Fuzzy weighted c-harmonic regressions clustering algorithm

As a well-known regression clustering algorithm, fuzzy c-regressions (FCR) has been widely studied and applied in various areas. However, FCR appears to be rather sensitive to the undesirable initialization and the presence of noise or outliers in data sets. As a modified alternative, possibilistic c-regressions (PCR) can ameliorate the problem of noise and outliers, but it depends more heavily on initial values. Besides, the number of models should be determined a priori in both algorithms. To overcome these issues, this paper proposes a generalized alternative, called fuzzy weighted c-harmonic regressions (FWCHR), in which, a dynamic-like weight term based on the distinguished feature of the harmonic average is first introduced to enhance robustness. Furthermore, FWCHR can encompass FCR and PCR if some conditions are satisfied. And then a generalized mountain method (GMM) is proposed to automatically determine the number of models and estimate the initial values, which makes the proposed FWCHR algorithm totally unsupervised. Some numerical simulations and real applications are conducted to validate the performance of our algorithms.