hopkins-statistic 0.2.0

Compute the Hopkins statistic to assess clustering tendency.

hopkins-statistic

hopkins-statistic is a library for computing the Hopkins statistic to test for departure from complete spatial randomness (CSR), i.e., the presence of clustering or regularity in point patterns.

This implementation defaults to the formulation of Cross and Jain (1982), raising distances to the power of the data dimension. In two dimensions this is equivalent to the original definition by Hopkins and Skellam (1954) and, under the CSR null hypothesis, the statistic has a Beta distribution, so p-values can be computed analytically.

Installation

pip install hopkins-statistic

Usage

import numpy as np
from hopkins_statistic import hopkins

rng = np.random.default_rng(42)

# Simple clustered example: two Gaussian blobs
centers = np.array([[0, 0], [0, 1]])
labels = rng.integers(len(centers), size=100)
X = centers[labels] + rng.normal(scale=0.1, size=(100, 2))

statistic = hopkins(X, rng=rng)
print(f"{statistic:.3f}")
#> 0.771

License

MIT. See LICENSE.