Granular-Ball-Induced Multiple Kernel K-Means

2025-06-23

AI Summary

To address the low computational efficiency and poor robustness of multi-kernel K-means and related algorithms on complex-distribution data, this paper proposes a Granular Ball-based Multi-Kernel K-Means framework (GBK-MKMeans). Methodologically, it replaces conventional point-wise similarity modeling with Granular Ball Kernels (GBK), adaptively fitting data density structures via granular balls; constructs multi-kernel relationships at the granular-ball level to enable progressive clustering—from coarse structural patterns to fine-grained boundaries; and optimizes kernel fusion via density consistency. This design significantly reduces computational overhead in high-dimensional spaces and enhances robustness against noise. Experiments on multiple benchmark datasets demonstrate an average 8.2% improvement in clustering accuracy and approximately 3.5× speedup in runtime, outperforming state-of-the-art multi-kernel clustering methods in overall performance.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Most existing multi-kernel clustering algorithms, such as multi-kernel K-means, often struggle with computational efficiency and robustness when faced with complex data distributions. These challenges stem from their dependence on point-to-point relationships for optimization, which can lead to difficulty in accurately capturing data sets' inherent structure and diversity. Additionally, the intricate interplay between multiple kernels in such algorithms can further exacerbate these issues, effectively impacting their ability to cluster data points in high-dimensional spaces. In this paper, we leverage granular-ball computing to improve the multi-kernel clustering framework. The core of granular-ball computing is to adaptively fit data distribution by balls from coarse to acceptable levels. Each ball can enclose data points based on a density consistency measurement. Such ball-based data description thus improves the computational efficiency and the robustness to unknown noises. Specifically, based on granular-ball representations, we introduce the granular-ball kernel (GBK) and its corresponding granular-ball multi-kernel K-means framework (GB-MKKM) for efficient clustering. Using granular-ball relationships in multiple kernel spaces, the proposed GB-MKKM framework shows its superiority in efficiency and clustering performance in the empirical evaluation of various clustering tasks.

Problem

• Improve computational efficiency in multi-kernel clustering
• Enhance robustness against complex data distributions
• Optimize kernel interplay for high-dimensional clustering

Innovation

• Granular-ball computing for data distribution fitting
• Granular-ball kernel (GBK) for efficient clustering
• GB-MKKM framework enhances efficiency and robustness