ACQC-LJP: Apollonius circle-based quantum clustering using Lennard-Jones potential

Abstract

Quantum Clustering (QC) is widely regarded as a powerful method in unsupervised learning problems. This method forms a potential function using a wave function as a superposition of Gaussian probability functions centered at data points. Clusters are then identified by locating the minima of the potential function. However, QC is highly sensitive to the kernel bandwidth parameter in the Schrödinger equation, which controls the shape of the Gaussian kernel, and affects the potential function's minima. This paper proposes an Apollonius Circle-based Quantum Clustering (ACQC) method using Lennard-Jones Potential (LJP), entitled ACQC-LJP, to address this limitation. ACQC-LJP introduces a novel approach to clustering by leveraging LJP to screen dense points and constructing Apollonius circle-based neighborhood groups, enabling the extraction of adaptive kernel bandwidths to effectively resolve the kernel bandwidth issue. Experimental results on real-world and synthetic datasets demonstrate that ACQC-LJP improves cluster detection accuracy by 50% compared to the original QC and by 10% compared to the ACQC method. Furthermore, the computational cost is reduced by more than 90% through localized calculations. ACQC-LJP outperforms state-of-the-art methods on diverse datasets, including those with small sample sizes, high feature variability, and imbalanced class distributions. These findings highlight the method's robustness and effectiveness across various challenging scenarios, marking it as a significant advancement in unsupervised learning. All the implementation source codes of ACQC-LJP are available at https://github.com/NAbdolmaleki/ACQC-LJP.