Piecewise weighted linear regression estimation based on Interval Type-2 Gustafson-Kessel fuzzy clustering

The presence of piecewise linearity in the parameter estimation of regression models necessitates appropriate clustering of the dataset. In this study, a novel multi-strategy algorithm is proposed for piecewise weighted linear regression. First, the optimal number of clusters is determined using a modified Davies–Bouldin Index (DBI), in which the Euclidean distance is replaced by the Mahalanobis distance to better accommodate ellipsoidal data structures. Second, the dataset is partitioned using an extension of the classical Gustafson–Kessel (GK) algorithm based on Interval Type-2 (IT2) fuzzy clustering, where the fuzziness index is defined as an interval rather than a single value. The resulting membership degrees are then employed as weights in the parameter estimation of piecewise weighted linear regression models. The proposed approach is evaluated using three synthetic and three real-world datasets and compared with Fuzzy C Means (FCM), IT2FCM, GK, and K-means methods. Performance is assessed using mean squared error (MSE), convergence iterations, and statistical significance tests. The proposed method achieves average error reductions of 71.58%, 39.76%, 47.99%, and 49.38% compared with FCM, IT2FCM, GK, and K-means, respectively. Wilcoxon signed-rank tests indicate statistically significant improvements, with p-values ranging from 0.0277 to 0.0464. These results demonstrate that the proposed approach provides more accurate parameter estimates for piecewise weighted linear data structures.