Python - coordinates density mean

Question

I've got few points (X,Y)

id,X,Y
1,11.60388710,48.10862135
2,11.60420372,48.10865659
3,11.60424066,48.10864778
4,11.60425121,48.10867597
5,11.60471031,48.10872354
6,11.60428551,48.10917455
7,11.60563380,48.10921331
8,11.60422219,48.10867773
9,11.60434356,48.10870064
10,11.60460214,48.10843284

and would like to find a center point (not centroid) heavily influenced by the points that are close to each other.

For example I could create a heatmap in QGIS and have something like this:

Maybe someone knows how to write a Python script to calculate this X, Y "density" center?

Thank you for help!

Answer 1

You could try using scipy's kernel density estimation. For example (inspired by code here):

from scipy.stats import gaussian_kde
import pandas as pd
import numpy as np
from matplotlib import pyplot as plt
%matplotlib inline

names = ["id","X","Y"]
data = [[1,11.60388710, 48.10862135],
        [2,11.60420372, 48.10865659],
        [3,11.60424066, 48.10864778],
        [4,11.60425121, 48.10867597],
        [5,11.60471031, 48.10872354],
        [6,11.60428551, 48.10917455],
        [7,11.60563380, 48.10921331],
        [8,11.60422219, 48.10867773],
        [9,11.60434356, 48.10870064],
        [10,11.60460214, 48.10843284]]
df = pd.DataFrame(data, columns=names).set_index("id")
min_x = df["X"].min()
max_x = df["X"].max()
min_y = df["Y"].min()
max_y = df["Y"].max()

kernel = gaussian_kde(df.values.T)   # get gaussian kernel density estimate

# set up grid
grid_xs, grid_ys = np.mgrid[min_x:max_x:50j, min_y:max_y:50j]
positions = np.vstack([grid_xs.ravel(), 
                       grid_ys.ravel()])            # 2-dim array with X, Y-coordinates from xs, ys
Z = np.reshape(kernel(positions).T, grid_xs.shape)  # get densities

fig, ax = plt.subplots(1)
ax.imshow(np.rot90(Z), cmap=plt.cm.jet, extent=[min_x, max_x, min_y, max_y])
ax.set_xlim(min_x, max_x)
ax.set_ylim(min_y, max_y)
ax.scatter(df["X"], df["Y"], color="white", marker="x")

Of course additional color maps and formatting options are available in matplotlib to tweak the output to look as desired.

To get the position of the center (defining the center as the grid position with the highest estimated density):

idx = np.unravel_index(np.argmax(Z), Z.shape)
center = grid_xs[idx], grid_ys[idx]  # (11.604243569387755, 48.108671759387754)