Conservative entropy-regularized feature-weighted fuzzy C-means clustering method

Abstract

This paper proposes the CERFW-FCM (Conservative Entropy-Regularized Feature-Weighted Fuzzy C-Means) method as a conservatively stabilized extension of the classical fuzzy C-means algorithm for fuzzy clustering of multidimensional numerical data with heterogeneous feature informativeness. The study is motivated by the observation that the standard FCM model uses an equal metric contribution of all coordinates and therefore does not account for their different structural significance in forming cluster geometry. In the presence of redundant, weakly informative, or noisy variables, such a scheme may weaken intercluster contrast and reduce the stability of fuzzy memberships in regions of partial cluster overlap. The CERFW-FCM method formalizes three coordinated mechanisms: adaptive feature reweighting, entropy-smoothed membership updates, and conservative stabilization of the weighting metric. In addition, a meta-adaptive parameter calibration procedure based on pilot FCM runs without external class labels is proposed, including label-free selection of the fuzziness parameter, robust aggregation of pilot estimates, and constraints that prevent excessive influence of the entropy component or the adaptive metric. The paper presents a stabilized iterative scheme for updating cluster centers, the fuzzy membership matrix, and the weight vector, and demonstrates that the proposed modification preserves the centroid-based nature of FCM and does not alter its dominant-order computational complexity. Experimental validation was conducted on the UCI Multiple Features Dataset, which contains a multi-view description of handwritten digits in a high-dimensional feature space. Compared with K-means, Classical FCM, and ablation variants of the proposed method using the ARI (Adjusted Rand Index), NMI (Normalized Mutual Information), and Hungarian Accuracy metrics, CERFW-FCM demonstrated consistent improvement in clustering quality. Additional analysis of robustness to artificially added noisy features and PCA (Principal Component Analysis) visualization confirm that the method retains competitive performance in a noisy feature space, although the dependence of the results on the noise level is not strictly monotonic. The obtained results justify CERFW-FCM as a specialized stabilized FCM scheme for high-dimensional problems in which the cluster structure is associated with heterogeneous coordinate informativeness and partial cluster overlap.