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Radius-Guided Post-Clustering for Shape-Aware, Scalable Refinement of k-Means Results

Stefan Kober

TL;DR

The paper addresses the limitations of k-means in handling non-convex cluster shapes and fixed k by introducing a radius-based post-processing step. After running an initial k-means with a potentially overestimated $k$, it assigns each cluster a radius $r_i = \max_{x \in C_i} \|x - c_i\|_2$ and merges clusters whose centers satisfy $\|c_i - c_j\|_2 \le r_i + r_j$, enabling recovery of complex shapes. It also enables scalable clustering via recursive partitioning: clustering within tiles followed by a global radius-based merge preserves global structure across partitions. Experiments on the FCPS benchmark show high median clustering success across various overestimated $k$ values, demonstrating the method's effectiveness as a lightweight, drop-in refinement for k-means suitable for distributed and large-scale pipelines, with straightforward integration into existing scikit-learn workflows.

Abstract

Traditional k-means clustering underperforms on non-convex shapes and requires the number of clusters k to be specified in advance. We propose a simple geometric enhancement: after standard k-means, each cluster center is assigned a radius (the distance to its farthest assigned point), and clusters whose radii overlap are merged. This post-processing step loosens the requirement for exact k: as long as k is overestimated (but not excessively), the method can often reconstruct non-convex shapes through meaningful merges. We also show that this approach supports recursive partitioning: clustering can be performed independently on tiled regions of the feature space, then globally merged, making the method scalable and suitable for distributed systems. Implemented as a lightweight post-processing step atop scikit-learn's k-means, the algorithm performs well on benchmark datasets, achieving high accuracy with minimal additional computation.

Radius-Guided Post-Clustering for Shape-Aware, Scalable Refinement of k-Means Results

TL;DR

The paper addresses the limitations of k-means in handling non-convex cluster shapes and fixed k by introducing a radius-based post-processing step. After running an initial k-means with a potentially overestimated , it assigns each cluster a radius and merges clusters whose centers satisfy , enabling recovery of complex shapes. It also enables scalable clustering via recursive partitioning: clustering within tiles followed by a global radius-based merge preserves global structure across partitions. Experiments on the FCPS benchmark show high median clustering success across various overestimated values, demonstrating the method's effectiveness as a lightweight, drop-in refinement for k-means suitable for distributed and large-scale pipelines, with straightforward integration into existing scikit-learn workflows.

Abstract

Traditional k-means clustering underperforms on non-convex shapes and requires the number of clusters k to be specified in advance. We propose a simple geometric enhancement: after standard k-means, each cluster center is assigned a radius (the distance to its farthest assigned point), and clusters whose radii overlap are merged. This post-processing step loosens the requirement for exact k: as long as k is overestimated (but not excessively), the method can often reconstruct non-convex shapes through meaningful merges. We also show that this approach supports recursive partitioning: clustering can be performed independently on tiled regions of the feature space, then globally merged, making the method scalable and suitable for distributed systems. Implemented as a lightweight post-processing step atop scikit-learn's k-means, the algorithm performs well on benchmark datasets, achieving high accuracy with minimal additional computation.
Paper Structure (13 sections, 2 equations, 2 figures, 4 tables)

This paper contains 13 sections, 2 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Algorithm Description
  4. Standard k-means (Recap)
  5. Radius-Based Post-Clustering
  6. Post-Processing Implementation
  7. Recursive Partitioning for Scalability
  8. Experimental Results
  9. FCPS Benchmark Results of Post-Processing Compared to k-Means
  10. FCPS Benchmark Results for Partitioning the Data Space
  11. Discussion and Conclusion
  12. Limitations and Future Work
  13. Conclusion

Figures (2)

  • Figure 1: Visual explanation of radius-based post-processing. (a) Naive k-means with $k=2$ fails to recover the circular structure. (b) With $k=20$, clusters oversegment the shape. (c) Voronoi cells offer no guidance for merging. (d) Circles around cluster center through farthest point reveal meaningful overlap. (e) The correct clustering is recovered by radius-based merging of the clusters in (b).
  • Figure 2: Overview of the FCPS datasets used in this paper, shown with ground-truth labels. These diverse cluster shapes—including rings, overlapping spheres, and complex symmetric forms—serve as a robust benchmark for evaluating radius-guided post-processing.