Research On The Robust And Adaptive Switching C-Regressions Models Based On Cluster Analysis

Switching regression algorithms have been widely studied and applied in many fields. This paper proposes methods to improve the robustness and adaptivity of the previous research, which are based on clustering.In order to improve the performance of noise insensitivity and convergence speed, a new algorithm called fuzzy c-means switching regression model with generalized improved fuzzy partitions (GIFP-FCRM) is proposed. It introduces a novel membership constraint function and provides a generalized model with the fuzziness index m for the fuzzy C-switching regression model with improved fuzzy partitions (IFP-FCRM). Furthermore, with fuzzy parameter? , the classical FCRM and IFP-FCRM can be taken as two special cases of the proposed algorithm.Traditional C-regression methods based on fuzzy clustering usually need to initialize the number of clusters. This paper proposes a new method to estimate the number of clusters in switching regression model, which is named as Modified Gap statistic method (mGap). The mGap is measured by combining within-cluster dispersion and between-cluster dispersion. It can get the optimal number of clusters by comparing the change of the value of mGap in reference data sets and observations. Experiments demonstrate that the mGap method not only is good at identifying well-separated clusters, but also can work on the overlapping data sets.In the family of switching regression algorithms based on fuzzy clustering (FCRs), these FCRs always depend heavily on initial values. Data transformation can solve this initial-value problem, but the data set of model parameter space transformed from the original space may become too large. To overcome this drawback, a novel adaptive C-regressions approach based on density sampling ideas called dsACR is proposed. According to sampling in original space by distance and sampling in accordance with the ranks of data density on the parameter space, the new dsACR approach can significantly reduce computational complexity. Moreover, it can adaptively estimate the number of models by embedding mGap method. Experiments demonstrate the advantages of dsACR both in noise insensitivity and robustness capability.