FRCM: A fuzzy rough c-means clustering method

Fuzzy c-means (FCM) clustering is a clustering method based on fuzzy theory. This method shows good adaptability by assigning membership values to each sample to represent the degree of membership of the sample to each cluster. However, when dealing with fuzzy boundary data, FCM also generates uncertainty and randomness, which in turn affects the accuracy of clustering results and the number of iterations required for algorithm convergence. In order to solve this problem, fuzzy rough set, as a method of dealing with uncertain data, provides a more accurate and strict description method for the processing of boundary data. Considering this advantage, this paper proposes a new fuzzy rough c-means (FRCM) clustering algorithm to improve the performance and iteration efficiency of FCM. Specifically, in this paper, the similarity based on the Gaussian kernel and the membership information of the object for each cluster are firstly used to construct a fuzzy rough set model to describe the fuzzy roughness between the object and the cluster center, which is used to more accurately represent the relationship between the object and the cluster. Secondly, based on the fuzzy rough model, the fuzzy rough degree of the object is calculated, which is used to describe the approximation degree of the object to the center of each cluster. This fuzzy expression can better handle the fuzzy boundary problem between the object and the cluster center, thereby improving the clustering results and enhancing interpretability. Finally, based on fuzzy rough degree information, the FRCM algorithm is designed. The experimental results show that our proposed method has better performance compared to other comparative clustering methods on both synthetic and real datasets. Specifically, compared to FCM, this algorithm exhibits higher iteration efficiency.