LGBQPC: Local Granular-Ball Quality Peaks Clustering

TL;DR

The local GB quality peaks clustering (LGBQPC) algorithm is proposed, which offers comprehensive improvements to GBDPC in both GB generation and clustering processes based on the principle of justifiable granularity (POJG), and substantially improves the performance of GBDPC on datasets with complex manifold structures or non-uniform density distributions.

Abstract

The density peaks clustering (DPC) algorithm has attracted considerable attention for its ability to detect arbitrarily shaped clusters based on a simple yet effective assumption. Recent advancements integrating granular-ball (GB) computing with DPC have led to the GB-based DPC (GBDPC) algorithm, which improves computational efficiency. However, GBDPC demonstrates limitations when handling complex clustering tasks, particularly those involving data with complex manifold structures or non-uniform density distributions. To overcome these challenges, this paper proposes the local GB quality peaks clustering (LGBQPC) algorithm, which offers comprehensive improvements to GBDPC in both GB generation and clustering processes based on the principle of justifiable granularity (POJG). Firstly, an improved GB generation method, termed GB-POJG+, is developed, which systematically refines the original GB-POJG in four key aspects: the objective function, termination criterion for GB division, definition of abnormal GB, and granularity level adaptation strategy. GB-POJG+ simplifies parameter configuration by requiring only a single penalty coefficient and ensures high-quality GB generation while maintaining the number of generated GBs within an acceptable range. In the clustering phase, two key innovations are introduced based on the GB k-nearest neighbor graph: relative GB quality for density estimation and geodesic distance for GB distance metric. These modifications substantially improve the performance of GBDPC on datasets with complex manifold structures or non-uniform density distributions. Extensive numerical experiments on 40 benchmark datasets, including both synthetic and publicly available datasets, validate the superior performance of the proposed LGBQPC algorithm.

Figures (6)

• Figure 1: Three GBs with average (red) and maximum (blue) radii.
• Figure 2: The LGBQPC clustering process illustrated on the Flame dataset WangYizhang2024ESWA. (a) The original Flame dataset. (b)-(c) GBs serving as leaf nodes in the binary tree: (b) each leaf node is sufficiently small, and (c) each abnormal leaf node has been completely divided. (d) The best combination of sub-GBs of derived from the Flame dataset. (e) GBs generated after applying anomaly detection to those in (d). (f) The GB $k$-NN graph ($k=3$). (g) Clustering results at the GB level. (h) Final clustering results at the instance level.
• Figure 3: Clustering results of LGBQPC on 27 synthetic datasets.
• Figure 4: Results of Nemenyi test on datasets D1-D38. (a) NMI. (b) ARI.
• Figure 5: Number of GBs generated by GB-POJG+ under varying penalty coefficients. (a)-(d) D32-D35.

Theorems & Definitions (15)

• Definition 1
• Definition 2
• Remark 1
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Definition 7
• Remark 2
• Definition 8