Improved SOSK-Means Automatic Clustering Algorithm with a Three-Part Mutualism Phase and Random Weighted Reflection Coefficient for High-Dimensional Datasets

Automatic clustering problems require clustering algorithms to automatically estimate the number of clusters in a dataset. However, the classical K-means requires the specification of the required number of clusters a priori. To address this problem, metaheuristic algorithms are hybridized with K-means to extend the capacity of K-means in handling automatic clustering problems. In this study, we proposed an improved version of an existing hybridization of the classical symbiotic organisms search algorithm with the classical K-means algorithm to provide robust and optimum data clustering performance in automatic clustering problems. Moreover, the classical K-means algorithm is sensitive to noisy data and outliers; therefore, we proposed the exclusion of outliers from the centroid update’s procedure, using a global threshold of point-to-centroid distance distribution for automatic outlier detection, and subsequent exclusion, in the calculation of new centroids in the K-means phase. Furthermore, a self-adaptive benefit factor with a three-part mutualism phase is incorporated into the symbiotic organism search phase to enhance the performance of the hybrid algorithm. A population size of 40+2g was used for the symbiotic organism search (SOS) algorithm for a well distributed initial solution sample, based on the central limit theorem that the selection of the right sample size produces a sample mean that approximates the true centroid on Gaussian distribution. The effectiveness and robustness of the improved hybrid algorithm were evaluated on 42 datasets. The results were compared with the existing hybrid algorithm, the standard SOS and K-means algorithms, and other hybrid and non-hybrid metaheuristic algorithms. Finally, statistical and convergence analysis tests were conducted to measure the effectiveness of the improved algorithm. The results of the extensive computational experiments showed that the proposed improved hybrid algorithm outperformed the existing SOSK-means algorithm and demonstrated superior performance compared to some of the competing hybrid and non-hybrid metaheuristic algorithms.