Efficiently create a density plot for high-density regions, points for sparse regions

Question

I need to make a plot that functions like a density plot for high-density regions on the plot, but below some threshold uses individual points. I couldn\'t find any existing

Answer 1

For the record, here is the result of a new attempt using scipy.stats.gaussian_kde rather than a 2D histogram. One could envision different combinations of color meshing and contouring depending on the purpose.

import numpy as np
from matplotlib import pyplot as plt
from scipy.stats import gaussian_kde

# parameters
npts = 5000         # number of sample points
bins = 100          # number of bins in density maps
threshold = 0.01    # density threshold for scatter plot

# initialize figure
fig, ax = plt.subplots()

# create a random dataset
x1, y1 = np.random.multivariate_normal([0, 0], [[1, 0], [0, 1]], npts/2).T
x2, y2 = np.random.multivariate_normal([4, 4], [[4, 0], [0, 1]], npts/2).T
x = np.hstack((x1, x2))
y = np.hstack((y1, y2))
points = np.vstack([x, y])

# perform kernel density estimate
kde = gaussian_kde(points)
z = kde(points)

# mask points above density threshold
x = np.ma.masked_where(z > threshold, x)
y = np.ma.masked_where(z > threshold, y)

# plot unmasked points
ax.scatter(x, y, c='black', marker='.')

# get bounds from axes
xmin, xmax = ax.get_xlim()
ymin, ymax = ax.get_ylim()

# prepare grid for density map
xedges = np.linspace(xmin, xmax, bins)
yedges = np.linspace(ymin, ymax, bins)
xx, yy = np.meshgrid(xedges, yedges)
gridpoints = np.array([xx.ravel(), yy.ravel()])

# compute density map
zz = np.reshape(kde(gridpoints), xx.shape)

# plot density map
im = ax.imshow(zz, cmap='CMRmap_r', interpolation='nearest',
               origin='lower', extent=[xmin, xmax, ymin, ymax])

# plot threshold contour
cs = ax.contour(xx, yy, zz, levels=[threshold], colors='black')

# show
fig.colorbar(im)
plt.show()