Thoughts about adaptive gaussian

[Ziqi-Li]

The adaptive gaussian and adaptive bisquare show totally different curves for the model PctBach~FB+Black+Pov. The optimal bandwidth found for adaptive gaussian would be local and for adaptive bisquare would be global. Test against GWModel is showing exactly same curves. Test against ArcGIS adaptive gaussian is showing similar curve as PySAL's adaptive bisqaure. BTW, ArcGIS claims their gaussian kernel is w = exp(-(d/b)**2), while we are using exp(-0.5*(d/b)**2) which is from the book. Will look into to see what it implies.

#Imports
import numpy as np
import matplotlib.pyplot as plt
import pysal
from pysal.contrib.gwr.gwr import GWR
from pysal.contrib.gwr.sel_bw import Sel_BW
from pysal.contrib.glm.family import Gaussian, Poisson, Binomial


#Load the GA data
data = pysal.open(pysal.examples.get_path('GData_utm.csv'))
y = np.array(data.by_col('PctBach')).reshape((-1,1))
fb  = np.array(data.by_col('PctFB')).reshape((-1,1))
pov = np.array(data.by_col('PctPov')).reshape((-1,1)) 
blk = np.array(data.by_col('PctBlack')).reshape((-1,1))
X = np.hstack([fb,pov,blk])
coords = list(zip(data.by_col('X'), data.by_col('Y')))

#Fit using each bandwidth
pysal_aicc_gau = []
pysal_aicc_bisq = []
for bw in range(20,160):
    results = GWR(coords, y, X, bw,fixed=False,kernel='gaussian',family=Gaussian()).fit()
    pysal_aicc_gau += [results.aicc]
    results = GWR(coords, y, X, bw,fixed=False,kernel='bisquare',family=Gaussian()).fit()
    pysal_aicc_bisq += [results.aicc]

#Plot
bw = range(20,160)
plt.figure(figsize=(12,8))
#plt.plot(bw,arc_aiccs,'r-',label="ArcGIS Adaptive 'Gaussian'") #Calculated from ArcGIS
plt.plot(bw,pysal_aicc_bisq,'b-',label='PySAL Adaptive Bisquare')
plt.plot(bw,pysal_aicc_gau,'y-',label='PySAL Adaptive Gaussian')
plt.xlabel('Bandwidth',fontsize=14)
plt.ylabel('AICc',fontsize=14)
plt.title('Georgia: Bach~ForeignBorn+Poverty+Black',fontsize=20)
plt.legend(fontsize=14)
plt.show()

[Ziqi-Li]

By default, the truncate parameter in adaptive_gauss from kernels.py is set to be False, while change that to True gives the following AICc curve. Also attached the kernel function lines. It is like after truncate point (beyond local neighbors), the gaussian still has pretty large weights.

def adapt_gauss(coords, nn, points=None, dmat=None,sorted_dmat=None):
    w = _Kernel(coords, fixed=False, k=nn-1, function='gwr_gaussian',
            truncate=**True**, points=points, dmat=dmat,sorted_dmat=sorted_dmat)
    return w.kernel

[TaylorOshan]

Closing this as the discussion was moved to a private repo.