Ensemble CART surrogate-assisted automatic multi-objective rough fuzzy clustering algorithm for unsupervised image segmentation

Multi-objective clustering algorithms (MOCAs) are popular in unsupervised image segmentation due to their merit of meeting multiple segmentation requirements and the prospect of automatically estimating the number of clusters. However, most of them suffer from high time costs and are easily to be influenced by the uncertainty when handling real complex images. To address these issues, we propose an ensemble classification and regression tree (CART) surrogate-assisted automatic multi-objective rough fuzzy clustering (ECS-AMRFC) algorithm for unsupervised image segmentation. Firstly, a cluster medoid-based encoding scheme is employed to represent solutions with different number of clusters and meanwhile lessen the length of encoding. Then, we design an ensemble CART as the surrogate model to significantly reduce the computational burden. Moreover, a surrogate model management strategy is proposed to accelerate the optimization and enhance the quality of surrogate modeling. To handle the uncertainty in data, we extend the rough fuzzy clustering into MOCAs and construct three complementary objective functions to seek proper cluster medoids from multiple perspectives. In addition, the Gaussian kernel is introduced into the objective functions to handle image pixels that cannot separate linearly in the feature space. Finally, a kernelized rough fuzzy clustering validity index is defined to automatically select the optimal solution with no requirements of any prior knowledge. Experiments show that ECS-AMRFC not only identifies appropriate number of clusters on different kinds of images, but also obtains better segmentation results than state-of-the-art rough fuzzy clustering algorithms and automatic MOCAs.