libpysal.weights.KNN

class libpysal.weights.KNN(data, k=2, p=2, ids=None, radius=None, distance_metric='euclidean', **kwargs)

Creates nearest neighbor weights matrix based on k nearest neighbors.

Parameters:

kdtreeobject

PySAL KDTree or ArcKDTree where KDtree.data is array (n,k) n observations on k characteristics used to measure distances between the n objects

kint

number of nearest neighbors

pfloat

Minkowski p-norm distance metric parameter: 1<=p<=infinity 2: Euclidean distance 1: Manhattan distance Ignored if the KDTree is an ArcKDTree

idslist

identifiers to attach to each observation

Returns:

wW

instance Weights object with binary weights

See also

libpysal.weights.weights.W

Notes

Ties between neighbors of equal distance are arbitrarily broken.

Further, if many points occupy the same spatial location (i.e. observations are coincident), then you may need to increase k for those observations to acquire neighbors at different spatial locations. For example, if five points are coincident, then their four nearest neighbors will all occupy the same spatial location; only the fifth nearest neighbor will result in those coincident points becoming connected to the graph as a whole.

Solutions to this problem include jittering the points (by adding a small random value to each observation’s location) or by adding higher-k neighbors only to the coincident points, using the weights.w_sets.w_union() function.

Examples

>>> import libpysal
>>> import numpy as np
>>> points = [(10, 10), (20, 10), (40, 10), (15, 20), (30, 20), (30, 30)]
>>> kd = libpysal.cg.KDTree(np.array(points))
>>> wnn2 = libpysal.weights.KNN(kd, 2)
>>> [1,3] == wnn2.neighbors[0]
True
>>> wnn2 = KNN(kd,2)
>>> wnn2[0]
{1: 1.0, 3: 1.0}
>>> wnn2[1]
{0: 1.0, 3: 1.0}

now with 1 rather than 0 offset

>>> wnn2 = libpysal.weights.KNN(kd, 2, ids=range(1,7))
>>> wnn2[1]
{2: 1.0, 4: 1.0}
>>> wnn2[2]
{1: 1.0, 4: 1.0}
>>> 0 in wnn2.neighbors
False

__init__(data, k=2, p=2, ids=None, radius=None, distance_metric='euclidean', **kwargs)

Methods

__init__(data[, k, p, ids, radius, ...])
asymmetry([intrinsic])	Asymmetry check.
from_WSP(WSP[, silence_warnings])	Create a pysal W from a pysal WSP object (thin weights matrix).
from_adjlist(adjlist[, focal_col, ...])	Return an adjacency list representation of a weights object.
from_array(array, *args, **kwargs)	Creates nearest neighbor weights matrix based on k nearest neighbors.
from_dataframe(df[, geom_col, ids, use_index])	Make KNN 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 PySAL W object.
from_shapefile(filepath, *args, **kwargs)	Nearest neighbor weights from a shapefile.
from_sparse(sparse)	Convert a scipy.sparse array to a PySAL W object.
full()	Generate a full numpy.ndarray.
get_transform()	Getter for transform property.
plot(gdf[, indexed_on, ax, color, node_kws, ...])	Plot spatial weights objects.
remap_ids(new_ids)	In place modification throughout W of id values from w.id_order to new_ids in all.
reweight([k, p, new_data, new_ids, inplace])	Redo K-Nearest Neighbor weights construction using given parameters
set_shapefile(shapefile[, idVariable, full])	Adding metadata for writing headers of .gal and .gwt files.
set_transform([value])	Transformations of weights.
symmetrize([inplace])	Construct a symmetric KNN weight.
to_WSP()	Generate a WSP object.
to_adjlist([remove_symmetric, drop_islands, ...])	Compute an adjacency list representation of a weights object.
to_file([path, format])	Write a weights to a file.
to_networkx()	Convert a weights object to a networkx graph.
to_sparse([fmt])	Generate a scipy.sparse array object from a pysal W.

Attributes

asymmetries	List of id pairs with asymmetric weights sorted in ascending index location order.
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 set id_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 in id_order.
nonzero	Number of nonzero weights.
pct_nonzero	Percentage of nonzero weights.
s0	s0 is defined as
s1	s1 is defined as
s2	s2 is defined as
s2array	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, *args, **kwargs)

Creates nearest neighbor weights matrix based on k nearest neighbors.

