## 2 Related Work  
There are existing works in the literature that reported hybridizations involving either K-means or symbiotic organism search or both. However, it is worth stating here that hybridizations for clustering problems are few. In [45], the SOS algorithm was hybridized with the improved opposition-based learning firefly algorithm (IOFA) to improve the exploitation and exploration of IOFA. SOS was combined with differential evolution (DE) in [46] to improve the convergence speed and optimal solution quality of shape and size truss structure optimization in engineering optimization problems. The conventional butterfly optimization algorithm (BOA) was combined with the first two phases of the SOS for enhancement of global and local search behavior of the BOA. In [47], a modified strategy of SOS was hybridized with the mutation strategy of the DE to ensure the preservation to the SOS local search capability, while maintaining its ability to conduct global search. Other reported hybrids involving SOS include the following: Ref. [48] combined GA, PSO and SOS algorithms for continuous optimization problems; Ref. [24] reported four hybrid algorithms for automatic clustering, combining SOS with FA, for teaching-learning based optimization (TLBO), DE, and PSO algorithms. Other hybridization algorithms involving SOS can be found in the review work on SOS algorithms conducted by [49].  
Several hybridizations involving K-means with other metaheuristic algorithms were reported in the review work presented by [2]. Recent hybridizations involving K-means include the following: Ref. [50] combined GA with K-means and support vector machine (SVM) for automatic selection of optimized cluster centroid and hyperparameters tunning; Ref. [51] combined multi-objective individually directional evolutionary algorithm (IDEA) with K-means for multi-dimensional medical data modeling using fuzzy cognitive maps; Ref. [52] presented an hybrid of K-means with PSO for semantic segmentation of agricultural products; Ref. [53], combined K-means algorithm with particle swarm optimization for customer segmentation.  
For hybridization involving SOS and K-means, as mentioned earlier, the reported literature works are very minimal showing that research in this aspect is still shallow. In [25], a clustering-based SOS for high-dimensional optimization problems was proposed, combining an automatic K-means with symbiotic organism search for efficient computation and better searching quality. The automatic K-means was used to generate subpopulations for the SOS algorithm to create a sub-ecosystem that made the combination of global and local searches possible. The mutualism and commensalism phases formed the local search, where solutions were allowed to interact within each cluster. For the global search, only best solutions from each cluster were allowed to interact across the clusters under the parasitism phase. In this case, the K-means algorithm was used as a pre-processing phase for the SOS algorithm to enhance its performance in finding solutions to high dimensional optimization problems. In [26], the standard algorithms SOS and K-means were combined to solve automatic clustering problems. The SOS phase resolved the initialization challenge for the K-means algorithm by automatically determining the optimum number of clusters and generating the corresponding initial cluster centers. This ensured the K-means algorithm avoided the possibility of local optimum convergence while improving the cluster analysis capability of the algorithm. However, the problem of low convergence persisted in the hybrid algorithm.  
In this work, we hoped to further improve on the clustering performance of the previous SOS-based K-means hybrid algorithm in [26] for automatic clustering of high-dimensional datasets, by incorporating some improvements into each of the standard algorithms, SOS and K-means, so as to achieve better convergence and more compact clusters.