
s0
is defined ass1
s1
is defined ass2
s2
is defined ass2array
Individual elements comprising
s2
.sd
Standard deviation of number of neighbors.
sparse
Sparse matrix object.
transform
Getter for transform property.
trcW2
Trace of \(WW\).
trcWtW
Trace of \(W^{'}W\).
trcWtW_WW
Trace of \(W^{'}W + WW\).

classmethod
from_array
(array, **kwargs)[source]¶ Construct a Kernel weights from an array. Supports all the same options as
libpysal.weights.Kernel
See also
libpysal.weights.weights.W