Enhanced Firefly-K-Means Clustering with Adaptive Mutation and Central Limit Theorem for Automatic Clustering of High-Dimensional Datasets

Abstract

Metaheuristic algorithms have been hybridized with the standard K-means to address the latter’s challenges in finding a solution to automatic clustering problems. However, the distance calculations required in the standard K-means phase of the hybrid clustering algorithms increase as the number of clusters increases, and the associated computational cost rises in proportion to the dataset dimensionality. The use of the standard K-means algorithm in the metaheuristic-based K-means hybrid algorithm for the automatic clustering of high-dimensional real-world datasets poses a great challenge to the clustering performance of the resultant hybrid algorithms in terms of computational cost. Reducing the computation time required in the K-means phase of the hybrid algorithm for the automatic clustering of high-dimensional datasets will inevitably reduce the algorithm’s complexity. In this paper, a preprocessing phase is introduced into the K-means phase of an improved firefly-based K-means hybrid algorithm using the concept of the central limit theorem to partition the high-dimensional dataset into subgroups of randomly formed subsets on which the K-means algorithm is applied to obtain representative cluster centers for the final clustering procedure. The enhanced firefly algorithm (FA) is hybridized with the CLT-based K-means algorithm to automatically determine the optimum number of cluster centroids and generate corresponding optimum initial cluster centroids for the K-means algorithm to achieve optimal global convergence. Twenty high-dimensional datasets from the UCI machine learning repository are used to investigate the performance of the proposed algorithm. The empirical results indicate that the hybrid FA-K-means clustering method demonstrates statistically significant superiority in the employed performance measures and reducing computation time cost for clustering high-dimensional dataset problems, compared to other advanced hybrid search variants.