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Two-dimensional kernel density estimate: comparing scikit-learn and scipy
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#!/usr/bin/env python3 | |
import numpy as np | |
import matplotlib.pyplot as plt | |
import matplotlib | |
matplotlib.rc('legend', fontsize=8, handlelength=3) | |
matplotlib.rc('axes', titlesize=8) | |
matplotlib.rc('axes', labelsize=8) | |
matplotlib.rc('xtick', labelsize=8) | |
matplotlib.rc('ytick', labelsize=8) | |
matplotlib.rc('text', usetex=True) | |
matplotlib.rc('font', size=8, family='serif', | |
style='normal', variant='normal', | |
stretch='normal', weight='normal', | |
serif='Times') | |
def kde1(x, y, ax): | |
from scipy.stats import gaussian_kde | |
# Calculate the point density | |
xy = np.vstack([x,y]) | |
kernel = gaussian_kde(xy, bw_method='silverman') | |
xmin = x.min() | |
xmax = x.max() | |
ymin = y.min() | |
ymax = y.max() | |
X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j] | |
positions = np.vstack([X.ravel(), Y.ravel()]) | |
Z = np.reshape(kernel(positions).T, X.shape) | |
ax.imshow(np.rot90(Z), cmap=plt.cm.viridis, | |
extent=[xmin, xmax, ymin, ymax]) | |
ax.scatter(x, y, c='k', s=5, edgecolor='') | |
def kde2(x, y, ax): | |
from sklearn.neighbors import KernelDensity | |
xy = np.vstack([x,y]) | |
d = xy.shape[0] | |
n = xy.shape[1] | |
bw = (n * (d + 2) / 4.)**(-1. / (d + 4)) # silverman | |
#bw = n**(-1./(d+4)) # scott | |
print('bw: {}'.format(bw)) | |
kde = KernelDensity(bandwidth=bw, metric='euclidean', | |
kernel='gaussian', algorithm='ball_tree') | |
kde.fit(xy.T) | |
xmin = x.min() | |
xmax = x.max() | |
ymin = y.min() | |
ymax = y.max() | |
X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j] | |
positions = np.vstack([X.ravel(), Y.ravel()]) | |
Z = np.reshape(np.exp(kde.score_samples(positions.T)), X.shape) | |
ax.imshow(np.rot90(Z), cmap=plt.cm.viridis, | |
extent=[xmin, xmax, ymin, ymax]) | |
ax.scatter(x, y, c='k', s=5, edgecolor='') | |
N1 = np.random.normal(size=500) | |
N2 = np.random.normal(scale=0.5, size=500) | |
x = N1+N2 | |
y = N1-N2 | |
fig, axarr = plt.subplots(1, 2) | |
fig.subplots_adjust(left=0.11, right=0.95, wspace=0.0, bottom=0.18) | |
ax = axarr[0] | |
kde1(x, y, ax) | |
ax.set_xlabel('$x$') | |
ax.set_ylabel('$y$') | |
ax.set_title('scipy') | |
ax.set_xlim((-2,2)) | |
ax.set_ylim((-2,2)) | |
ax = axarr[1] | |
kde2(x, y, ax) | |
ax.set_xlabel('$x$') | |
ax.set_ylabel('$y$') | |
ax.set_title('scikit-learn') | |
ax.set_xlim((-2,2)) | |
ax.set_ylim((-2,2)) | |
plt.tight_layout() | |
plt.savefig('kde.png') | |
plt.show() |
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line 47, the bandwidth calculation expression is incorrect.