LGBQPC: Local Granular-Ball Quality Peaks Clustering

TL;DR

LGBQPC is a novel clustering algorithm that enhances density peaks clustering by incorporating local granular-ball quality measures and improved granularity generation, effectively handling complex data structures.

Contribution

The paper introduces LGBQPC, a new clustering method that improves granular-ball generation and density estimation for complex datasets, surpassing previous algorithms in performance.

Findings

Outperforms existing methods on 40 benchmark datasets.

Effectively handles complex manifold structures and non-uniform densities.

Simplifies parameter tuning with a single penalty coefficient.

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.