Robust Fuzzy Clustering Algorithms for Change-Point Regression Models

This article presents a robust fuzzy procedure for estimating change-point regression models. We propose incorporating the fuzzy change-point algorithm with the M-estimation technique for robust estimations. The fuzzy c partitions concept is embedded into the change-point regression model so the fuzzy c-regressions and fuzzy c-means clustering can be employed to obtain the estimates of change-points and regression parameters. The M estimation with a robust criterion is used to make the estimators robust to the presence of outliers and heavy-tailed distributions. We create two robust algorithms named FCH and FCT by using Huber's and Tukey's functions as the robust criterion respectively. Extensive experiments with numerical and real examples are provided for demonstrating the effectiveness and the superiority of the proposed algorithms. The experimental results show the proposed algorithms are resistant to atypical observations and outperform the existing methods. The proposed FCH and FCT are generally comparable but FCT performs better in the presence of extremely high leverage outliers and heavy-tailed distributions. Real data applications show the practical usefulness of the proposed method.