Robust and Sparse n-Pythagorean Fuzzy K-Means Clustering

Abstract

In this paper, we propose a novel clustering approach termed the Robust and Sparse n-Pythagorean Fuzzy K-Means algorithm, which extends the standard n-Pythagorean fuzzy K-Means by addressing two key limitations: sensitivity to outliers and lack of membership sparsity. To enhance robustness, we replace the conventional squared distance term with a robust loss function, making the algorithm more resilient to noise and outliers. Furthermore, we introduce an additional sparsity-inducing regularization term that encourages each data point to be associated with a limited number of clusters, thereby improving interpretability and reducing overfitting. Experimental evaluations on several benchmark datasets demonstrate that the proposed method achieves superior clustering performance by effectively balancing robustness and sparsity in soft clustering scenarios.