Persistent Leaves Spatial Clustering for Applications with Noise

This library provides a new clustering algorithm based on HDBSCAN*. The primary advantages of PLSCAN over the hdbscan and fast_hdbscan libraries are:

• PLSCAN automatically finds the optimal minimum cluster size.
• PLSCAN can easily use all available cores to speed up computation.
• PLSCAN has much faster implementations of tree condensing and cluster extraction.
• PLSCAN does not rely on JIT compilation.

To use PLSCAN, you only need to set the min_samples parameter. This parameter controls how many neighbors are considered when measuring distances between points. Setting a higher value for min_samples makes the algorithm group points into larger, smoother clusters, and usually results in fewer, more stable clusters.

import numpy as np
import matplotlib.pyplot as plt

from fast_plscan import PLSCAN

data = np.load("docs/data/data.npy")

clusterer = PLSCAN(
  min_samples = 5, # same as in HDBSCAN
).fit(data)

plt.figure()
plt.scatter(
  *data.T, c=clusterer.labels_ % 10, s=5, alpha=0.5, 
  edgecolor="none", cmap="tab10", vmin=0, vmax=9
)
plt.axis("off")
plt.subplots_adjust(left=0, right=1, top=1, bottom=0)
plt.show()

The algorithm creates a hierarchy of leaf-clusters by changing the minimum cluster size. As this parameter varies, clusters appear or disappear. For each minimum cluster size, the algorithm measures how long these leaf-clusters persist. It then selects the minimum cluster size where the total persistence is highest, giving the most stable clustering. You can visualize this hierarchy using the leaf_tree_ attribute, which provides an alternative to HDBSCAN*'s condensed cluster tree.

clusterer.leaf_tree_.plot(leaf_separation=0.1)
plt.show()

You can also explore how the clustering changes for other important values of the minimum cluster size. The cluster_layers method automatically finds the most persistent clusterings and returns their cluster labels and membership strengths.

layers = clusterer.cluster_layers(max_peaks=4)
for i, (size, labels, probs) in enumerate(layers):
  plt.subplot(2, 2, i + 1)
  plt.scatter(
    *data.T,
    c=labels % 10,
    alpha=np.maximum(0.1, probs),
    s=1,
    linewidth=0,
    cmap="tab10",
  )
  plt.title(f"min_cluster_size={int(size)}")
  plt.axis("off")
plt.subplots_adjust(left=0, right=1, top=1, bottom=0)
plt.show()

Installation instructions

Pre-build binaries are available on pypi, so the package can be installed with pip and similar package managers on most systems:

pip install fast_plscan

Conda forge builds are in progress. See our documentation for instructions on compiling the package locally.

Citing

When using this work, please cite our preprint:

@misc{bot2025plscan,
  title         = {Persistent Multiscale Density-based Clustering},
  author        = {Dani{\"{e}}l Bot and Leland McInnes and Jan Aerts},
  year          = {2025},
  eprint        = {2512.16558},
  archiveprefix = {arXiv},
  primaryclass  = {cs.LG},
  url           = {https://arxiv.org/abs/2512.16558}
}

Licensing

The fast-plscan package has a 3-Clause BSD license.