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GCAO: Group-driven Clustering via Gravitational Attraction and Optimization

Qi Li, Jun Wang

TL;DR

GCAO addresses clustering in high-dimensional, non-uniform data by replacing pointwise contraction with group-level gravitational contraction. It introduces Group Formation Process (GFP) to form collaboratively moving groups around low-density boundary points and Group Gravitational Optimization (GOP) to apply group forces and update group positions via $x_j^{t+1}=x_j^{t}+\\Delta x_j^{t}$, guided by density-aware interactions. The approach yields theoretical stability in contraction directions and practical improvements over 11 baselines across metrics such as NMI, ARI, Homogeneity, and ACC on datasets like HAR and CIFAR-10, while maintaining efficiency through parallelization. These findings illustrate the method’s robustness for preserving cluster integrity and boundary separability in complex distributions, highlighting the value of group-level cooperation in gravity-inspired clustering.

Abstract

Traditional clustering algorithms often struggle with high-dimensional and non-uniformly distributed data, where low-density boundary samples are easily disturbed by neighboring clusters, leading to unstable and distorted clustering results. To address this issue, we propose a Group-driven Clustering via Gravitational Attraction and Optimization (GCAO) algorithm. GCAO introduces a group-level optimization mechanism that aggregates low-density boundary points into collaboratively moving groups, replacing the traditional point-based contraction process. By combining local density estimation with neighborhood topology, GCAO constructs effective gravitational interactions between groups and their surroundings, enhancing boundary clarity and structural consistency. Using groups as basic motion units, a gravitational contraction strategy ensures globally stable and directionally consistent convergence. Experiments on multiple high-dimensional datasets demonstrate that GCAO outperforms 11 representative clustering methods, achieving average improvements of 37.13%, 52.08%, 44.98%, and 38.81% in NMI, ARI, Homogeneity, and ACC, respectively, while maintaining competitive efficiency and scalability. These results highlight GCAO's superiority in preserving cluster integrity, enhancing boundary separability, and ensuring robust performance on complex data distributions.

GCAO: Group-driven Clustering via Gravitational Attraction and Optimization

TL;DR

GCAO addresses clustering in high-dimensional, non-uniform data by replacing pointwise contraction with group-level gravitational contraction. It introduces Group Formation Process (GFP) to form collaboratively moving groups around low-density boundary points and Group Gravitational Optimization (GOP) to apply group forces and update group positions via , guided by density-aware interactions. The approach yields theoretical stability in contraction directions and practical improvements over 11 baselines across metrics such as NMI, ARI, Homogeneity, and ACC on datasets like HAR and CIFAR-10, while maintaining efficiency through parallelization. These findings illustrate the method’s robustness for preserving cluster integrity and boundary separability in complex distributions, highlighting the value of group-level cooperation in gravity-inspired clustering.

Abstract

Traditional clustering algorithms often struggle with high-dimensional and non-uniformly distributed data, where low-density boundary samples are easily disturbed by neighboring clusters, leading to unstable and distorted clustering results. To address this issue, we propose a Group-driven Clustering via Gravitational Attraction and Optimization (GCAO) algorithm. GCAO introduces a group-level optimization mechanism that aggregates low-density boundary points into collaboratively moving groups, replacing the traditional point-based contraction process. By combining local density estimation with neighborhood topology, GCAO constructs effective gravitational interactions between groups and their surroundings, enhancing boundary clarity and structural consistency. Using groups as basic motion units, a gravitational contraction strategy ensures globally stable and directionally consistent convergence. Experiments on multiple high-dimensional datasets demonstrate that GCAO outperforms 11 representative clustering methods, achieving average improvements of 37.13%, 52.08%, 44.98%, and 38.81% in NMI, ARI, Homogeneity, and ACC, respectively, while maintaining competitive efficiency and scalability. These results highlight GCAO's superiority in preserving cluster integrity, enhancing boundary separability, and ensuring robust performance on complex data distributions.
Paper Structure (20 sections, 2 theorems, 39 equations, 8 figures, 4 tables)

This paper contains 20 sections, 2 theorems, 39 equations, 8 figures, 4 tables.

Table of Contents

  1. INTRODUCTION
  2. Related Work
  3. Preliminary
  4. Problem Definition
  5. Research Background
  6. PROPOSED METHOD: GCAO
  7. Overview
  8. GFP
  9. GOP
  10. Time Complexity Analysis
  11. EXPERIMENTS
  12. Experimental Setting
  13. Datasets
  14. Evaluation Metrics
  15. Evaluation Metrics (continued)
  16. ...and 5 more sections

Key Result

Theorem 4.1

During the contraction process of collaboratively moving groups, let $C_1$ and $C_2$ be two distinct clusters, and define the minimum distance between clusters as where $B_1$ and $B_2$ are the sets of boundary points of $C_1$ and $C_2$, respectively. After the $t$-th group contraction iteration, it holds that i.e., the relative boundary clarity between clusters does not decrease.

Figures (8)

  • Figure 1: Visualization of Gravitational Mechanism
  • Figure 2: Overview of the proposed GCAO algorithm.
  • Figure 3: An example of inter-cluster forces affecting a low-density boundary point
  • Figure 4: An example of local density.
  • Figure 5: An example of processing shared points.
  • ...and 3 more figures

Theorems & Definitions (15)

  • Definition 4.1: Truncation Radius
  • Definition 4.2: Local Density
  • Definition 4.3: Density Lower Bound
  • Definition 4.4: Low-Density Point Set
  • Example 4.1
  • Definition 4.5: Collaboratively Moving Group
  • Definition 4.6: Gravitational Response Mechanism
  • Definition 4.7: Member Force
  • Definition 4.8: Group Force
  • Definition 4.9: Group Contraction Vector
  • ...and 5 more