An Improved Black Hole Algorithm Designed for K-means Clustering Method

Data clustering has attracted the interest of scholars in many fields. In recent years, using heuristic algorithms to solve data clustering problems has gradually become a tendency. The black hole algorithm (BHA) is one of the popular heuristic algorithms among researchers because of its simplicity and effectiveness. In this paper, an improved self-adaptive logarithmic spiral path black hole algorithm (SLBHA) is proposed. SLBHA innovatively introduces a logarithmic spiral path and random vector path to BHA. At the same time, a parameter is used to control the randomness, which enhances the local exploitation ability of the algorithm. Besides, SLBHA designs a replacement mechanism to improve the global exploration ability. Finally, a self-adaptive parameter is introduced to control the replacement mechanism and maintain the balance between exploration and exploitation of the algorithm. To verify the effectiveness of the proposed algorithm, comparison experiments are conducted on 13 datasets creatively using the evaluation criteria including the Jaccard coefficient as well as the Folkes and Mallows index. The proposed methods are compared with the selected algorithms such as the whale optimization algorithm (WOA), compound intensified exploration firefly algorithm (CIEFA), improved black hole algorithm (IBH), etc. The experimental results demonstrate that the proposed algorithm outperforms the compared algorithms on both external criteria and quantization error of the clustering problem.