Hierarchical Boundary Coefficient Clustering

HBCC is a clustering algorithm is inspired by the work of Peng et al. [4]. Their CDC algorithm detects regions that separate clusters by quantifying how spread out points' neighbors are in feature space. The intuition for this process is as follows: (1) points within a clusters have near neighbors on all sides, and (2) points in-between clusters or on the edge of a cluster predominantly have neighbors in the direction of the cluster's core.

The same intuition was previously used by Vandaele et al. [2] to quantify how close points are to the boundary of the data's manifold. They used their boundary coefficient to extract manifold skeletons.

HBCC combines Vandaele et al. [2]'s boundary coefficient with HDBSCAN's [1], [3] principled density-based cluster selection strategies. This approach removes CDC's ratio parameter. Instead a clustering hierarchy is evaluated over all boundary coefficient values and clusters are selected from the hierarchy.

The implementation relies on McInnes' fast_hdbscan and its support for lensed clustering introduced for Bot et al. [5] to detect branches.

The HBCC algorithm works as follows:

1. Compute k nearest neighbors and minimum spanning tree [3].
2. Compute n-hop distances from nearest neighbors [2]
3. Compute the boundary coefficient for each point [2].
4. Compute minimum spanning tree from boundary coefficient weighted knn--mst graph union [5].
5. Compute HDBSCAN cluster hierarchy and selection [1].

How to use HBCC

import numpy as np
import matplotlib.pyplot as plt
from fast_hbcc import HBCC

data = np.load('data/flareable/flared_clusterable_data.npy')
c = HBCC(
    num_hops=4,
    min_samples=10,
    min_cluster_size=100,
    cluster_selection_method="leaf",
).fit(data)
plt.scatter(*data.T, c=c.labels_ % 10, s=2, cmap='tab10', vmin=0, vmax=9)
plt.axis("off")
plt.show()

How to install HBCC

This repository is published on pypi as the fast-hbcc package:

pip install fast-hbcc

Example Notebooks

A notebook demonstrating how the algorithm works is available on nbviewer.

Citing

Citing information not available yet.

Licensing

The fast_hbcc package has a 2-Clause BSD license.

References

• [1] Campello, R. J., Moulavi, D., & Sander, J. (2013, April). Density-based clustering based on hierarchical density estimates. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 160-172). Springer Berlin Heidelberg.

• [2] Vandaele, R., Saeys, Y., & De Bie, T. (2019). The Boundary Coefficient : a Vertex Measure for Visualizing and Finding Structure in Weighted Graphs. 15th International Workshop on Mining and Learning with Graphs (MLG).

• [3] McInnes, L., & Healy, J. (2017). Accelerated Hierarchical Density Based Clustering. 2017 IEEE International Conference on Data Mining Workshops (ICDMW), 2017-Novem, 33–42. https://doi.org/10.1109/ICDMW.2017.12.

• [4] Peng, D., Gui, Z., Wang, D., Ma, Y., Huang, Z., Zhou, Y., & Wu, H. (2022). Clustering by measuring local direction centrality for data with heterogeneous density and weak connectivity. Nature Communications, 13(1), 1–14. https://doi.org/10.1038/s41467-022-33136-9.

• [5] Bot D.M., Peeters J., Liesenborgs J., Aerts J. 2025. FLASC: a flare-sensitive clustering algorithm. PeerJ Computer Science 11:e2792 https://doi.org/10.7717/peerj-cs.2792.