In this paper, we propose a general model for plane-based clustering. The general model contains many existing plane-based clustering methods, e.g., k-plane clustering (kPC), proximal plane clustering (PPC), twin support vector clustering (TWSVC) and its extensions. Under this general model, one may obtain an appropriate clustering method for specific purpose. The general model is a procedure corresponding to an optimization problem, where the optimization problem minimizes the total loss of the samples. Thereinto, the loss of a sample derives from both within-cluster and between-cluster. In theory, the termination conditions are discussed, and we prove that the general model terminates in a finite number of steps at a local or weak local optimal point. Furthermore, based on this general model, we propose a plane-based clustering method by introducing a new loss function to capture the data distribution precisely. Experimental results on artificial and public available datasets verify the effectiveness of the proposed method.

Traditional plane-based clustering methods measure the cost of within-cluster and between-cluster by quadratic, linear or some other unbounded functions, which may amplify the impact of cost. This letter introduces a ramp cost function into the plane-based clustering to propose a new clustering method, called ramp-based twin support vector clustering (RampTWSVC). RampTWSVC is more robust because of its boundness, and thus it is more easier to find the intrinsic clusters than other plane-based clustering methods. The non-convex programming problem in RampTWSVC is solved efficiently through an alternating iteration algorithm, and its local solution can be obtained in a finite number of iterations theoretically. In addition, the nonlinear manifold-based formation of RampTWSVC is also proposed by kernel trick. Experimental results on several benchmark datasets show the better performance of our RampTWSVC compared with other plane-based clustering methods.