| Summary: | Twin support vector clustering based on Hinge loss and twin support vector clustering based on Ramp loss are two new twin support vector clustering algorithms, which provide a new research idea for solving the clustering problem, and gradually become a research hotspot in pattern recognition and other fields. However, they often have poor performance when dealing with the clustering problem with noisy data. To solve this problem, in this paper, an asymmetric Ramp loss function is constructed and then an improved Ramp-based twin support vector clustering algorithm is also proposed. The asymmetric Ramp loss function not only inherits the advantages of the Ramp loss function, but also uses asymmetric bounded functions to measure the within-cluster and between-cluster scatters, which makes the algorithm more robust to data points far from the clustering center plane. The introduction of parameter t makes the asymmetric Ramp loss function more flexible. In particular, when t is equal to 1, the asymmetric Ramp loss function degenerates into Ramp loss function, such that the Ramp-based twin support vector clustering becomes a special case of proposed algorithm. In addition, its nonlinear clustering formation is also proposed via kernel trick. The non-convex optimization problems in linear and nonlinear models are solved effectively through the alternating iterative algorithm. Experiments are carried out on several benchmark UCI datasets and artificial datasets, and the experimental results verify the effectiveness of the proposed algorithm.
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