This work highlights issues that were not deeply investigated in previous studies on clustering solutions, which have essential impacts on performance in long-term real-world applications that are challenging to detect instantly. Thus, we addressed these issues by proposing two novel techniques: first, we expand the idea of clustering based on centroids to multiple sub-centroids that assist assignment functions in finding the optimal solution. In contrast to recent studies, we extended the concept of gravitational force toward clustering solutions. Finally, the introduced gap generation concept has been associated with these techniques to support a superior clustering solution. Our model is termed semi-supervised gravity clustering (SSGC). To demonstrate the strength of SSGC, we consider multiple performance measurements besides the traditional ones to validate the clustering models in various scenarios. The experimental results show that SSGC outperforms baseline models and successfully obtains the best performance of 30 different domain datasets. Finally, our methodology code is already released.

The robust unsupervised framework of clustering models is essential in numerous machine learning tasks due to its ability to identify hidden relations between samples, resulting in a comprehensive understanding and interpretation. Many datasets contain samples that naturally cannot link to each other, but the degree of similarity between them makes it almost impossible for clustering models to distinguish the differences; this is called the overlapping issue. However, integrating support vector machines, feature selection, and dimensional reduction techniques with clustering models might still be incapable of providing an optimal solution. As a result, it adversely affects performance and leads to inconsistent partitioning, unreasonable interpretation, and false confidence. This study addresses these issues by proposing a novel unsupervised data separation equation that is based on the concepts of tension and separation gained by finding the cannot-link relations based on cluster centroids. The equation validated in diverse scenarios to demonstrate its ability to improve outcomes. The experimental results prove that the proposed equation assists in reducing the reliance on parameter tuning and constraints, thereby enhancing performance and effectively addressing the challenge of outliers.