How can I make a scatter plot colored by density in matplotlib?

I'd like to make a scatter plot where each point is colored by the spatial density of nearby points.

I've come across a very similar question, which shows an example of this using R:

R Scatter Plot: symbol color represents number of overlapping points

What's the best way to accomplish something similar in python using matplotlib?

Solution 1:

In addition to hist2d or hexbin as @askewchan suggested, you can use the same method that the accepted answer in the question you linked to uses.

If you want to do that:

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

# Generate fake data
x = np.random.normal(size=1000)
y = x * 3 + np.random.normal(size=1000)

# Calculate the point density
xy = np.vstack([x,y])
z = gaussian_kde(xy)(xy)

fig, ax = plt.subplots()
ax.scatter(x, y, c=z, s=100)
plt.show()

If you'd like the points to be plotted in order of density so that the densest points are always on top (similar to the linked example), just sort them by the z-values. I'm also going to use a smaller marker size here as it looks a bit better:

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

# Generate fake data
x = np.random.normal(size=1000)
y = x * 3 + np.random.normal(size=1000)

# Calculate the point density
xy = np.vstack([x,y])
z = gaussian_kde(xy)(xy)

# Sort the points by density, so that the densest points are plotted last
idx = z.argsort()
x, y, z = x[idx], y[idx], z[idx]

fig, ax = plt.subplots()
ax.scatter(x, y, c=z, s=50)
plt.show()

Solution 2:

Also, if the number of point makes KDE calculation too slow, color can be interpolated in np.histogram2d [Update in response to comments: If you wish to show the colorbar, use plt.scatter() instead of ax.scatter() followed by plt.colorbar()]:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.colors import Normalize 
from scipy.interpolate import interpn

def density_scatter( x , y, ax = None, sort = True, bins = 20, **kwargs )   :
    """
    Scatter plot colored by 2d histogram
    """
    if ax is None :
        fig , ax = plt.subplots()
    data , x_e, y_e = np.histogram2d( x, y, bins = bins, density = True )
    z = interpn( ( 0.5*(x_e[1:] + x_e[:-1]) , 0.5*(y_e[1:]+y_e[:-1]) ) , data , np.vstack([x,y]).T , method = "splinef2d", bounds_error = False)

    #To be sure to plot all data
    z[np.where(np.isnan(z))] = 0.0

    # Sort the points by density, so that the densest points are plotted last
    if sort :
        idx = z.argsort()
        x, y, z = x[idx], y[idx], z[idx]

    ax.scatter( x, y, c=z, **kwargs )

    norm = Normalize(vmin = np.min(z), vmax = np.max(z))
    cbar = fig.colorbar(cm.ScalarMappable(norm = norm), ax=ax)
    cbar.ax.set_ylabel('Density')

    return ax


if "__main__" == __name__ :

    x = np.random.normal(size=100000)
    y = x * 3 + np.random.normal(size=100000)
    density_scatter( x, y, bins = [30,30] )