A Fuzzy Granular K-Means Clustering Method Driven by Gaussian Membership Functions

The K-means clustering algorithm is widely applied in various clustering tasks due to its high computational efficiency and simple implementation. However, its performance significantly deteriorates when dealing with non-convex structures, fuzzy boundaries, or noisy data, as it relies on the assumption that clusters are spherical or linearly separable. To address these limitations, this paper proposes a Gaussian membership-driven fuzzy granular K-means clustering method. In this approach, multi-function Gaussian membership functions are used for fuzzy granulation at the single-feature level to generate fuzzy granules, while fuzzy granule vectors are constructed in the multi-feature space. A novel distance metric for fuzzy granules is defined along with operational rules, for which axiomatic proof is provided. This Gaussian-based granulation enables effective modeling of nonlinear separability in complex data structures, leading to the development of a new fuzzy granular K-means clustering framework. Experimental results on multiple public UCI datasets demonstrate that the proposed method significantly outperforms traditional K-means and other baseline methods in clustering tasks involving complex geometric data (e.g., circular and spiral structures), showing improved robustness and adaptability. This offers an effective solution for clustering data with intricate distributions.