Parameter setting.

The retrieval of important information from a dataset requires applying a special data mining technique known as data clustering (DC). DC classifies similar objects into a groups of similar characteristics. Clustering involves grouping the data around k-cluster centres that typically are selected randomly. Recently, the issues behind DC have called for a search for an alternative solution. Recently, a nature-based optimization algorithm named Black Hole Algorithm (BHA) was developed to address the several well-known optimization problems. The BHA is a metaheuristic (population-based) that mimics the event around the natural phenomena of black holes, whereby an individual star represents the potential solutions revolving around the solution space. The original BHA algorithm showed better performance compared to other algorithms when applied to a benchmark dataset, despite its poor exploration capability. Hence, this paper presents a multi-population version of BHA as a generalization of the BHA called MBHA wherein the performance of the algorithm is not dependent on the best-found solution but a set of generated best solutions. The method formulated was subjected to testing using a set of nine widespread and popular benchmark test functions. The ensuing experimental outcomes indicated the highly precise results generated by the method compared to BHA and comparable algorithms in the study, as well as excellent robustness. Furthermore, the proposed MBHA achieved a high rate of convergence on six real datasets (collected from the UCL machine learning lab), making it suitable for DC problems. Lastly, the evaluations conclusively indicated the appropriateness of the proposed algorithm to resolve DC issues.

从数据集中提取关键信息，需应用一种被称为数据聚类（data clustering, DC）的特殊数据挖掘技术。数据聚类将相似对象归为具有同类特征的组别，其核心是围绕k个聚类中心对数据进行分组，而这些聚类中心通常随机选取。近年来，数据聚类领域面临的挑战推动了替代解决方案的探索。近期，一种名为黑洞算法（Black Hole Algorithm, BHA）的自然启发式优化算法被提出，用于解决各类经典优化问题。该算法属于基于种群的元启发式算法，模拟了黑洞相关的自然现象：单个恒星代表解空间中旋转的潜在候选解。原版黑洞算法在基准数据集上的表现优于其他同类算法，但其探索能力存在不足。为此，本文提出了黑洞算法的多种群推广版本MBHA，该算法的性能不再依赖于单一最优解，而是基于一组生成的最优解集合。所提方法通过九种广泛使用的经典基准测试函数开展了测试，实验结果表明，相较于本研究中的黑洞算法及其他同类算法，该方法生成的结果精度更高，且鲁棒性优异。此外，所提MBHA在六个取自UCL机器学习实验室的真实数据集上展现出了优异的收敛速度，适用于数据聚类任务。最终的评估结果充分验证了所提算法解决数据聚类问题的适用性。