The results of the statistical analysis tests.

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，需借助一类被称为数据聚类（data clustering, DC）的专用数据挖掘技术。数据聚类将具有相似特征的对象划分为若干组群，其过程围绕k个聚类中心展开，此类中心通常随机选取。近年来，数据聚类技术现存的局限性促使研究者寻求替代解决方案。近来，一款名为黑洞算法（Black Hole Algorithm, BHA）的自然启发式优化算法应运而生，用于解决诸多经典优化问题。该算法属于基于种群的元启发式算法，其设计灵感源自黑洞相关的自然物理现象：算法中将单颗恒星视作解空间中围绕核心运行的潜在候选解。尽管原始黑洞算法的探索能力存在不足，但在基准数据集上的测试结果显示，其性能优于诸多同类算法。为此，本文提出一种多种群扩展的黑洞算法变体（简称MBHA），作为原始黑洞算法的泛化版本。该算法的性能不再依赖于单一最优候选解，而是基于一组生成的优质候选解。本文所提出的方法通过9个通用经典基准测试函数开展了性能验证，实验结果表明，相较于原始黑洞算法及本研究中的对比算法，所提方法生成的结果精度更高，且具备优异的鲁棒性。此外，所提MBHA算法在6个取自UCL机器学习实验室的真实数据集上均展现出较快的收敛速度，使其适用于数据聚类任务。最终的评估结果充分证明，所提算法能够有效解决数据聚类相关问题。