# Ramp-based Twin Support Vector Clustering

## TL;DR

This paper introduces RampTWSVC, a robust and efficient plane-based clustering method utilizing a ramp cost function, which improves cluster detection and performance over traditional methods, especially on benchmark datasets.

## Contribution

The paper proposes a novel ramp cost function for plane-based clustering, enhancing robustness and efficiency, and extends it with a kernel-based nonlinear formulation.

## Key findings

- RampTWSVC outperforms existing plane-based clustering methods.
- The method is robust due to its bounded cost function.
- Experimental results demonstrate superior clustering performance.

## Abstract

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.