Parameters:

arraynp.ndarray

(n, k) array representing n observations on k characteristics used to measure distances between the n objects

**kwargskeyword arguments, see Rook

Returns:

wW

instance Weights object with binary weights

See also

libpysal.weights.weights.W

Notes

Ties between neighbors of equal distance are arbitrarily broken.

Examples

>>> from libpysal.weights import KNN
>>> points = [(10, 10), (20, 10), (40, 10), (15, 20), (30, 20), (30, 30)]
>>> wnn2 = KNN.from_array(points, 2)
>>> [1,3] == wnn2.neighbors[0]
True
>>> wnn2 = KNN.from_array(points,2)
>>> wnn2[0]
{1: 1.0, 3: 1.0}
>>> wnn2[1]
{0: 1.0, 3: 1.0}

now with 1 rather than 0 offset

>>> wnn2 = KNN.from_array(points, 2, ids=range(1,7))
>>> wnn2[1]
{2: 1.0, 4: 1.0}
>>> wnn2[2]
{1: 1.0, 4: 1.0}
>>> 0 in wnn2.neighbors
False

classmethod from_dataframe(df, geom_col=None, ids=None, use_index=True, *args, **kwargs)

Make KNN weights from a dataframe.

Parameters:

dfpandas.dataframe

a dataframe with a geometry column that can be used to construct a W object

geom_colstr

the name of the column in df that contains the geometries. Defaults to active geometry column.

idslist-like, str

a list-like of ids to use to index the spatial weights object or the name of the column to use as IDs. If nothing is provided, the dataframe index is used if use_index=True or a positional index is used if use_index=False. Order of the resulting W is not respected from this list.

use_indexbool

use index of df as ids to index the spatial weights object.

See also

libpysal.weights.weights.W

classmethod from_shapefile(filepath, *args, **kwargs)

Nearest neighbor weights from a shapefile.

Parameters:

datastr

shapefile containing attribute data.

kint

number of nearest neighbors

pfloat

Minkowski p-norm distance metric parameter: 1<=p<=infinity 2: Euclidean distance 1: Manhattan distance

idslist

identifiers to attach to each observation

radiusfloat

If supplied arc_distances will be calculated based on the given radius. p will be ignored.

Returns:

wKNN

instance; Weights object with binary weights.

See also

libpysal.weights.weights.W

Notes

Ties between neighbors of equal distance are arbitrarily broken.

Examples

Polygon shapefile >>> import libpysal >>> from libpysal.weights import KNN >>> wc=KNN.from_shapefile(libpysal.examples.get_path(“columbus.shp”)) >>> “%.4f”%wc.pct_nonzero ‘4.0816’ >>> set([2,1]) == set(wc.neighbors[0]) True >>> wc3=KNN.from_shapefile(libpysal.examples.get_path(“columbus.shp”),k=3) >>> set(wc3.neighbors[0]) == set([2,1,3]) True >>> set(wc3.neighbors[2]) == set([4,3,0]) True

Point shapefile

>>> w=KNN.from_shapefile(libpysal.examples.get_path("juvenile.shp"))
>>> w.pct_nonzero
1.1904761904761905
>>> w1=KNN.from_shapefile(libpysal.examples.get_path("juvenile.shp"),k=1)
>>> "%.3f"%w1.pct_nonzero
'0.595'

reweight(k=None, p=None, new_data=None, new_ids=None, inplace=True)

Redo K-Nearest Neighbor weights construction using given parameters

Parameters:

new_datanp.ndarray

an array containing additional data to use in the KNN weight

new_idslist

a list aligned with new_data that provides the ids for each new observation

inplacebool

a flag denoting whether to modify the KNN object in place or to return a new KNN object

kint

number of nearest neighbors

pfloat

Minkowski p-norm distance metric parameter: 1<=p<=infinity 2: Euclidean distance 1: Manhattan distance Ignored if the KDTree is an ArcKDTree

Returns:

A copy of the object using the new parameterization, or None if the

object is reweighted in place.