A Novel Fuzzy Clustering Framework With Manhattan Distance and Weighted Median Centroids for Outlier-Resilient Data Analysis

Clustering performance often deteriorates in the presence of outliers, as extreme values distort centroid estimation and distance computations. Classical fuzzy clustering methods, including Fuzzy C-Means (FCM) and Kernel FCM, are particularly sensitive to such contamination because they rely on mean-based centroids and Euclidean distance metrics. To address this limitation, this paper proposes a novel fuzzy clustering framework that integrates Manhattan distance with weighted median centroids. The framework introduces a new objective function and centroid updating rule while maintaining the same computational complexity as classical FCM. The proposed method is comprehensively evaluated on three benchmark datasets: (i) the Chronic Kidney Disease (CKD) dataset with naturally occurring outliers, and (ii) the Iris andWine datasets with controlled outlier injection at 5%, 10%, and 15%. Experimental comparisons include five baselines—Classical FCM, K-Means, Kernel FCM (RBF), Adaptive Weighted Possibilistic FCM (AWPFCM), and Revised FCM (RFCM)—along with a runtime analysis against Classical FCM. Results show that the proposed model achieves the best overall performance across all metrics, including a recall of 0.91 on CKD, while maintaining stable accuracy under increasing contamination on Iris (0.83 → 0.66) and Wine (0.70 → 0.60). Across all scenarios, it consistently outperforms existing baselines in both accuracy and robustness, confirming its effectiveness as a reliable and computationally efficient clustering framework for noisy and outlier-prone data.