02pysal距离权重矩阵

距离权重矩阵主要是借助距离来构建权重矩阵。

import numpy as np
import pysal as ps
import libpysal as lps
import geopandas as gpd

1.1k最近邻二元权重

需要指定最近邻居个数，默认值为2，p是距离度量的方幂次数，默认值是2，即欧几里得距离，idVariable是点变量的编号，必须包含dbf文件并且与shape文件一致；radius：地球半径，在使用经纬度计算时起作用

wk1 = ps.knnW_from_shapefile(ps.examples.get_path('baltim.shp') , k=4 , idVariable='STATION')
wk1.id_order[:3]

[1, 2, 3]

wk1.weights[1]

[1.0, 1.0, 1.0, 1.0]

wk1.neighbors[1]

[96, 16, 90, 133]

# 进行行标准化
wk1.transform = 'r'
wk1.weights[1]

[0.25, 0.25, 0.25, 0.25]

1.2距离范围二元权重

得到距离权重需要两步：

1. 计算范围下届，确保每个点都有邻居
2. 利用下届值作为函数参数，生成权重矩阵

path = ps.examples.get_path('baltim.shp')
df = gpd.read_file(path)
df.head(2)

	STATION	PRICE	NROOM	DWELL	NBATH	PATIO	FIREPL	AC	BMENT	NSTOR	GAR	AGE	CITCOU	LOTSZ	SQFT	X	Y	geometry
0	1	47.0	4.0	0.0	1.0	0.0	0.0	0.0	2.0	3.0	0.0	148.0	0.0	5.70	11.25	907.0	534.0	POINT (907.000 534.000)
1	2	113.0	7.0	1.0	2.5	1.0	1.0	1.0	2.0	2.0	2.0	9.0	1.0	279.51	28.92	922.0	574.0	POINT (922.000 574.000)

df.plot()

mdist = ps.min_threshold_dist_from_shapefile(ps.examples.get_path('baltim.shp'))
print(mdist)

21.319005605327842

上述得到的参数就是每个点与其最近邻邻居距离的最大值，即21.3。

wk2 = ps.threshold_binaryW_from_shapefile(path , mdist-0.0001)
wk2.islands

[101]

wk2 = ps.threshold_binaryW_from_shapefile(path , mdist)
wk2.islands

[]

wk2.weights[3]

[1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0]

需要将权重矩阵转化为r型，即行标准化，在此不在操作。

1.3核权重对象

核权重对象是利用核函数来生成的，其实和距离权重矩阵是有点像的。
公式为：$$w_{ij}=K(z_{ij})$$，其中$z_{ij}$为：$$z_{ij}=d_{ij}/h_i$$，其中hi是带宽,K()是核函数，如果两个点间的距离大于带宽的话，则这两点间的权重就是0了，下面列举几种常见的核函数：三角核函数：$$K(z)=(1-|z|,|z|<1$$。均匀核函数为$$K(z)=1/2,|z|<1$$
核函数的带宽有可变带宽和固定带宽两种，可变带宽一般来说更好一点，固定带宽当点分布很不均匀的时候往往就会出现问题了。

len(df)

211

# spreg的HAC估计需要最少的邻居数量大于等于样本数的三次方根，样本数是211，三次方根是5.x，因此每个样本的邻居数量需要大于等于6.
# 默认是使用三角形核函数进行计算
wk3= ps.adaptive_kernelW_from_shapefile(path ,function='triangular', k=6)
wk3.weights[2]

[1.0,
 0.6512571186428303,
 0.5573422238830965,
 0.4015787132074117,
 0.4015787132074117,
 0.08743761653449622,
 9.99999900663795e-08]

# 转化为numpy的权重矩阵进行观察
wk3.full()

(array([[1.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,
         0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
        [0.00000000e+00, 1.00000000e+00, 0.00000000e+00, ...,
         0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
        [0.00000000e+00, 4.01578713e-01, 1.00000000e+00, ...,
         0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
        ...,
        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,
         1.00000000e+00, 2.39883126e-01, 2.54644082e-01],
        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,
         3.67544531e-01, 1.00000000e+00, 2.05790264e-01],
        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,
         2.19131269e-01, 9.99999901e-08, 1.00000000e+00]]),
 [0,
  1,
  2,
 ...
  210])

wk3.full()[0].shape

(211, 211)

wk3.neighbors

{0: [0, 95, 15, 89, 132, 177, 90],
 1: [1, 4, 3, 6, 184, 14, 179],
 2: [2, 3, 6, 1, 4, 184, 14],
 3: [3, 1, 2, 6, 4, 184, 14],...
}

wk3.weights

{0: [1.0,
  0.29289328952412363,
  0.12294206839876398,
  0.0880073449393135,
  0.056907799290817906,
  0.007237830111578081,
  9.99999900663795e-08],
 1: [1.0,
  0.3615305562728467,
  0.34188076119589894,
  0.28616946113480424,
  0.21397565474242586,
  0.20191319534105834,
  9.99999900663795e-08],
 2: [1.0,
  0.6512571186428303,
  0.5573422238830965,
  0.4015787132074117,
  0.4015787132074117,
  0.08743761653449622,
  9.99999900663795e-08],
 3: [1.0,
  0.544679199127337,
  0.5314787611863058,
  0.40530809165277093,
  0.2928932895241235,
  0.23291818137604625,
  9.99999899553572e-08],...
]}