Minimum Spanning Tree applied to Design of Experiments

minimum_spanning_tree.py

"""Minimum Spanning Tree.

MST is used here as a discrepancy criterion.
Comparing two different designs: the higher the mean, the better the design is
in terms of space filling.

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MIT License

Copyright (c) 2018 Pamphile Tupui ROY

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"""
import numpy as np
from scipy.sparse.csgraph import minimum_spanning_tree
from scipy.spatial.distance import cdist
import matplotlib.pyplot as plt

# Define here your sample of shape (n_samples, n_dims)
sample = np.random.random_sample((50, 2))

dist = cdist(sample, sample)
mst = minimum_spanning_tree(dist)

mean = mst.data.mean()
var = mst.data.var()

print(f'Mean: {mean} - Variance: {var}')

mst = mst.toarray()
edges = np.where(mst > 0)
edges = np.array(edges).T

print(f'Edges:\n{edges}')

fig, ax = plt.subplots()
for edge in edges:
    ax.plot(sample[edge, 0], sample[edge, 1], c='k')
ax.scatter(sample[:, 0], sample[:, 1])
plt.show()