def gauss2D(sigma, kernel_size):
if kernel_size % 2 == 0:
raise ValueError(
'kernel_size must be odd, otherwise the filter will not have a center to convolve on'
)
# solution
Gx = gauss1D(sigma, kernel_size)
Gy = gauss1D(sigma, kernel_size)
G2 = Gx.reshape(kernel_size, 1) @ Gy.reshape(1, kernel_size)
return G2
def gauss2D(sigma, kernel_size):
## solution
# compute 1D filters
G_x = gauss1D(sigma, kernel_size)
G_y = G_x.copy()
# compute product and re-normalize
G = np.outer(G_y, G_x)
G /= np.sum(G)
return G
import numpy as np
from parameters import parameters
from knn import knn
from kde import kde
from gauss1D import gauss1D
import matplotlib.pyplot as plt
h, k = parameters()
print('Question: Kernel/K-Nearest Neighborhood Density Estimators')
# Produce the random samples
samples = np.random.normal(0, 1, 100)
# Compute the original normal distribution
realDensity = gauss1D(0, 1, 100, 5)
# Estimate the probability density using the KDE
estDensity = kde(samples, h)
# plot results
plt.subplot(2, 1, 1)
plt.plot(estDensity[:, 0],
estDensity[:, 1],
'r',
linewidth=1.5,
label='KDE Estimated Distribution')
plt.plot(realDensity[:, 0],
realDensity[:, 1],
'b',
linewidth=1.5,